Parabolic thinking: story as mental instrument 1 I will open my mouth in parables, I will utter what has been hidden since the foundation of the world.

Introduction

Cognitive linguistics explores the link between symbolic structure and conceptual structure. A major claim made by cognitive linguists is that the semiotic conventions of language are not arbitrary but motivated. Linguistic conceptualisation is related to general cognitive processing and organization. "Lexicon, morphology and syntax form a continuum of symbolic units (…) characterized relative to knowledge systems" (Langacker 1991: 1). Knowledge itself is conceived as embodied and imaginative, a hybrid phenomenological construct that is dependent on "neural networks" (Lakoff and Johnson 1999: 16) and crucially linked to "sensory, kinaesthetic, and emotive experience" (Langacker 1991: 2). The study of language is thus conducted with essential reference to body-based cognitive abilities and mechanisms, language being viewed simultaneously as a product, an instrument and a reflector of human cognition at large. A central -but often underestimated -feature of human cognition is narrative imagining [START_REF] Turner | The Literary Mind[END_REF], a process best defined as the adoption of narrative format to report and analyse experience, and more generally to make sense of the world. Humans are fundamentally storytelling creatures that are constantly engaged in the socio-cognitive process of giving narrative accounts or rationalizations 2 of their lives (Johnson 1993: 150-84). The narrative framing of self and action requires the conversion of experience into mental, perceptual, physical, or communicative events 3 , involving actors, plots and settings. As Mark [START_REF] Turner | The Literary Mind[END_REF] hypothesizes, story could well be the backbone of syntax, and participant roles the foundation of argument structure. "Narrative structure" would thus form the conceptual and communicative basis of "grammatical structure":

[T]he basic abstract story in which an animate agent performs a physical action that causes a physical object to move in a spatial direction is projected to create 1 Published in Métaphore et anglais de spécialité, Marie-Hélène Fries (ed.), p.p. 21-44. Bordeaux: Travaux E.A. 20.25. Unviversité Victor Segalen, 2005 (ISBN 2-9506462-3-9). The title of this paper makes overt reference to Turner's theory of parabolic thinking (1996). "Mental instrument" suggests that cognizers are metaphorically construed as concept-manipulators using various "conceptual tools." Turner himself remarks that "[w]hen we talk of 'cognitive instruments' or 'conceptual tools' (...) we are understanding the action of thought by projection from the body action of manipulation, specially manipulation for the purpose of manufacture." (Turner 1996: 44). 2 Building on [START_REF] Ricoeur | Time and Narrative[END_REF] and [START_REF] Macintyre | After Virtue[END_REF], Johnson (1993) claims that the sociocognitive function of narrative is not confined to mere "storytelling" (154). Narrative, he remarks, is "a culturally accepted mode of explanation" (158). Pragmatically, "What's the story?", "Give us a full account!" function as invitations to report events and "account" for them. 3 Grammar is instrumental in forcing us to convert experience into events and reporting them as stories. E.g. She understood… (mental event); They felt… (perceptual event); You broke… (physical event); I talked to … (communicative event), etc.

the grammatical structure we see in "John pushes the ball onto the court," "David tosses the can into the yard," and "Mary throws the stone over the fence." The abstract narrative structure is projected to create the abstract grammatical structure. The abstract narrative structure includes an agent, an action, an object and a direction. The abstract grammatical structure includes a noun phrase followed by a verb phrase followed by a prepositional phrase, with the first noun phrase as Subject and Agent and the second noun phrase as Direct Object and Patient. The first abstract structure is conceptual and narrative. The second abstract structure is grammatical. As Turner's repeated use of "projection" suggests, stories can be mapped onto other stories (or domains) -a cognitive process referred to as parabolic projection.

Story is a basic principle of the mind. Most of our experience, our knowledge, and our thinking is organized as stories. The mental scope of story is magnified by projection -one story helps us make sense of another. The projection of one story onto another is parable, a basic cognitive principle that shows up everywhere. (Turner 1996 : v) It is this powerful combination of story with projection4 that yields parabolic thinking 5 , a universal and indispensable mode of thought (Turner 1996: 7), possibly the most fundamental mechanisms of imaginative cognition 6 , as the present paper intends to demonstrate.

Key structural features of parable

Parables 7 are first and foremost stories that display the central properties of prototypical narratives, such as the establishment of spatial and temporal location, the definition and sequencing of events, the identification of participants, the distribution of roles, the imposition of beginning-middle-end structure and the monitoring of movement towards some conclusion or resolution. Such "rhetorical conventions" relate to general capacities of the human brain: the capacity to locate (objects, people, sounds, events, etc.); the capacity to construct sequences (of movements, actions, events, etc.); the capacity to assign roles or functions (to people, to things); the capacity to apply image schematic structure to domains of knowledge and experience (as when the SOURCE-PATH-GOAL 8 schema is applied to narrative progression 9 or logical reasoning 10 ), and so forth.

But parables are not just any kind of narrative. Their internal configuration must be suited to their specific interpretive or explanatory function.

1. Brevity. Parables are brief narratives. As such, they function as short synthesizing structures that connect and compress events and meanings. In a way similar to that of myth or proverbs, parables act as "integrative mind tools" (Donald 1991: 215).

2. Clarity and consistency. Parables have an argumentative function that rests on a clear communicative contract between storyteller and listener: simplicity of dramatic structure; plausibility of causal structure; accessibility of thematic content. Events must be readily identified and connected by simple narrative ordering, in strict conformity with the culturally established rules of logical or chronological linkage.

3. Descriptive containment. Some amount of guessing 11 has to be performed by the hearer: the target notion is "not described but circumscribed", as "a circle of words [is] drawn around it" [START_REF] Frye | Anatomy of Criticism[END_REF][START_REF] Frye | Anatomy of Criticism[END_REF]: 300).

4.

End-focus. The narrative development of parable is determined by the thematic resolution of the story. The true point of the story is its endpoint.

5.

Impact. The choice of plot, participants and setting must instantly and forcibly strike the listener's feelings and imagination, while powerfully appealing to his or her reason. 6. Familiarity. The "stories" featured in parables are often drawn from a stock of cultural narratives, like "farmer sows wheat seeds", "wealthy man-throws a big party", "traveller embarks on a journey", "sick man wants to be cured", etc. Each comes with a relatively typified pattern of action and participants, emblematic of culturally validated world experience. Conventional expectations are raised from the outset and prepackaged causal and inferential structure remain available throughout the narrative as background cognition 12 . operative at least three levels in stories: in the "physical journeys" made by characters; in the mental journeys we make, as readers or listeners that "follow the story itself metaphorically along its path, (…) from start to finish" and eventually as we make sense of "purposive activity" through "the purposes are destinations metaphor" (166). 10 Reasoning is commonly construed as a mental journey along a PATH -or line of thought. Ideally, the conceptualizer's mind moves step-by-step from premise (SOURCE) to conclusion (GOAL). 11 "La parabole invite à chercher (…) [C'est] un texte [à la fois] clair et voilé" (Antoine Moussali. Dictionnaire international des termes littéraires / International Dictionary of Literary Terms. Edited by Jean-Marie Grassin. Web version: www.ditl.info. 12 The most thought-provoking Gospel parables have "conventional expectations" clashing. In The Parable of the Prodigal Son , the tension between the father's joy and forgiveness and his elder son's anger and resentment is by no means easy to resolve, since both are perfectly consistent with "normal" and therefore "anticipated" behaviour. The Parable of the Dishonest Steward (Luke 16.1-9) in which "the master commended the dishonest steward for his shrewdness" has caused much debate among Bible scholars because of the surprising twist in the conclusion: "And I tell you, make friends for yourselves by means of unrighteous mammon, so that when it fails they may receive you into the eternal habitations" (16. 9). The shocking incongruity of the message is not easily dispelled, despite commentators' attempts to show that shrewdness and resourcefulness are praised -not dishonesty -and Anna Wierzbicka's insightful As will become apparent later, the "familiar stories" used in parables may also include more basic stories of body action -like moving through space, grasping a physical object (Turner 1996: 33-34) -or scenes and event types essential to human experience (Goldberg 1995: 39), like "someone experiencing something", "something having an effect on someone", etc.

The following Gospel parables epitomize the central properties listed above. All target the same entity -"the kingdom of heaven" -and attempt to characterizerather than define -the barely nameable or conceivable 13 .

The Parable of the Mustard Seed. The kingdom of heaven is like a grain of mustard seed which a man took and sowed in his field; it is the smallest of all seeds, but when it has grown it is the greatest of shrubs and becomes a tree, so that the birds of the air come and make nests in its branches. The Parable of Leaven The kingdom of heaven is like leaven which a woman took and hid in three measures of flour, till it was all leavened. (Matthew 13.33)

The Parable of the Hidden Treasure. The kingdom of heaven is like a treasure hidden in the field, which a man has found and covered up; then in his joy he goes and sells all that he has and buys that field. (Matthew 13.44) The Parable of the Precious Pearl Again, the kingdom of heaven is like a merchant in search of fine pearls, who, on finding one pearl of great value, went and sold all that he had and bought it. (Matthew 13. 45)

Parable in religious or literary format: from dramatic to interpretational structure

Go your way; behold, I send you out as lambs in the midst of wolves. (Luke 10.3) Parable is traditionally defined as a particular type of allegory 14 -that is, "a narrative in which the agents and action, and sometimes the setting as well, are contrived not only to make sense in themselves, but also to signify a second, correlated order of persons, things, concepts, or events" (Abrams, 1971: 4). Like the exemplum 15 , the fable 16 or proverbs 17 , the parable is a short, meaningful remark that Jesus resorts to "a technique that consists of using mixed or even predominantly negative models to illustrate positive characteristics." (2001: 418). 13 "Dans les Evangiles, la parabole (…) dit plus qu'elle ne dit. [Elle] veut dire par le langage ce qui échappe au langage. (…) Une manière de nommer l'innommable" (Antoine Moussali. Dictionnaire international des termes littéraires). 14 From Greek allegorein "to speak figuratively", from allos "other" + agoreuein "to make a speech in public." 15 An anecdote supporting a moral point in a sermon. By extension, a tale that sustains an argument in a formal exhortation. In the Middle Ages, it was common for preachers to borrow stories from extensive, purpose-made collections of exempla. 16 From Latin fabula "story", "narrative", from fari "to speak, say". A short story devised to convey a moral lesson, which is typically summarized by the narrator or one of the characters in story designed to convey some "moral thesis" or exemplify some "principle of human behavior" with clarity, concision and a sense of wholeness. But whereas the "useful moral lesson" 18 taught by the fable is normally explicit 19 , much is left unsaid in the parable. On occasion though, moral instruction may be overtly inculcated through analogical extension, as in the Gospel parables of The Unforgiving Servant and The Two Builders:

The Parable of the Unforgiving Servant (conclusion) Then his lord summoned him and said to him, 'You wicked servant! I forgave you all that debt because you besought me; and should not you have had mercy on your fellow servant, as I had mercy on you? And in anger his lord delivered him to the jailers, till he should pay all his debt. So also my heavenly Father will do to every one of you, if you do not forgive your brother from your heart." 20 The Parable of the Two Builders "Every one who hears these words of mine and does them will be like a wise man who built his house upon the rock; and the rain fell, and the floods came, and the winds blew and beat upon that house, but it did not fall, because it had been founded on the rock. And everyone who hears these words of mine and does not do them will be like a foolish man who built his house upon the sand; and the rain fell, and the floods came, and the winds blew and beat against that house, and it fell; and great was the fall of it." 21 In some extreme forms of clarification, the entire allegorical code of the parable is cracked by the narrator, as in The Parable of the Weeds, reported in Matthew 13.36-40, or the more complex Parable of the Sower 22 , told in Matthew 13. [3][4][5][6][7][8] The Parable of the Weeds explained. And his disciplines came to him, saying "Explain to us the parable of the weeds of the field." He answered, "He who sows the good seed is the Son of man; the field is the world, and the good seed means the sons of the kingdom; the weeds are the sons of the evil one, and the enemy who sowed them is the devil; the harvest is the the form of an epigram. Fables may also be composed to reveal aspects of human behavior. Most common is the beast fable, employing animals to represent human types. (M.H. Abrams 1971:5 ; M. Drabble and J. Stringer 1987: 192). 17 "Proverbs frequently present a condensed, implicit story to be interpreted through projection. (...) 'When the cat's away, the mice will play,' said at the office, can be projected on a story of boss and workers. Said in the classroom, it can be projected onto a story of teacher and students." (Turner 1996: 5-6). 18 Drabble and Stringer 1987: 192. 19 In many of Lafontaine's beast fables -like The Wolf and the Lamb ("Le Loup et l'Agneau")the "moral thesis" is stated before the illustrative tale unfolds: The strong are always best at proving they're right. Witness the case we're now going to cite ("La raison du plus fort est toujours la meilleure. Nous l ' allons montrer tout à l ' heure"). 20 The threatening final verses are probably Matthew's own creation (cf. Wierzbicka 2001: 311). Italics ours. 21 Italics ours. 22 "A sower went out to sow. And as he sowed, some seeds fell along the path, and the birds came and devoured them. Other seeds fell on rocky ground, where they had not much soil, and immediately they sprang up, since they had no depth of soil, but when the sun rose they were scorched; and since they had no root they withered away. Other seeds fell upon thorns, and the thorns grew up and choked them. Other seeds fell on good soil and brought forth grain, some a hundredfold, some sixty, some thirty." .

close of the age, and the reapers are angels. Just as the weeds are gathered and burned with fire, so will it be at the close of the age." The Parable of the Sower explained. "Now the parable is this: The seed is the word of God. The ones along the path are those who have heard; then the devil comes and takes away the word from their hearts, that they may not believe and be saved. And the ones on the rock are those who, when they hear the word, receive it with joy; but these have no root, they believe for a while and in time of temptation fall away. And as for what fell among the thorns, they are those who hear, but as they go on their way they are choked by the cares and riches and pleasures of life, and their fruit does not mature. And as for that in the good soil, they are those who, hearing the word, hold it fast in an honest and good heart, and bring forth fruit with patience. The "explanation" -which was probably appended by the evangelists (Wierzbicka 2001: 258) -involves a careful deconstruction of the metaphorical relations -or mappings [START_REF] Lakoff | The Contemporary Theory of Metaphor[END_REF]) -between source domain (seeds) and target domain (Christ's words). The mapping may also be analyzed as the metaphorical transfer of dramatic and conceptual structure from a source story (laborer sowing seeds; seeds growing differently in different places) to a target story (Jesus disseminating the truth of the kingdom of God; different people responding differently to his teachings). Elucidation introduces a rigid interpretational frame which destroys much of the parable's inspirational force and imaginative resources. Yet, clarification may be a way of underscoring the special spiritual significance of the message. This certainly applies to Christ's Parable of the Sower, but also to other foundational narratives, such as the Tendai 23 Parable of The Burning House 24 .

The Parable of the Burning House explained (excerpts) He sees how the creatures are burnt, tormented, vexed, distressed by birth, old age, disease, death, grief, wailing, pain, melancholy, despondency; how for the 23 Tendai Buddhism spread from China to Japan in the 8 th Century. The Tendai sect was established by Dengyo Daishi on Mount Hiei (where the main temple and headquarters of Tendai Buddhists have remained to this day). The "founding father" was given imperial permission to teach the Lotus Sutra -a collection of dialogues and discourses regarded by the Tendai as the final and most authentic revelation of the Buddha. Tendai Buddhists believed that all humans could be redeemed and reach universal "enlightenment" (David J. Lu, 1974: 52-54). A summary of Tendai Lotus teachings and history can be obtained on www.tendai-lotus.org, the official website of the sect. 24 The use of parables was one of the favorite methods of Tendai teaching. The Parable of the Burning House was quite obviously designed to show the superiority of the Lotus (of the Wonderful Law) over traditional Buddhist teaching. The parable opens with a vision of the overcrowded and tottering house of tradition which has caught fire and is about to collapse. "Ignorant boys" -that is, ordinary, trusting believers in the infancy of enlightenment -play around, heedless of the impending disaster. A wise man, "knowing the disposition of the boys", tells them that some beautiful toys are lying outside the house: "Come, run out, leave the house, to each of you I shall give what he wants. Come soon, come out for the sake of these toys." On hearing the names of their favorite toys ("bullock-carts, goat-carts, deer-carts"), the children "quickly rush out from the burning house," are saved, and soon wonder at the sight of the new treasure ("the inconceivable bliss of [true] Buddha knowledge." In the lengthy analysis that immediately follows, the storyteller comments on "skilful device" used by the wise man "to persuade the children to get out of the burning house and save their lives". The ontological and epistemic correspondences between the old house and tradition, the fire and "the burning mass of misery" brought by worldly pain and illusion, the beautiful "carts" (used to lure the boys out of the house) and the superior "vehicles" of knowledge (brought by the Lotus). sake of enjoyment, and prompted by sensual desires, they suffer various pains. (...) And while incessantly whirling in that mass of evils they are sporting, playing, diverting themselves; they do not fear, nor dread, nor are they seized with terror; they do not know, nor mind; they do not try to escape, but are enjoying themselves in [a] world which is like a burning house. (...)

Here, as in The Parable of the Sower, the truth revealed is the most fundamental of all: those who give up their corrupt ways and abandon their old, illusory beliefs will be saved. As they listen to the new words of wisdom and adhere to the higher order of meaning contained in the Lotus Sutra, converts will become enlightened, etc.

"Speaking in parables"

Again he began to teach beside the sea. And a very large crowd gathered about him (...). And he taught them many things in parables. Mark 4.1-2

In Western Culture, parable is the hallmark of Christ's teachings. Matthew notes that Jesus "said nothing to them without a parable" (13.34). As the frequent mention of "large crowds" suggests, Gospel parables have a marked communal dimension. Parables are socially and cognitively cohesive. They are instrumental in creating a "collectivity of mind" (Donald 2001) among believers. The common narrative generates common thinking and establishes a "cognitive community." Just as mythic narratives "ruled" and "glued" the minds of "every tribe and village" in "oral-mythic culture" (295-96), Christ's parables made it possible for "individual minds [to be] integrated into a corporate cognitive process" (298). As stories encapsulating shared moral and spiritual values, Gospel parables were able to develop into a repertoire of narrative models for human thought and action that has survived to this day. It is interesting to note that the contemporary definitions of parable given in reference dictionaries and glossaries display striking similarities in wording and emphasis:

A short story teaching a moral lesson. (Holy Bible. Dictionary-Concordance. Revised Standard Version. Nashville / New York: Thomas Nelson)

A short simple story that teaches a moral or religious lesson, especially one of the stories told by Jesus in the Bible. (Longman Dictionary of Contemporary English)

A short story that uses familiar events to illustrate a religious or ethical situation. Any of the stories of this kind told by Jesus Christ. (Collins English Dictionary)

The focus is on instruction and the protagonist of the parabolic act is the teacher-narrator, not the listener. Interestingly, Christ takes a more cognitive approach to his own parabolic preaching than modern lexicographers and Bible scholars. The stories "put before the crowd" are for people to "hear", so that they might "know the secrets of heaven." The emphasis is placed on the process of understanding ("know", "perceive", "understand") and the true protagonist, is not the storyteller but the audience, as the three synoptic versions of The Parable of the Sower attest:

Why speak in parables?

Then the disciples came and said to him, "Why do you speak to them in parables?" And he answered them, "To you it has been given to know the secrets of the kingdom of heaven, but to them it has not been given (…) This is why I speak to them in parables, because seeing they do not see, and hearing they do not hear, nor do they understand (…) (Matthew 13.10-13) And when he was alone, those who were about him with the twelve asked him concerning the parables. And he said to them, "To you has been given the secret of the kingdom of God, but for those outside everything is in parables; so that they may indeed see but not perceive, and may indeed hear but not understand; lest they should turn again and be forgiven." "He who has ears to hear, let him hear." And when his disciples asked him what the parable meant, he said, "To you it has been given to know the secrets of the kingdom of God; but for others they are in parables." (Luke 8.8-10)

The Parable of the Sower is undoubtedly the "key" to the reception of Christ's other parables as it "highlights the importance of hearing" (Wierzbicka 2001: 264). As he answers the disciples' question -"Why do you speak to them in parables?" -Jesus plays on both the perceptual and conceptual senses of "hearing" (and "seeing"). In doing this, he sets up a ceptual blend (Lapaire 2004), in which perception and conception are integrated: "He who has ears to hear [and a mind to know], let him hear [and understand]". Gospel parables are thus rooted in ception (Talmy 2000) and designed to be listener-, viewer-and cognizer-friendly. Their remarkable cognitive efficiency is imputable to the following set of properties: a. Access. Gospel parables present themselves as ways25 of accessing God's Wisdom, and are accordingly ruled by "the principle of access" (Fauconnier & Sweetser 1996: 7):

The Principle of Access : an expression which names or describes one entity (the trigger) can be used to access (and hence refer to) an entity (the target) in another domain if the second domain is cognitively accessible from the first, and if there's a connection between trigger and target. ( 7)

b. Integration. Not only do parables integrate hybrid conceptual structure into a single narrative space but they also integrate outsiders into the people of God and its shared understanding of divine wisdom (cf. "for those outside everything is in parables" Mark 4.11).

c. Cultural storage. From the outset, Gospel parables were meant to enter the communal memory system and quite successfully did, thus becoming part of the cognitive network of culture (especially in the Middle Ages).

d. Recoverability. Having entered the shared universe of the religious community, major Gospel parables function as definite cultural referents that can be instantly accessed by all members of the cognitive network.

e. Situatedness26 : Gospel parables were originally told from a perspective and located in a specific spatial, historical and epistemic context. Through conventionalisation and "spiritualization", the stories and their messages freed themselves from contextual limitation and eventually acquired the conceptual extensionality of "timeless of truths."

f. Thematic salience: Gospel parables bring a particular aspect of divine truth into cultural awareness. This involves: -the selection of the relevant aspects of moral and spiritual experience which are to be profiled (highlighted) -the focussing of attention on a bounded conceptual regionthat is, the "theme" or the parable.

g. Dramatic simplification. The characters in Gospel parables are usually indeterminate (faceless) social actors (e.g. "a woman", "a certain king", "a servant") or types (e.g. the pious and self-righteous "Pharisee", the [money-grubbing] "tax collector", the "house builder") involved in some simple activity like baking bread, buying a field, observing established religious ritual, erecting a house, etc.

h. Compression of intricate conceptual structure. Parables are small containers for condensed notional content. Indeed, the short story told in parable compresses over time, space, personality and thought. Identity and interaction are quite schematic. Yet, the "bare essentials" of dramatic structure are enough to invoke, condense and simplify complex or elusive conceptual structure.

i. Extension. Gospel parables are small local stories endowed with global spiritual significance. This is achieved through a twofold process of extension:

extension through metaphorical projection from source to target story. -extension through generalisation 27 . Parable rests on a cognitive shift from specific to generic reference / relevance. Thus, the metaphysics of building (in Matthew 7. 24-27) is extended to all serious human endeavor. The "truth" that holds for a particular character somewhere, involved in some meaningful activity, is relevant to any human being, anywhere, who is willing to embrace the timeless, boundless wisdom of God, j. Pragmatic identification. Gospel parables are both doctrinal and utilitarian pieces. They are designed to bring practical change (to the world), to encourage people to alter their ways and reconsider their misconceptions. For this pragmatic design to be achieved, individual listeners must at some point identify with the protagonists. A shift from "external" to "internal" perspective must thus take place, negotiated through metaphorical extension. As we listen to the Parable of the Wise and Foolish Builders, we are led to think of ourselves as the "foolish builders" of our own lives. All the more easily, as it is common to construe life as a container or building -the "house of experience" (Henry James).

k. Paradox. Gospel parables are paradoxical in nature. Christ both used and attacked the religious order and the cultural frames of his times. In The Parable of the Pharisee and the Tax Collector (Luke 18.9-14), the protagonists conform to the social stereotypes of the pious, God-fearing Pharisee and the mean (or dishonest) tax collector. But, as it turns out, the self-righteous Pharisee's prayer is a piece of arrogant self-praise, compared to the "humble" breast-beating of the sinful tax collector. The parabolic twist brought about by Christ's interpretation of the scene, defied conventional expectations and provocatively established a new and higher order of moral perception.

He also told this parable to some who trusted in themselves that they were righteous and despised others: "Two men went up into the temple to pray, one a Pharisee and the other a tax collector. The Pharisee stood an prayed thus with himself, 'God, I thank thee that I am not like other men, extortioners, unjust, adulterers, or even like this tax collector. I fast twice a week, I give tithes of all that I get.' But the tax collector, standing far off, would not even lift up his eyes to heaven, but beat his breast saying, 'God, be merciful to me a sinner!' I tell you, this man went down to his house justified rather than the other; for every one who exalts himself will be humbled, but he who humbles himself will be exalted."

Such is the cognitive efficiency of Gospel parables -old and new 28 -that many are still used today by Evangelical Christians to define the essence of Faith, 28 Some Evangelical websites, such as web-ministry.com, list and interpret the parables of Christ with a literalness and explicitness that destroys their imaginative character and ultimately converts them into sermons. Other sites, such as caterpillar.org.uk, do just the opposite. More imagery and dramatic structure are added to existing configurations and encourage -rather than restrict -imaginative rationalizations of Christian doctrine. The Parable of the Sower is thus reframed and animated as The Parable of the Rooster. New narratives, based on simple plots that "make more sense" to young readers of our times, are sometimes added to the existing repertoire. E.g. The purpose or effect of the annual performance was evidently that of a ritual, namely to give significance or meaning to life for that year. The significant past had to be, and therefore was, annually recreated in order to make, and make fortunate, the future for that year, fortunate for the community as a whole and for each individual member of it. Between the Creation and the Judgement the central mystical events -central for everyone concerned -are the birth, death, and resurrection of Christ. The whole corresponds to the cycle of the Christian year." (Speirs 1959: 45-49) 35 E.g. The Castell of Perseverance (c. 1405), Wisdom (c. 1460), Everyman (c. 1509). Morality plays were "attempts to project moral conflict onto a stage" (Speirs 1959: 59), and focused on "man as an object of contention" between the lower and the higher qualities of the soul (Sampson and Churchill 1972: 201). In the typical Morality Play, characters are personifications of "impulses, moods, attitudes and states of mind, qualities, virtues and vices, physical and mental conditions such as old age and youth" (Speirs 1954: 59). 36 E.g. Greed, Temptation, Wisdom, Perseverance.

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-the origins of life and natural phenomena; -the principles of human existence, social organization, moral behavior; -the conflicts between worldly or spiritual powers, etc.

But unlike the dramatic script of the source story, which always achieves some degree of explicitness, the more symbolic thematic or metaphysical script of the target story may be more covert. Special mention deserves to be made of allegory in the Middle Ages. As Speirs notes in his survey of English medieval verse, "allegory was the established medieval method of visualizing or imagining the inner workings of the mind." (1959: 59). Allegory was a cultural mode of understanding, "the way the medieval mind characteristically worked", as it tried to make "the barely intelligible" visible or imaginable (25). Allegory thus defined, was first and foremost a frame of mind, a representational strategy that led to the production of art forms in which some "figurative narrative" was told to convey some more abstract "moral meaning" (Drabble and Stringer1987: 10). What might be termed the allegorical spirit was the deep cognitive foundation of allegorical modes of depiction, expression or dramatization.

The "medieval mind" showed a particular fondness for miracle and mystery plays. Those popular reenactments of key biblical stories or salient episodes in the lives of saints were meant to represent -i.e. make "present" again, to the mind and to the senses -moments of high moral and spiritual significance. The stories -which eventually "got out of hand" [START_REF] Speirs | A Survey of Medieval Verse[END_REF]: 47) -were extraordinary conceptual mixes, compressing spatial, temporal and causal relations into a single dramatic space, blending respectful biblical remembrance, tragic accounts of human destiny 37 with myth, legend, pagan ritual, buffoonery and satiric reference to the surrounding social context. And just as mass was the symbolic reenactment of Christ's sacrifice on the Cross, culminating on Palm Sunday and Good Friday (when readings of the Passion turned into actual "liturgical drama"), so the mystery cycles traditionally performed in June during the Corpus Christi processions were reenactments of the central mystical events connected to the birth, death and resurrection of Christ 38 . On a broader cultural basis, the story of Christ born, growing, living and dying is the story that shapes the Christian Year and much of our calendar year. Even if Gospel stories are no longer perceived as major cultural narratives in modern Western society, the narrative construal of time is still very much with us.

37 "Lord, they are well off who are dead and gone, For they do not suffer vicissitudes. Here is much unhappiness, and it lasts long, Now in sickness, now in health, now in wet, now in blast, Now in care, Now in comfort again, Now in fair weather, now in rain, Now in heart full of gladness, And after of sorrow. Thus goes this world, I say, on every side…." Opening of The Townley First Shepherds' Play, quoted in Speirs (1959: 437). The play was composed by an anonymous writer ("The Wakefield Master"), and based on a large portion of the traditional (Mystery) Cycle. 38 The coming of a savior, Jesus, is announced. Then Jesus Christ is born, grows up, teaches, is tried and crucified. He resurrects from the Dead, appears to the apostles, ascends into Heaven and eventually sends his spirit. Corresponding religious festivals (e.g. Christmas, Easter, Whitsuntide) and special liturgical times (e.g. Advent, Lent) are story-based. Story and liturgy are never so closely integrated as during Holy Week, which rests entirely on the central Passion narrative.

Indeed, it is important to remember that our experience of time is essentially narrative. Although the established calendar model may look like a strict measuring system that divides time into sequences of years, months, weeks and days, astronomy plays a minor role in everyday human cognition, compared to myth, ritual and life-cycle stories.

a. Many of the names given to days and months refer to deities or ritual activities 39 . b. Seasons -from French seson, related to Latin serere "to sow" -are obviously related to agricultural activity and nature's fertility cycle.

Spring and fall conjure up stories of growth and decay. More generally, narrative models are used to construe the cycle of seasons. In the journey model, for example, seasons are described as animate actors that "come" and "go." "Approaching" seasons are "ushered in" by typical cultural events or natural phenomena, "set in" and are eventually "driven away" by the season that "comes" next. In the cyclical rebirth model, seasons come to life, mature, decay and die. They "return" (resurrect, are borne again) the following year. c. The sun's daily cycle is construed narratively, via the perception-based story of the sun "rising", "shining" and "setting".

Other stories structure our experience of time. Thus, the academic year is first and foremost the story of schools "opening" and "closing"; terms and holidays "beginning" and "ending". This is quite striking in French culture where la rentrée 40 and la sortie 41 are cognitively salient narratives. Politicians, artists, fashion designers, and more generally professional people returning to work after a long break are all involved in a rentrée of some kind 42 .

Among illuminating cases of parabolic thinking found in literature are also beast fables, which epitomize what Johnson (1993) so aptly calls imaginative rationality. For beast fables require a shift from the simple projection model invoked so far, to the more sophisticated blending model described by Fauconnier and Turner 43 . Beast fables are improbable stories that teach sensible moral lessons, extraordinary products of "the literary mind" that reveal the ordinary workings of "the fundamental mind" (Turner 1996: v). The fables are obtained by mixing rather than transferring stories -that is, by blending identities, abilities and roles. The result is a hybrid, imaginary mental space, peopled with its own hybrid, fancy creatures, following their own hybrid motivations for action. Thus, in La Fontaine's "Cicada and the ant" (La Cigale et la Fourmi), a hardworking talking ant flatly refuses to lend any food to an improvident talking cicada. The blended dramatic and moral space, in which animals negotiate 14| their specific animal needs, using human verbal language and reasoning, develops its "own logic" (Turner 1996: 61), while remaining "hooked' to the original input spaces that have contributed actors and conceptual structurerespectively the animal world and the human world. La Fontaine44 -who was later imitated by John Gay45 -built on many of Aesop's stories46 , praising the author's choice of characters and topics, as well as his elegant concision ("élégance laconique"). La Fontaine's own animal tales (contes) were all written with a clear motive of instruction: "Je me sers des animaux pour instruire les hommes" 47 . The imaginary events related in the "tales" (contes) were intended to "please" (plaire) and "edify" (instruire).

Narrative imagining was purposefully used by the poet and moralist as a "crafty device" (feinte) to philosophise about human character while avoiding the "dullness" (ennui) of "bare moral instruction" (Une Morale nue): The talking animals of Lafontaine's beast fables are perfect illustrations of parabolic blending48 . Two stories, with two sets of characters belonging to two different "worlds" blend into a single narrative, governed by its own emergent logic. A blended space is thus set up in which a gaunt wolf can quite naturally interact with a fat house dog and exchange views about diets and destinies, as in Le Loup et le Chien49 . Each protagonist in the fable is a unique mix of human and animal properties. The talking wolf is zoomorphic enough to be featured as a wild beast living in the woods, preying on weaker animals, and anthropomorphic enough to converse in French with the "fat and polite" (gras et poli) house dog.

In the imaginative blended space that is constructed, both wolf and dog enjoy the totally unrealistic status of literate beasts, endowed with true-to-life animal instincts and improbable human capacities. Such is the conceptual and dramatic integration of the two input spaces that a thoroughly impossible situation is made to appear credible and "objective" 50 , as well as "illuminating" 51 .

The blending mechanism detected in beast fables also applies to Gospel parables and, more extensively, to all linguistic expressions of parabolic thinking. Two or more "input stories" merge into a single blended narrative, as when Christ sends his disciples out into the world as "lambs in the midst of wolves" (Luke 10.3) or when ordinary speakers say that "they can see trouble ahead" :

50 "After a blend has been constructed, the correspondences -the identities, the similarities, the analogies -seem to be objectively part of what we are considering, not something we have constructed mentally." (Fauconnier & Turner 2002: 19) 51 "Blending is a dynamic activity. It connects input spaces; it projects partial structure from input spaces to the blend, creating an imaginative blended space that, however odd or even impossible, is nonetheless connected to its inputs and can illuminate those inputs." (Turner 1996: 83) Figure 1: parable as blended narrative

The mental (and dramatic) space imaginatively constructed in the blended narrative is the locus of conceptual integration, a complex process involving "matching", "selective projection" (from the contributing stories), "composition", "elaboration", "emergent meaning" and "compression" (Fauconnier & Turner 2002: 345). Compression 52 is an essential aspect of blending. It applies to all "vital relations" 53 , in particular time and space relations, as well as cause and effect. Fables, parables, proverbs are thus "compressed blends" (Fauconnier & Turner 2002: 312), compact cognitive packets that cut out, condense and simplify experience, while providing a striking sense of transparency and wholeness.

The daily workings of parabolic thinking

Projection and blending 54 are "some of our most basic and common mental abilities" (Fauconnier & Turner 2002: 18). So is the narrative organization of experience. Parable, which combines those three fundamental cognitive mechanisms, is a powerful conceptualizing and representational strategy that "has the widest utility in the everyday mind." (Turner 1996: 7). It is "a literary capacity indispensable to human cognition generally" ( 5). Yet, outside marked moral, mythical or religious contexts, parabolic thinking remains an unconscious form of narrative imagining, a hidden hand 55 in the cognitive laboratory of human invention.

52 For a detailed discussion of "compression" see Fauconnier & Turner (2002:312-324) 53 "We call all-important conceptual relations 'vital relations'. (Fauconnier & Turner 2002: 92) E.g. "Change, Identity, Time, Space, Cause-Effect, Part-Whole, Representation, Role, Analogy, Disanalogy, Property, Similarity, Category, Intentionality, Uniqueness." (111) 54 "[B]lending produces ads in magazines, hyperbolic geometry, grammatical constructions, counterfactual arguments, cause-effect compressions, literary allegories, computer interface designs, and many other inventions." (Fauconnier & Turner 2002: 110) 55 "Our unconscious conceptual system functions like a 'hidden hand' that shapes how we conceptualize all aspects of our experience" (Lakoff & Johnson 1999: 13). The aim of this new section is to show that parable is indeed a basic mental tool, especially in biology and medical science, where anthropomorphic conceptions of bacteria and viruses invite socio-cultural narratives.

The "virus infection" stories 56

Viral and bacterial infections are central members of the infectious diseases category. Viruses are the smallest form of life and, unlike bacteria, can only reproduce in the living cells they infect. In microbiological terms, viruses show "host specificity," meaning that a certain virus will only able to replicate itself within a certain species or group of species. The center or "core" of a virus contains the genetic material necessary for it to survive and replicate itself within host cells. But more relevant to our purpose than biological specifications are the embedded or interrelated stories typically used to conceptualize biological virus infections, in particular:

-the central war and invasion story: a virus is construed as an assailant; infection as "attack" followed by "invasion" of the "target cells"; immunization as protection; the production of antibodies as organized defense, etc. It is interesting to note that in the world of computer hacking, this traditional war scenario is realized as the more modern terrorist attack story. "Hard disks" are "exposed" to the "threats", "attacks" and "deadly actions" of viruses. -the foreign detection story: the body's immune system recognizes some of the protein molecules in the virus as "foreign" (and "attacks" the virus by producing antibodies against them). This story is adapted to the computer world as the virus scan story, performed by "anti-virus software", loaded with updated "virus definitions". -the fertility story: technically, viruses "copy" or "replicate" themselves.

Although the process tends to be described in sexless, mechanistic fashion, the story of "reproduction" is clearly part of backstage cognition 57 , both in the microbiological and the computer domains. Replication -the process by which a virus "spawns" or "makes copies of itself" -is "one of the major criteria separating viruses from other computer programs." -the friendly home (or environment) story: in microbiological terms a "host" is an organism in which a virus can copy itself. The "host cell" is construed as the virus's fixed abode, elected home or favourite breeding ground.

the recovery (or get better) story: the body's immune system naturally and efficiently copes with most virus infections. Laboratory-made vaccines have been developed to protect humans from serious viral diseases. Interestingly, this story does not transfer well to the computer world. Although certain forms of "vaccination" can be carried out, the 56 All terms and definitions related to virus infections are borrowed from online glossaries and articles: National Foundation of Infectious Diseases (www.nfid.org), McAfee Security (www.mcafee.com) and BBC International recommendations on "How to avoid computer viruses" (www.bbc.co.uk/dna/h2g2/A354638). 57 "Backstage cognition" is all the "imaginative work (…) invisible to us and taken for granted" (Fauconnier & Turner 2002: 23).

electronic "immunization" of systems is not performed. Computer systems have no natural, self-regulating immune systems. As a result, there are no self-recovery scripts in the restoration story of damaged files. (The latter is construed as a voluntary "cleaning", "disinfection" or "fixing" episode, performed by users, with the assistance of security experts).

The above list is not complete, but long enough to establish the narrative construal of biological viruses and outline some common extensions to computer viruses. "Virus attacks" are microbiological stories, understood via the common socio-physical stories of war, fertility, home, etc. Applied to the world of computer programming, the complex virus reproduction and infection story functions as a compressed and simplified input story, which is selectively blended with another input story -the story of malignant manmade programs capable of attaching themselves to files, replicate themselves and damage entire computer systems. The projection of the two input stories into a single, blended narrative yields the computer virus infection story that all office workers live by.

Technically, a computer virus is a malignant program purposefully created by programmers. The "malicious piece of code" is designed to damage a system or the data it contains, compromise security and confidentiality, prevent the computer from being used in its normal manner. A virus can be "malignant" enough to bog down an entire computer system or even destroy it utterly. The rogue program has a "source code" that "virus technicians" must identify in order to devise the "fix tools" that will "remove" or "eradicate" it. The process is known as "disinfection" or "cleaning". It is interesting to note that "repairing" damaged computer files or disks is narratively construed via different stories: disinfecting (a contaminated area), cleaning (something), removing (some unwanted item), repairing (some broken object). Matters can be made more complex and eerie, when the virus has been programmed to "resurrect itself." A creepier story is then added to the blend.

Computer viruses seem to "spread", "propagate", "infect" and "mutate" indefinitely, just as biological viruses do 58 . Central "virus types" include "mutating viruses", "macro viruses", "armoured viruses", "zoo viruses". The "damage" they are capable of inflicting to computer systems can be "lethal".

Their destructiveness rivals that of other "parasitic" or "malicious" computer programs that invoke different narrative frames, such as "worms" and "Trojan horses." Although "host specificity" is not mentioned as such, computer viruses typically attach themselves to specific (program) files. File types that play host to computer viruses -like .EXE, .COM, .BAT, .ZIP, .VBS, .DOC, .XLS -act as "common carriers" capable of "passing the virus along." As the specialized vocabulary of virus "attacks" and "infections" suggests, viruses are partly construed as assailants -or rather terrorists -capable of 58 The contagion script is an important component of the computer virus story. Many viruses "propagate" or "spread" through email address books and "infect" other systems by sending themselves out to personal email accounts, contacts and friends, who end up "contracting the virus." Infection and removal (disinfection) methods may carry biological names but denote thoroughly different procedures: "processing a malignant code" (infection); repair, deletion or restoration (disinfection).

"carrying major Net attacks" by "building large network of slave machines" and "exploiting vulnerabilities in security systems." And just as counter-terrorist units are usually unable to prevent major terrorist attacks or disarm terroristnetworks, "security experts" are rarely able to prevent damage being done. But unlike special security forces that can launch pre-emptive strikes or engage in counterattacks, "virus technologists" are peaceful criminal investigators. Norton and McAfee teams do not pose (or act) as armed peacekeepers, engaged in the dismemberment of "the cybercrime community" and the inactivation of "attack networks." The best they can do is issue special "warnings"; devise "firewalls"; offer "virus removal tools" that will "repair" the "harm" done to computers; sell "antidotes"59 or "vaccines" and eventually suggest methods of "safe computing" that will allow users to "protect themselves" and "keep virus-free". (The discourse of "safe computing" is strongly reminiscent of the "safe sex" campaigns launched after the outbreak of Aids).

The computer virus infection story just outlined is the blended narrative that allows us to understand how a malignant piece of code might damage computer systems and spread across networks. But it is much more than that: it is the original creative script that has shaped the nature and destiny of computer viruses ever since they were invented. Computer viruses attack and replicate the way they do because they were initially conceived as viruses. The same holds for "worms" and "Trojans", which have specific ways of disabling computers, based on original biological or mythical scripts. Lastly, it should be noted that the cognitive efficiency of the conceptual integration network created by the computer virus blend rests on the shared conceptual and dramatic structure originally connecting the input stories:

-Input story # 1: "a microbiological entity that infects or contaminates a healthy organism and threatens it with destruction" -Input story # 2: "a manmade program or piece of code that causes a negative event in a computer system"

The common structural properties shared by the biological virus story and the malignant computer program story are aptly defined by [START_REF] Fauconnier | The Way We Think[END_REF]:

The element is present, but unwanted; it comes in, or is put in, from the outside. It does not naturally belong.

The element is able to replicate; new copies of it appear that have the same undesirable properties as the original.

The element disrupts the original functioning of the system. The element is harmful to the system and, hence, to its users. ( 275)

In other words, the presence of some rational common denominator is indispensable for the imaginative blending process to take place.

More importantly, they suggest that the specialized language, concepts and methodology of scientific inquiry owe more to cultural narratives than is commonly assumed. The criminal investigation and court trial stories detailed in their paper are proof enough that narrative imagining and, more specifically, parabolic blending are essential dimensions of construal in science.

Parabolic projection and grammar

Grammar makes abundant use of small spatial and perceptual stories to structure key temporal, aspectual, modal and causal concepts. Grammar is deeply poetic (Lapaire 2002: 25) and dramatic.

Common stories of body action and perception found in grammar systems include journey stories, object-production stories and viewing scenes [START_REF] Lapaire | The conceptual structure of events : the go-, make and get-/give-/have-scenarios[END_REF](Lapaire , 2004a(Lapaire , 2004b)). Each story profiles a particular body part and type of sensory-motor activity.

The following examples may be given: a. Legs / feet. Walking. In the successful journey story coded by the French aspectual idioms arriver à, parvenir à 61 doers are construed as travelers moving along an action path 62 and their achievements as destinations reached.

(1) J'y suis arrivé! ("I succeeded", "I made it"; literally "I got there", "I arrived in that place"). (2) Je n'arrive pas à lire ton écriture ("I can't read your hand").

(3) Il est parvenu à ouvrir la fenêtre. ("He managed to open the window") (4) Je ne parviens pas à trouver la solution. ("I can't find the answer").

"Thematic roles" -like « agent », « experiencer », "cognizer" -are subsumed under a single narrative role: that of the fortunate (or unfortunate) "traveller", encountering obstacles on the way to a desired action-location. The predictive idioms known as "go-futures" illustrate a subvariety of journey story: the mental journey to an envisaged event. The French aller + infinitive construction (Vous allez tomber) and the English be going to construction (You are going to fall) involve "subjective motion" along an imaginary "temporal path" to the "infinitival event" (Langacker 2000: 302-04). b. Hands. Physical manipulation. In the object-production story "things done" are construed as "things made", and finished actions as "finished products" (with "no part missing"). The "workshop model" for human 61 Literally "to arrive", "to come to a place". When used aspectually: "to manage to do sth", "to succeed in doing sth."

  62 "ACTIONS ARE MOTIONS ALONG PATHS from one location (= state) to another state-location. (…) STATES ARE LOCATIONS along such metaphorical action-paths (…) CHANGES ARE MOVEMENTS from one state-location to another. (…) PURPOSES ARE DESTINATIONS toward which we move."(Johnson 1997: 37).

Parable in literary format: from parabolic projection to parabolic blending

  Classical myths, allegories and fables, English medieval ballads 29 , metric 30 or prose 31 romances, debate poems 32 , tales 33 , miracle, mystery 34 and morality 35 plays, to mention but a few examples in European literary history, use the cognitive resources of narrative imagining and projection. The overt source story(Turner 1996:6) -in which gods, heroes, talking beasts, personified virtues and vices 36 interact -is projected onto some more essential target story focused on:

	explain the blessings of God or trace the path of self-improvement and
	salvation.
	Science fiction writers also show a special taste for the conceptual and
	imaginative resources of (Gospel) parables, as exemplified by Octavia Butler's
	Earthseed series, named after the original New Testament Parables: Parable of
	the Sower (1993) and Parable of the Talents (1998). But long before Butler's
	heroine, Lauren Olamina, was shown preaching the simple creed of her new
	religion (Earthseed) in a violent 21 st -century America plagued by global
	warming, massive unemployment, gang warfare and corporate greed, parabolic
	thinking was thriving in oral and written "literature."
	2.2

The Parable of the Caterpillar: "The Caterpillar struggles with his everyday existence, munching his way through the leaves (...) He doesn't know that one day he will be fluttering from flower to flower(...) gloriously adorned with the colours of the rainbow, as light as the air on which he floats. His future God has planned -the wonderful change from what he is now to what he will become once time has passed. He cannot see the future, nor the butterflies which flit across the sky. On that day, though, he shall become like them.", etc. 29 Ballads were "sung or recited dramatically". In many, the themes were "recognizably those of medieval romances"

(Speirs 1959: 39)

.

30

Famous English verse (or metrical) romances include King Horn (c. 1225), Havelok the Dane (c. 1275). Many English romances were based on earlier French romances, which were themselves related to Celtic tales forming the substance of the Arthurian romances and the Breton lays. All have recurring themes: the problematic union between a mortal and a other-worldly being; the boy born to be king but exposed or exiled; cycles of separation and restoration undergone by a wife or queen; successions of tests (rites of passage / initiation) which a knight must undergo to prove his manhood; contests between a knight and some other other-world character with a combat as climax; ritual combat, followed by ritual marriage, etc. (Adapted from

[START_REF] Speirs | A Survey of Medieval Verse[END_REF]

). 31 E.g. Malory's Morte D'Arthur (c. 1485) . 32 E.g. The Owl and the Nightingale (c. 1220). 33 E.g. Chaucer's Canterbury Tales (c. 1386-1400); Gower's Confessio Amantis (c. 1390)

34

Named after the trade (Fr. mestier) of their performers. A form of ritual drama based on great biblical stories (from the Creation to the Ascension) that was extremely popular in England from the 13 th to the late 16 th cent. Mystery plays were performed annually during Corpus Christi processions. "The Mystery Cycle represents or reproduces what might perhaps be called a history of the world -of mankind in relation to God -from the Creation to the Last Judgement. (...)

"The essence of parable is its intricate combining of two of our basic forms of knowledgestory and projection."(Turner

1996: 5)5 A term coined by Mark Turner in The LiteraryMind (1996: 168).6 The phrase is Mark Johnson's in MoralImagination (1993: 33).7 Parable, from Old French parabole, from Latin parabola "comparison", from Greek parabole "analogy", from paraballein "to throw alongside", from para-"alongside" + ballein "to throw". Collins English Dictionary. London & Glasgow:Collins, 1979. 8 The "internal spatial logic" of this schema is well summarized by GeorgeLakoff and Rafael Núñez (2000: 37-38): "[T]here is a moving entity (called a trajector), a source of motion, a trajectory of motion (called a path), and a goal with an unrealised trajectory approaching that goal."9 In his discussion of "the narrative context of self and action" (1993: 150-84), Mark Johnson argues that "the beginning-middle-end structure" of the prototypical narrative "is an instance of an even more basic recurring imaginative pattern -the SOURCE-PATH-GOAL SCHEMA -that structures so much of our bodily movement and perception." This schema, he claims, "is

The word "way" is here to be taken in its spatial ("path") and related modal sense ("manner").

For a definition of situatedness, seeCroft and Cruse (2004: 58-59).

The French linguist GustaveGuillaume (1883Guillaume ( -1960)), whose theory of pschyomechanics was essentially cognitive, regarded the shift from generic (or universal) to specific (or singular) scope as the most fundamental thought process of all. « Dans la langue (...) sont inscrits (...) les grands mouvements inhérents à la pensée humaine, ceux qui sont inséparables d'elle et dont on serait fondé à dire qu'ils la créent autant et plus qu'elle ne les crée. Ils se confondent avec son existence même, et s'ils n'étaient point en elle, elle ne serait point, tenant d'eux sa puissance. Les deux plus importants de ces mouvements créateurs de la puissance de la pensée sont l'accession au général au travers du particulier et, inversement, l'accession au particulier à partir du général.» (1969 : 145-46)

The French poet Jean de La Fontaine (1621-1695) is mostly remembered for his fables. Popular animal stories include La Cigale et la Fourmi (The Cicada and the Ant), Le Loup et l'Agneau (The Wolf and the Lamb), Le Corbeau et le Renard (The Crow and the Fox), Le Lièvre et la Tortue (The Hare and the Tortoise), Le Lion et le Rat (The Lion and the Rat).

John Gay (1685-1732) brought out his Fables in 1727. A second volume was posthumously published in 1738.

The name of Aesop (620?-564? BC) -probably a legendary figure to whom tradition attributes a wide stock of Greek fables -is associated with the beast fable -or aesopian / aesopic fable -in which animals are given human characters and chiefly used to satirize human failings.

"Talking animals are a conceptual blend. (…) Talking animals, seemingly so trivial, are created through a general and central parabolic activity of the everyday mind -blending."(Turner 1996: 58)

"The Wolf and the Dog." In this fable, a starving wolf comes upon a well-fed dog. The wolf agrees to follow the dog into town and "work" for his master. But on the way, the envious wolf notices that hair is missing on the dog's neck and realizes that his fortunate cousin normally wears a collar: "Attaché? dit le loup; vous ne courrez donc pas où vous voulez?" (Chained up? Is that it? You can't go about as you please?). Appalled by the discovery, the distraught wolf runs off.

The imaginative world of myth and magic is never far, as "firewalls" and "antidotes" attest. These clearly refer to anthropologically meaningul cultural narratives.

To suit the present purpose, the original terms used by the authors -"metaphor", "metaphoric", etc. -have been replaced by "story", "script" or "narrative". The shift in "dramatic emphasis" does not alter Faber and Márquez Linares's cognitive account.

"Humans are fundamentally imaginative creatures whose understanding of experience is built up with the imaginative materials of cognition."(Johnson 1997: 3)

Trial by medical jury: oncology as criminal investigation followed by court proceedings

In "The Role of Imagery in Specialized Communication" (2003), Pamela Faber and Carlos Márquez Linares claim that the stories of armed conflict which are routinely used to frame "the fight against cancer" in medical oncology texts are less central and meaningful than other narratives, such as the police investigation and the trial stories 60 :

[T]he frequently cited arm conflict [story] is not the only one in medicine, nor is it necessarily the most important, especially in highly specialized research articles. A more frequent [story] in this type of discourse is the police investigation [scenario]. In this case the doctor is the police detective who (…) rounds up the usual suspects. This kind of sleuthing activity activates the police investigation frame as well as a subsequent courtroom frame within the context of which the culprit is brought to trial."

The police investigation story is essential in providing the four participant roles and basic investigation script present in the oncological inquiry blend: detective / doctor; culprit / disease; evidence / data; conviction /diagnosis. The wide body of linguistic evidence produced by Faber and Márquez shows that medical research is indeed construed as a kind of "sleuthing business" requiring "detective-like laboratory skill." The detective is both an agent and an experiencer, who must "solve a mystery." "Clues" are provided by abnormalities and by chemical or genomic "footprinting." The doctor may find a "suspect" (e.g. "suspect lymph nodes") who is put under "surveillance." If "circumstantial evidence" is found, the "culprit" is "accused" and "brought to trial." Once the investigation phase is over, the trial may start. As the trial begins, "the doctor changes roles." He is no longer "a detective", but "a lawyer who 'interrogates' the witness (affected body-part) by means of a diagnostic instrument."

The "testimony" of the "witness" many or many not "implicate" the accused (…) After the testimony of the witnesses and the presentation of "evidence" (…) a "verdict" is emitted by the jury (…) The accused many be "exonerated" or declared to be the culprit and "incriminated."

Faber and Márquez note that "what licenses the whole frame is the fact that inanimate entities such as germs, cells, antibodies, etc. are conceptualized as animate ones."

Oncology texts basically focus on cells. Depending on whether the cells are malignant or healthy, they may take the role of agent or patient. Since these are conceptual roles generally ascribed to animate entities, this is conducive to personification. Consequently, at different levels, cells acquire human roles as well as the prototypical characteristics of these roles. This is particularly true of genes, which can have general conceptual roles such as effector, activator, or receptor.

undertakings has performers cast in the role of creators of "artefacts" (Lapaire 2004a). It is extremely productive in French grammar:

(5) C'est chose faite! (« It's done ! »; literally « It's a thing made ») (6) Voyons, fais quelque chose ! (« Why don't you do something ! »;

literally "Please, make something!") The model is relevant to English grammar too. The object-production story is subliminally told in some causal and aspectual makeconstructions: (7) She makes me cry. (= "She causes me to cry") (8) We've made it! (= "We've succeeded") c. Eyes. Observation. Prediction and epistemic certainty are often construed in visual terms. In the common epistemic viewing scene, cognizers are cast in the role of observers scanning the horizon. Perfect knowledge is clear vision; prediction is foresight; predictable or likely events are visible things lying "out there" in the conceivable world / "foreseeable future" (Lapaire 2004b).

(9) Just try to picture the future! (10) I can see this happening quite soon.

(11) Analysts foresee that oil prices will rise sharply.

The projection of story structure onto grammatical form and meaning allows narrative compression and simplification to take place. Evasive thematic roles, complex aspectual configurations, subtle causal links are reduced to fixed participant roles ("traveler", "creator", "viewer") and purposes ("reaching one's destination", "producing an object", "seeing something clearly") in genericlevel scripts.

Concluding remarks

Humans are imaginative 63 storytelling animals. Narrative imposes dramatic organization on target configurations and plays a vital role in the cognitive fluidity of meanings (Fauconnier & Turner 2002: 174). More generally, the prevalence of parabolic thinking in human language and cognition supports Turner's controversial claim that "the literary mind is the fundamental mind" (1996: v).


Rosa Di Lorenzo

Giuseppe Ingarao

Fabrizio Micari

Francisco Chinesta

A PARETO OPTIMAL DESIGN APPROACH FOR SIMULTANEOUS CONTROL OF THINNING AND SPRINGBACK IN STAMPING PROCESSES

Keywords: sheet metal stamping, thinning, springback, response surface method, multi-objective optimization

One of the most relevant research issues in automotive field is focused on the reduction of stamped parts weight also increasing their strength. In this way, a strong research effort is developed on high strength steels which are widely utilized and they require a proper springback control. Springback reduction in sheet metal forming is a typical goal to be pursued which is conflicting with thinning reduction for instance. Thus, such problems can be considered as multi-objective ones characterized by conflicting objectives. What is more, nowadays, a great interest would be focused on the availability of a cluster of possible optimal solutions instead of a single one, particularly in an industrial environment. In this paper, integration between numerical simulations, response surface methodology and Pareto optimal solutions search techniques was applied in order to design a DP 600 U-channel shape stamping operation. In particular the friction conditions and blank holder force were optimized as design variables in order to accomplish two different objectives: reduce excessive thinning and avoid excessive geometrical distortions due to springback occurrence.

INTRODUCTION

One of the most relevant research issues in automotive field is focused on the reduction of stamped parts weight also increasing their strength. Such issue led to the success of materials such as high strength steels (TRIP, DP etc) which are characterized by a strong springback occurrence after forming operations [START_REF] Banu | Simulation of springback and wrinkling in stamping of dual phase steel rail-shaped part[END_REF][START_REF] Koc | Simulation of springback variation in forming of advanced high strength steels[END_REF][START_REF] Asgari | Statistical analysis of finite element modeling in sheet metal forming and springback analysis[END_REF]. One of the main topics, for springback control in sheet metal forming concerns, nowadays, the numerical simulations calibration. In particular, the main issues regard: calibration of numerical parameters [START_REF] Xu | Sensitive factors in springback simulation for sheet metal forming[END_REF][START_REF] Fratini | On the springback prediction in 3d sheet metal forming processes[END_REF]; constitutive model influence on springback [START_REF] Faust | Numerical springback evaluation for modern high strength steels using advanced material models[END_REF] process parameters effects [START_REF] Mangas | Improvement of springback FEM simulation by means of an optimization procedure based on an experimental trial[END_REF]. In sheet metal forming most of the problems are multi objective problems, generally characterized by conflicting objectives. A typical example of optimization problem in sheet metal forming characterized by conflicting goals is the definition of proper parameters aimed to prevent both fracture and springback shape defects. What is more, nowadays, a great interest would be focused on the availability of a cluster of possible optimal solutions instead of a single one. Thus, the design parameters calibration, accomplishing all the objectives, is difficult and sometimes unsuccessful. In order to overcome this drawback a multi-objectives optimization procedure based on Pareto optimal solution search techniques seems a very attractive approach to deal with sheet metal forming processes design [START_REF] Messac | A computationally efficient metamodeling approach for expensive multiobjective optimization[END_REF][START_REF] Marler | System identification of simplified crash models using multi-objective optimization[END_REF]. In this paper, integration between numerical simulations, response surface methodology and Pareto optimal solutions search techniques was applied in order to design a DP 600 U-channel shape stamping operation. In particular the friction conditions and blank holder force were optimized as design variables in order to accomplish two different objectives: reduce excessive thinning and avoid excessive geometrical distortions due to springback occurrence [START_REF] Firat | U-channel forming analysis with an emphasis on springback deformation[END_REF][START_REF] Papeleux | Finite element simulation of springback in sheet metal forming[END_REF]. The steps of the optimization procedure include the application of Central Composite Design (CCD) for the identification of the necessary data over the domain of variation of the design variables; then numerical simulations (explicit-implicit formulation) of the samples identified by CCD are run and data on output variables are collected. The following steps concern the development of a response surface model to interpret the final objectives as functions of the design variables and their validation; finally, Pareto optimal solutions analysis to reach the most performing design variables is performed.

The final aim is to develop a predictive tool able to identify a sort of process window for the analyzed process also minimizing the computational effort, in particular with respect to mono-objective optimization techniques or traditional trial and error methods. Many possible technological scenarios were investigated by the implemented procedure and a set of reliable solutions, able to satisfy different design requirements, was obtained.

THE ANALYZED PROCESS

The considered forming process is a typical stamping one aimed to obtain an S-shaped U-channel (See Figure1 for a sketch of the investigated process). A drawn height of 15 mm was taken into account. The utilized material was a 1mm thick DP-600 high strength steel for which the following flow rule was obtained through a campaign of tensile tests developed on 0° direction specimens: The following Lankford's anisotropy parameters were also determined: r 0°= 0.73; r 45°= 0.9; r 90°= 0,93. The process was numerically simulated using the explicit code LS-DYNA, and a subsequent springback analysis was carried out with the implicit solver of LS-DYNA. According to previous experiences on these numerical models [START_REF] Fratini | On the springback prediction in 3d sheet metal forming processes[END_REF], a full integrated quadrilateral shell element with 9 integration points along thickness was utilized; in particular, the starting element size is 3mm and a three levels geometric remeshing strategy was applied all over the numerical simulations. The total number of elements at the end of the explicit simulations was higher than 4000; a Coulomb model was considered for frictional actions. In order to take into account material anisotropy the Barlat-Lian constitutive model [START_REF] Barlat | Plastic behaviour and stretchability of sheet metal Part1. A yield function for orthotropic sheets under plane stress conditions[END_REF] with an isotropic work hardening was utilized. In order to evaluate the entity of springback, at the end of the implicit simulation, a comparison with a reference target shape was performed utilizing a CAD tool. In particular, the total deviation error between such target shape and the obtained one was calculated (i.e. the maximum normal distance between the two overlapped surfaces).

σ=1008ε 0.169 [MPa].

THE OPTIMIZATION PROBLEM

The optimization problem taken into account aims to minimize thinning in the final part (in order to prevent fracture) and also to minimize springback occurrence. Thus, two objective functions were defined in the modeling phase of the investigated problem: t% measuring the maximum thinning on the final part and d[mm] which is the maximum deviation of the final part shape from the fixed target shape. The problem modeling also consists of the design variables definition: in the investigated process two design variables were chosen, namely friction coefficient (µ) and blank holder force value (BHF [kN]). Actually, the chosen design variables are related to the analyzed objective functions since such variables strongly influence the restraining forces over the sheet during the process thus influencing both thinning and springback entity. Once the optimization problem was modeled, the workflow procedure applied in the present paper was developed according to the following steps: Step1. Planning of the numerical simulations to be run through a proper Design of Experiments (DOE) definition; Step2. Numerical simulations development according to the designed DOE; Step3. Collection of numerical data obtained on thinning (t%) and springback amount (d) for each of the conditions identified by the DOE; Step4. Meta-modeling step: analytical formulation of a response surface describing each objective function as a function of the design variables; Step5. Evaluation of the accuracy of the obtained response surfaces in terms of error of the predictions provided by the response surfaces with respect to the actual numerical values (such evaluation was developed on properly selected points of the design domain); Step6. Application of the ε-constraint procedure in order to perform a multi objective optimization i.e. to determine optimal Pareto solutions. As step 1 is regarded, the Central Composite Design (CCD) architecture was selected to design the set of experiments/simulations; actually, such approach is one of the most utilized for fitting a second order response surface. In particular, the design of experiments illustrated in Table1 was formulated for the two design variables. The designed simulations were carried out at the varying of the design variables, thus, the maximum thinning (t%) and the springback amount (d) were obtained. Figure 2 shows springback numerical distribution and Figure 3 shows thinning distribution for one of the simulations of the DOE, in particular the one with µ=0.12 and BHF=120[kN].

DISCUSSION OF THE RESULTS AND CONCLUSIONS

Once the designed numerical simulations were developed, Step 4 and 5 of the procedure were developed and two response surfaces were determined for the two objective functions (see Figure 4 and5 showing respectively thinning response surface and springback one; all the values are normalized). The best performing response functions were obtained by an "heuristic" regression procedure (developed within Minitab Environment) by subsequent exclusions of factors which are statistically less significant [START_REF] Myers | Response Surface Methodology Process and Product Optimization using Designed Experiments[END_REF]. Such procedure led to a third order polynomial function for thinning and to a second order one for springback both providing very satisfying correlation index. The obtained equations were tested measuring the prediction errors derived from the comparison between the predicted values of t% and d and the actual numerical values; such tests demonstrated the good prediction capability of the two surfaces. Once the effectiveness of the response surfaces was tested, the determination of Pareto optimal solutions was performed. The technique utilized to determine Pareto solutions was the ε-constraint procedure. In particular, the thinning function was chosen as primary function to be optimized in the development of the ε-constraint method. The resulting Pareto curve was determined and it is reported in Figure 6 in which the Pareto frontier is illustrated by plotting the curve t% vs. d. The obtained frontier is an effective design tool since it provides a set of Pareto optimal solutions: by fixing a desired level of thinning, for instance, it is possible to foresee which minimum possible level of springback has to be expected. Furthermore, some points belonging to the Pareto frontier were numerically reproduced (for instance, see points from 1 to 3 evidenced in Figure 6). The results corresponding to the three Pareto points are illustrated in Figure 7 as springback is concerned and in Figure 8 as thinning is regarded. Moreover, for each point belonging to the Pareto frontier, it is possible to know which combination of the design variables (BHF and friction coefficient values) corresponds to the given thinning and springback levels. Thus, it is possible to consider the obtained curve as a design tool in order to define design variables with a strong awareness of the final results in terms of goals which can be reached. Table 3 shows the design variables values for the chosen points. The obtained values are very coherent with the corresponding thinning and springback occurrence. Such consideration allows assessing the effectiveness of the developed design tool. Actually, the obtained results prove the efficacy of the proposed approach.

Figure 1 :

 1 Figure 1: Sketch of the analysed process

Figure 2 :Figure 3 :

 23 Figure 2: Springback distribution (d [mm])

Figure 4 :Figure 5 :Figure 6 :

 456 Figure 4: Response surface for thinning

Figure 7 :Figure 8 :

 78 Figure 7: Comparison between desired shape and obtained one (springback effect) for points 1-2-3 of the Pareto frontier

Table 1 :

 1 The utilized design variables levels

	Design			DOE Levels
	variables	-α	-1	0	1	+α
	µ	0.092 0.1	0.12	0.14 0.148
	BHF [kN]	64	80	120	160	176

Table 2 :

 2 Design variables for points 1-2-3 of the Pareto frontier

	Design		Pareto points
	variables	1	2	3
	µ	0.138 0.125	0.09
	BHF [kN]	160	104	64


F Grondin

M Bouasker

P Mounanga

A Khelidj

A MULTISCALE APPROACH FOR THE PHYSICO-CHEMICAL DEFORMATIONS OF SOLIDIFYING CEMENT-BASED MATERIALS

At early stages of hydration, solidifying cementitious systems exhibit dimensional variations caused by their thermal, hydrous, chemical and microstructural evolutions. If restrained, these deformations can induce the development of internal stresses high enough to generate cracking of the hardening material. This study focuses on early-age autogenous strain of cement-based materials, which develops following two main processes: Le Chatelier contraction (also called chemical shrinkage) and self-desiccation shrinkage. Chemical shrinkage results from the difference of absolute density between reactants (anhydrous cement and water) and hydration products. Early-age self-desiccation shrinkage is generally attributed to the development of a negative capillary pressure in the porous network related to the water consumption by the hydration reactions. The purpose of this research work is to propose a multiscale approach to model the rate of autogenous shrinkage of cement-based materials at very early-age, between 0 and 48h. Le Chatelier contraction is computed from the chemical equations of hydration and the specific volume of each phase, whereas a homogenization method based on the self-consistent scheme is applied to calculate the self-desiccation shrinkage. Computed results are discussed and analyzed. Good agreements between experiments and simulations are achieved and a sensitivity study is performed to assess the influence of the cement fineness and the fraction of granular inclusion on early-age autogenous strain.

1.

INTRODUCTION

Under autogenous conditions, the setting and the hardening of cementitious matrices are accompanied by strains related to hydration heat release, Le Chatelier contraction and selfdesiccation of the porous network. This paper focuses on the two latter phenomena. Le Chatelier contraction is related to the phase change of anhydrous elements of the cement (clinker) in hydrated elements. This chemical transformation is associated to a decreasing of the specific volume of the cement paste [START_REF] Chatelier | Sur les changements de volume qui accompagnent le durcissement des ciments[END_REF][START_REF] Powers | Studies of the physical properties of hardened portland cement paste[END_REF]. The self-desiccation is related to the progressive desaturation of the porous medium caused by the water consumption during the hydration process and prevails on the chemical shrinkage at the setting time. According to various studies, it would be associated mainly to the capillary pressure which increases with the reduction in interstitial water used for cement hydration [START_REF] Kovler | Overview and future trends of shrinkage research[END_REF]. Models based on empirical relations have been developed with an aim of calculating the strains due to autogenous shrinkage in cement pastes and mortars [START_REF] Tazawa | Chemical shrinkage and autogenous shrinkage of hydrating cement paste[END_REF]. But these macroscopic models do not take into account the microstructure heterogeneities. The homogenization methods have been developed for the determination of the equivalent mechanical properties of heterogeneous materials. Explicit methods are based on simple representations of the microstructure with analytical resolutions of cellular problems [START_REF] Bornert | Homogénéisation en mécanique des matériaux[END_REF]. Numerical methods enable to consider a richer microstructure but need a numerical resolution of cellular problems [START_REF] Bentz | Application of digital-image-based models to microstructure, transport properties, and degradation of cement-based materials' in 'Modelling of Microstructure and Its Potential for Studying Transport Properties and Durability[END_REF][START_REF] Guidoum | 3d numerical analysis of long term behaviour on concretelike composite material[END_REF][START_REF] Grondin | Multi-scales modelling for the behaviour of damaged concrete[END_REF]. Recently, these methods have been applied to the calculation of the mechanical properties and the autogenous shrinkage of cement pastes at early-age [START_REF] Acker | Creep and shrinkage of concrete: physical origins and practical measurements[END_REF][START_REF] Bernard | A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials[END_REF][START_REF] Pichler | A multiscale micromechanics model for the autogenousshrinkage deformation of early-age cement-based materials[END_REF][START_REF] Torrenti | Mechanical threshold of cementitious materials at early age[END_REF]. However, these various models do not link the chemical shrinkage observed before the setting and the autogenous shrinkage at earlyage.

In this work, we propose a model to compute the autogenous strain evolution of cement paste and mortar at very early-age. This model makes it possible to calculate, at first, the chemical shrinkage related to Le Chatelier contraction, and then the self-desiccation shrinkage. A hydro-mechanical cellular problem is solved in a Representative Elementary Volume (REV) and the equivalent mechanical properties are deduced by applying the selfconsistent scheme with an iterative method. Then, the macroscopic autogenous shrinkage is computed from the local stresses average.

First of all, a brief review enounces the relations used for the calculation of the phase volumes during the cement hydration. Then, the resolution of the hydro-mechanical problem is presented. In the last part of this paper, calculation results are compared to experimental measurements.

THE MULTISCALE APPROACH

2.1

The microstructure evolution of the cement paste during hydration The degree of hydration i ξ of each clinker is calculated according to the Arrhenius law defined by its normalized affinity ( ) i A ξ and its characteristic time associated with the reaction X τ in the following way [START_REF] Taylor | Cement Chemistry[END_REF]:

( ) i i i d A dt ξ τ ξ = (1)
The volume of each residual cement phase i V can be calculated as [START_REF] Bernard | A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials[END_REF]:

0 ( ) (1 ( )) i i i V t V t ξ = - (2)
where 0 i V is the initial volume of clinker i. In the same way, the volume of the residual water is equal to:

0 0 0 ( ) ( ) . . ( ) i C w w w w w i w i i i i w i i n M V t V V t V V t n M ρ ξ ξ ρ = - = - (3)
where 0 w V is the initial volume of water, i w V the volume of consumed water to hydrate the cement phase i of molar mass i M , w M the molar mass of water and / w i n n the mole number of water consumed to hydrate one mole of cement phase of the apparent density C ρ . The volume of hydrated phases can be calculated according to the volume of elements which have reacted as for the following chemical reaction:

1 1 1 1 ... ... R R R R P P P P n n m m n V n V n V n V + + → + +
. And we can write: 0 ( ) ( ) 1,

P n P k k C k i l R l l l k n M V t V t k m n M ρ ξ ρ = = (4)

2.2

The equivalent hydro-mechanical behaviour law We consider a representative elementary (REV) volume V formed by a matrix m V and several types of inclusions i V , supposed to be spherical and with the same size. The choice of the matrix depends on the evolution of the cement hydration. The material is very fluid before the setting of the cement paste and its elastic modulus can be neglected [START_REF] De Schutter | Specific heat and thermal diffusivity of hardening concrete[END_REF]. At the beginning of the setting, the material becomes solid and its elastic modulus increases according to the age of the cement paste. The stiffness of the material starts to increase when there is percolation of the solid elements in the volume. Some numerical methods [START_REF] Torrenti | Mechanical threshold of cementitious materials at early age[END_REF][START_REF] Bentz | Percolation phases in a three-dimensional cement paste microstructure model[END_REF] and experimental methods [START_REF] Weiss | Experimental determination of the "Time-Zero". Early-age cracking in cementitious systems[END_REF] have been developed for the determination of the percolation threshold. In the model presented in this paper, we suppose a theoretical percolation defined by the self-consistent scheme. In fact, the percolation takes place when the volume fraction of the solid phase becomes higher than that of the liquid phase. So, before the setting of the cement paste, the matrix is formed by the capillary porosity (water and voids) and the solid phases are the inclusions. After the setting, we consider a matrix formed by the CSH phase in which all other phases are included as well as the capillary porosity. We define the cement paste as a biphasic medium composed of: a porous medium ( s V ) composed by the anhydrous and hydrous elements and the fraction of capillary pores ( ett V ) in which the ettringite can be formed with the crystallization pressure ( 57MPa π =

), and a medium ( p V ) formed by the capillary porosity with the capillary pressure c p . The following cellular problem is solved on the REV:

s p ett : in V in V in V i c C p σ ε σ δ σ πδ = = - = - (5)
Whereσ is the stress tensor, ε the strain tensor, i C the stiffness tensor of the phase i and δ the second-order identity tensor. After the setting, the desaturation of the capillary pores generates a capillary pressure c p . We have chosen to use an empirical law of the capillary pressure in relation to the liquid saturation (S) [START_REF] Baroghel-Bouny | Characterization and identification of equilibrium and transfer moisture properties for ordinary and high-performance cementitious materials[END_REF]:

(1 1/ ) ( ) ( 1)
m m c p S M S - = - (6)
where M and m are constant parameters depending on the material, such as for a cement rich in [START_REF] Kovler | Overview and future trends of shrinkage research[END_REF] C S (57.28 %) ( 37.5479

M M P a = , 2.1648 m =
for a cement paste with a water to cement ratio W/C = 0.34).

In this work, we are interested in the behaviour of cement-based materials at the very early age (from 0 to 48h). By applying the Levin's theorem for the homogenization of elastic heterogeneous media, the resolution of the cellular problem allows to deduce the equivalent macroscopic behaviour law on the macroscopic scale [START_REF] Dormieux | Micromechanical approach to the behavior of poroelastic materials[END_REF] which is defined by the relation between the average stresses V σ and the average strains V ε .

Before the setting, the chemical shrinkage of the cement paste is the main component of the autogenous strain. The model developed by Mounanga et al. [START_REF] Mounanga | Predicting Ca(OH) 2 content and chemical shrinkage of hydrating cement pastes using analytical approach[END_REF] is adopted to calculate the chemical shrinkage of the cement paste as:

( )

i i i t M ε ε ∆ = ∆ . Where i ε ∆ is the chemical shrinkage (in 3 / cement mm g
) produced for the hydration of 1g of the anhydrous phase i

( 3 C S , 2 C S , 3 C A , 4 C AF , 2
CSH and 6 3 3 2 C AS H ) and i M the mass fraction (in / cement g g ) of this phase hydrated at the time t.

At the setting, the material begins to gain stiffness and the capillary pressure starts to exert a tensile load on the mineral skeleton of the cement paste. By supposing that the volume is free to deform under a uniform pressure, we deduce the relation from the macroscopic strain by applying the self-consistent scheme for cement pastes (eq. 7) and the Mori-Tanaka model for mortars (eq. 8 inspired by the works of Pichler et al. [START_REF] Pichler | A multiscale micromechanics model for the autogenousshrinkage deformation of early-age cement-based materials[END_REF]).

hom 2 2 2 2 2 1 hom 2 1 1 ( (1 ) ) ( ( 1
) ) 3 cp c c c c p s p dE p f f p k f k f k k k k π π - = ---- - - - -- - ( 7
) 1 hom hom 1 hom hom 1 ( )/ cp m c p a cp m a c p m k f dE f dE k P k k k - = + - (8)
where hom cp k hom s k is the homogenized compressibility modulus of the cement paste, hom s k that of its solid phase and hom m k that of mortar. In the case of mortars, all aggregates are supposed to be spheres of the same diameter with a volume fraction a f and a compressibility modulus a k .

APPLICATIONS

Calculations have been made considering a cement whose Bogue's composition is: 62% of . The kinetic parameters of the cement hydration and the elastic modulus of each cement paste phase have been chosen from the literature review [START_REF] Bernard | A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials[END_REF][START_REF] Haecker | Modeling the linear elastic properties of portland cement paste[END_REF]. For each phase a minimum and a maximum value are given: min E and max E respectively. To take into account the pore pressure in the calculation of the mechanical behaviour law, two pore phases have been distinguished: a volume fraction of pores saturated with water and a volume fraction of pores saturated with air and water vapour. The following compressibility moduli for these phases have been retained: 2.2

w k GPa =
for the water pores and 0.141

g k G P a =
for the air pores [START_REF] Haecker | Modeling the linear elastic properties of portland cement paste[END_REF].

Comparison between numerical and measurement results

For the calculation of the Young modulus, we suggest to use the following algorithm based on a progressive increase in the moduli of phases starting from the beginning of the diffusion Calculated results obtained for cement pastes with W/C = 0.3 and W/C = 0.4 are in good agreement with experimental measurements (figure 2). Results obtained on the calculation of the chemical shrinkage and the autogenous shrinkage are closed to the experimental strain curves, measured by gravimetry, since the first water-cement contact up to 24h (figure 3). After 24h, the calculated results underestimate the experimental values of autogenous shrinkage. It can be explained by a real capillary pressure higher than that simulated by the model.

dif t t = up to 72 s t h = for which the macroscopic modulus is closed to max E : if dif t t ≤ : i i m i n E E = , then if dif s t t t < < : max min min ( )/ ( ) i i i i d i f E E E t t E = - - + and if s t t ≥ : max i i E E = .

Influence of the granular inclusion

In this part, we present simulation results on the early-age autogenous strain of mortars with a W/C ratio of 0.4. The Young modulus of the sand grains has been chosen equal to 60GPa and the Poisson's ratio equal to 0.28. The numerical results show that the increase of the sand to cement ratio (S/C) leads to an increase of the calculated Young modulus (figure 4). On figure 5, the ratio between the autogenous shrinkage (µm/m) of mortars on the autogenous shrinkage of the cement paste is plotted after setting (8h). The augmentation of the Young modulus as a function of the sand content is explained by the higher stiffness of the granular inclusions in comparison with the cement paste. The early-age deformations due to capillary pressure effects are therefore lower when the sand content increases.

CONCLUSION

In this work, we propose a multiscale approach for the calculation of the early-age autogenous shrinkage of cement-based materials. The cement paste components are taking into account in the calculation by using the chemical relations of the cement hydration [START_REF] Bernard | A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials[END_REF]. Before the setting of the cement paste, a chemical shrinkage occurs and has been computed from the chemical shrinkage of each cement components [START_REF] Mounanga | Predicting Ca(OH) 2 content and chemical shrinkage of hydrating cement pastes using analytical approach[END_REF]. After the setting of the cement paste, the material can be modelled by a porous medium formed by a solid phase and a capillary porosity. By solving a hydro-mechanical cellular problem in a representative elementary volume, taking into account the pore pressure, and by applying the self-consistent scheme, we have calculated the homogenized mechanical properties and the macroscopic strain of cement pastes and mortars. Results obtained by the multiscale model show that we can predict the advance of the evolution of the chemical and autogenous shrinkage and the elastic properties. Calculations of the autogenous shrinkage are relatively close to the experimental measurements. However, during the setting, we have observed a small difference between the experimental and numerical values for the Young modulus of cement pastes. That can be explained by a viscous behaviour of the cement paste during the setting time, which changes from a fluid behaviour to a solid state. The modelling of this viscous part of the material behaviour will be the next step of this research work.

Figure 1 :

 1 Figure 1: Confrontation of the calculated Young modulus and experimental measurements.

Figure 2 :

 2 Figure 2: The chemical shrinkage and the autogenous shrinkage of a cement paste with W/C=0.4 (IS: initial setting, FS: final setting).

Figure 3 :

 3 Figure 3 : Influence of the sand content S/C on the homogenized Young modulus.

Figure 4 :

 4 Figure 4 : Influence of the sand content S/C on the autogenous shrinkage.