Milena Tsvetkova
email: milenaic@uni-sofia.bg

HOW THE COMPUTER VINDICATES THE CULTURE OF READING

Keywords: new literacy studies, theories and models of reading, pyramid model, information literacy, reading literacy, media literacy, history of reading, history of writing, media evolution, mediamorfosis, evolution of reading

The computer screen is an emanation of the evolution and on its spiral of the linear language of writing: first appears the level language of the art, afterwards the cinema image with a real sequence of movements on the closed space of the screen,

INTRODUCTION

Each new form of culture -from the first culture of the spontaneous, live communication, written culture and audiovisual culture to the current phenomenon of virtual culture -is a generator of some form of sign transformation -not only in the cultural layer of civilization, but also in the individual cultural skills and characteristics. Audiovisual culture, for example, legitimizes itself through the technical novelties for maintaining and transmitting images and sounds (television, video, and multimedia). It provides a new medium for fixing and translating of cultural information, not only additional information, but also an alternative to its superiorverbal-written communication; the visible result of this metamorphosis can be seen in two major aspects:

Firstly: we can talk of "duplication of the cultural medium" -that is all cultural products have an audio-visual expression, the written and audio-visual texts exist as mutually translatable, relative equivalents of the "prototext" and Secondly: a pluralistic cultural medium appears and what we have in this medium is a "peaceful co-existence" of texts of different nature.

Audiovisual culture and the cultural practice have delineated the pluralistic tendencies of the cultural medium (feedback, eclectics, postmodernism) -which, according to many humanitarians have not produced anything particularly new but have resulted in a paralysis of the achievements of the written "veteran-cultural" and making-up or simply collating of the already discovered technologies and manners, and a certain "quoting" of the classical means by new technical ones.

The technically determined metamorphosis called computer culture, however, cannot be explained in one aspect, neither can it be reduced to just "coping" or "multiplying" because, up to this point, it theoretically comprises two phases:

CULTURE OF THE COMPUTER PAGE AND VIRTUAL CULTURE

The second phase is a precedent to the evolution of civilizations. Computer culture, as a qualitatively new type of medium for communication through digital texts, interacts effectively with the traditional types of live or "interpersonal", "written" and "audiovisual" cultures and forms itself on the basis of a synthesis between computers and video technology, by using completely new means of connection and channels for transmitting information, which eventually form "the infrastructure of the global space" (Prohorov 1989).

Which was the new aspect, which was brought to our cultural background by the technologically determined computer culture? Firstly, this is the technological discipline, which was introduced as a corrective of the discipline "on foot", which is characteristic of the cultures of the conveyer industry and the "immobile" cultures -one which is based on the concept of mobility (literal and mental).

Secondly -computer culture offers us a new type of communication, related to the opportunity for free gravitation in the information space (for example, an opportunity for reading an on-line newspaper from every point of the world and an open access for everyone) and for a fulfilling polilogue, providing multiple possibilities for feedback with the help of the screen.

Thirdly, computer culture enforced a new type of education and thinking:

Intertwining of the logical and the metaphorical, a synthesis of the conceptual and the visual, a visualization of the sense and materialization of feelings, a rehabilitation of the sense of the historical, an archeological passion for the opportunities for the "in-depth" and distance drilling by the computer "time-machine".

Maybe the most contradictory cultural metamorphosis of the end of the 20 th century has been legitimized as "the culture of the computer page", as a type of metascreen culture. It has appeared at the peak of the so called "cultural pyramid", which is built on the basis of the continuity between the live, written and audiovisual cultures.

Is there a regularity, which could account for this cultural continuity?

It was Sergei Eisenstein in his research called "Perspectives" who discovered the spiral return to a new step for world viewing.

He was referring to the invention of the civilization called "cinema", which rehabilitates the perspective and the images in movement.

Later on -another civilization creation -the television posed such a big threat to the balance of the cultural medium that a great number of media-ecological movements and trends were formed.

At that time the Director of the Congress library in Washington DC, Daniel Boorstin, said from the viewpoint of his eco-civilizational position: The antidote to the image imposed on us is in the books, in an escape from the stream of the trivial.

Books are a stable fortress of survival, they sift the experience and the experiences not in the short-term actuality of the happening but in the longevity and the correlation. If today we protect books, we will protect the future of civilization and keep it from the vicissitudes of fortune, and we guarantee the survival of the ideas of the great people.

And it was these ideas which stimulated people in their progress [START_REF] Прохоров | Культура грядущего тысячилетия[END_REF].

The discovery of Eisenstein is reinforced even today: "the civilization of image" is at a turning, after which begins the spiral "return" of the "civilization of books", of course at a new step. peak of the "cultural pyramid". By looking at the layers of the spiral of evolution on the cultural pyramid we can trace the mechanism, leading to the rehabilitation of practices of the written culture with their metamorphoses -"computer page", "digital text" and "screen reading" (see Fig. 1).

The discussion of the problem of rehabilitation of the practices of written cultures or the defense of books as, like Daniel Boorstin said -a stable fortress for survival and an antidote to the imposed on us image from the screen, necessitates firstly an operationalization and actualization of our concept of "consuming" the book or the concept "the culture of reading". Fig. 1. A regularity, according to which computers rehabilitate "books" and "reading" On an individual level the culture of reading reflects the perceptive capacity and the mental predisposition, which helps the typographic symbols, perceived by the retina, to create a spiritual sense.

And from an informational-cognitive viewpoint reading is a peculiar conceptual activity for forming the informational culture of people, conceived as a degree of perfection in the discovery, reception, storage, processing and organization of information, creation of new knowledge and its practical application. The appearance and constant actualization of the criteria for perfecting the culture of reading are socially and mentally determined by the following circumstances in the framework of written culture.

An exponentially developing exchange of social and scientific information, a necessity for overcoming space and time, a necessity of technology for reproducing the historical memory, opportunities for building indirect (mediated and generalized) past experience, as well as by the specifics of the intellectual efforts in the work with the book and most of all the psycho-physiological difficulties in perceiving the written text as a virtual image of reality.

The rehabilitation of the practices of written culture involves mostly rehabilitation of reading as an adequately disseminated cultural activity.

From an evolutional point of view the first question is which the catalyst is for the rise, and respectively the sunset of a given cultural practice.

The retrospective look back to the history of the media, the technical means and forms of communication shows that this is the conflict, the clash between old and new media. The situation of rehabilitation arises after the critical fight in the relationship "suppression-survival", in relation to two cultures (live and written, written and visual) and as a reflection of the tense coexistence of two different sign systems (verbal speech and alphabet, alphabet and audiovision).

In spite of this, there has always existed a time zone of co-existence, mutual reconciliation of the conflicting cultural antipodes.

The first such precedent was seen in the Ancient Greece in the 5 th century BC when the transition from live (ante-written) to written culture took place. What could be made was a certain analogy with the present cultural state in relation to the common to the two epochs conflict, but also a form of tolerance between opposite intellectual skills and biologically determined differences in the communication means: on the one side we have writing and on the other side -image, movement and sound.

The communicative practice both then and now involves observance and reading, reception and perception in its compiled version called hyperception.

A certain form of convergence can be noticed in the rise of the visual mass commuincativeness in the first decades of the XX century, when the European literary vanguard was formed -as a combination or union between the verbal and the visual.

In a similar way today, on the threshold of the global hypertextual communicativeness, the conflict between writing and the audiovision was resolved in the dimensions of the post-modernity.

However, do we have the basis to talk of regularity in the evolution of cultural practices?

If we go back to the rise of human civilization, we will find out that there is no extinct form of communication. The reason for the immortality of the informational phenomena is the unique natural and social homeostasis of the human brain and the informational medium, created by the humankind, which are mutually formed and transformed.

And because culture forms in a complex spiral of evolution, there are phases at one time of "falling asleep" and at other times ones of "waking-up" of the already used technical means and forms of informational exchange. This is the essence of the so-called Law for protection of informational means and technologies [START_REF] Subotin ; Subotin | Hypertext: New form of Written Communication[END_REF]. The mechanism of this law is something like the nostalgia for the "Golden century": throughout the whole history of the verbal, written, printed and even audiovisual culture the humankind has strived towards the abandoned forms of communication, the lost synthesis of the "sensory" technologies.

The strive towards resurrecting the completeness of the perceptions was registered back in the ancient mitograms (a non-linear form of writing, an ancestor of the hypertext according to the researchers of the primitive culture and mostly in the opinion of Liorua-Guron), through the manuscripts with miniatures to the contemporary illustrated books, from books and magazines with enclosed gramophone records or optical discs to the contemporary multimedia on-line editions, which use the most-successful rehabilitation of the ante-written means -image, movement and sound, provided by the television. This whole evolution is an evolution of looking for that informational technology, which will bring humans to their primary hypertext medium.

The spiral approach to the development of the cultural practices and the forms of exchange of information showed that the engine or the motivating drive for the development are the innovations in the technical means for communication, in the sphere of the informational technologies.

Each new cultural practice is a rehabilitation of an older one, which realizes itself at a higher technological level.

Apart from this, each new means, each new mediaform is a continuation of the previous one: the cinema appeared as a "synthetic sound-perceivable reading" (N.

Milev), screening -as a continuation of the novel, the videofilm -as a continuation of the movie, as a result of the inner individualization of the means for mass communication with the strive to "reiterate the personal contact with the book" (Vl.

Mihailov), the video cassette and the CD -as a mobile form of communication, continuing the static (theatre, cinema, television), just like the book appeared as a mobile form of texts on walls and obelisks.

The very presence of the computer became a motive for global transformations in the "cultural pyramid". Its popularization and acceleration as a self-transforming system led to the "mediamorphoses" in the net community.

What appeared as a result of the Web, which in practice reproduces itself, was a tribal community of its kind of citizens of the world, another type of a shared space, with its rules and laws, with its own culture. And this is namely the "computer culture" which is based on a new material medium -not writing but "screening", not on linear writing but on a system of level images, not on written speech, but on screen speech in the sense of a time stream of screen images, which has synchronized behaviors, sentences, animation, collages and vitrages.

The "computer culture" which showed also the spiral of cultural development is only the predecessor of another, much different one, which nowadays we conditionally mark as "virtual culture". Whatever the changes in the sphere of the new informational technologies might be, it is a matter of fact that each of them has triggered and will continue to trigger metamorphoses of the texts and their perception.

The computer screen is an emanation of the evolution and the metamorphoses on its spiral of the linear language of writing: first appears the level language of the art, afterwards the cinema image with a real sequence of movements on the closed space of the screen, after it the television, which brought at home "the page", but already animated, the video arises as a "live book", which is stacked at the library shelves, and at the end comes the computer display as a "computer page" and the PC as an open and "alive", dialogical book. This is the basis for determining the contemporary "culture of the computer page" as a metamorphosis of the book culture, a result of the evolution of the book or more precisely of its text.

The computer text has kept many of the specifics of the traditional written text: it contains written, fixed information, but before that it starts from the idea on a "manuscript", it can be destroyed, it can become personal property, moves from one version (hard) to another one (soft) and backwards (the written text is screened, and the screening can result in written text), needs identification, that is bibliographic data -address, localization and so on.

However, the main similarity between the written text and the e-text remains their common digital nature, which makes possible both the continuity and the metamorphosis.

The human language is digital by origin (and the structure of the brain is also digital), it transmits meanings, complex and abstract concepts. The consents of the communication is transmitted digitally, by digits, which don't have a semantic potential and are organized in an almost arbitrary system, for example, alphabet.

The alphabet letters are in reality signs of nothing: b-o-o-k is a combination of four letters, which are only a semantic agreement, an analogical way (as opposite to the digital) "means" one and the same object both to the writer and the reader.

However, the digital existence of the e-text does not make a reference to its object analogue. It is because the digital technologies in the computer communications pulled out the written text from the materiality and infiltrated it in the air of duality.

As Nicholas Negroponte insisted -the metamorphosis in the communication with the new media should begin from the difference between the atom and the "way of life". Although both forms of the text contain information, in the book version this information is disseminated in a material way and in the e-text -in a non-material, signal and digital.

While the traditional book gets to the reader on a long and fraught with hurdles physical road, the digital book is always here, never gets printed, does not come in circulation and does not run out of copies.

Hence the new characteristics of the digital text:  it is stored in an electronic database and is accessible in an on-line regime  it multiplies itself not only in copies but as identical to the original and is distributed in the form of CDs or floppies; it turned into a compulsory preliminary version of every written document  it released the existence of parallel editions, providing one and the same information. (in a written and digital format).

The Digital text increased in a mechanism not seen so far in the text evolution its informational capacities: digitalization provided compression of volume, acceleration of creation, optimization of distribution and searching.

The digital text offered in the form of the computer page new opportunities to its user: an opportunity for dialogue with the screen text, and in this case "dialogue" does not involve the "interaction" traditional for the natural sciences, but "interactivity", a spiral growth of the dialogue, which is now called polilogue (an expanded exchange of meanings and senses, in which every new author and new text enter), and its object is the "intertext", which raised to a qualitatively new stage on the spiral the "polyphony" of Mikhail Bakhtin.

Whereas contemporary civilization develops in parallel with technology, whatever the metamorphosis of the new media be, the computer will continue to exist as a main source of the "screen culture", as a main object -"a herald of future" (Abraham Moles) on the contemporary cultural terrain.

It came as an "extension" to the human functional power, together with all its preceding inventions but whereas in the past they were an instrument for increasing by ten times the intellectual power, now computers are the ones which surpass men.

It is because computers are not only "a technical means" but a phenomenon in the culture of sign systems: it introduced a new concept of the mediated function of the sign; the sign is no longer "signifying" of real objects but programming of the immaterial object.

The computer is not a mediator in the communication with traditional written or audiovisual text and creates principally a new synthetic text, which in addition to this is self-transforming, due to the programmed in it interactivity, with which it rehabilitates the dialogue with man, mediated by texts for deciphering.

After the rise of the new media (computerized, on-line media), the concept of "new" literacy came out. However, as it has been already mentioned, computer culture is not a new culture, but a new type of "synthetic culture" formed and co-existing with the traditional ones -live culture of communication, written and audiovisual cultures. It is based on the synthesis between computers and video technology, between written and audio-visual communication and being such it is not unattached, autonomous, but is sitting on the shoulders of the "veteran cultures", existing, together with them as the peak of the cultural pyramid.

We could take a similar look at the "new" type of literacy -the computer one. In the sphere of conventional ideas the phenomenon "computer" is often compared with the phenomenon "literacy", followed by book publishing, in which the intellectual efforts for receiving the common "computer literacy" leave the idea of comparability solely with receiving the "first type" of literacy in the written culture civilization.

The definition of computer literacy as "secondary" and the insistence on a new interpretation of literacy, free from old terms such as "reading", "writing, "arithmetic" are to a certain extent nonfunctional and historically unjustified.

WHAT IS CONTAINED WITHIN THE CONCEPT "LITERACY"?

This is the ability of people to acquire, process and use information, necessary for their fulfilling practical activity in society or "literacy" coincides with the level of "fundamental informational culture" in its pragmatic projection.

Literacy is not an antiquated term but a functional determinate of that which was called by the United Nations Secretary-General, Kofi Annan, "success in life": functional literacy, which is not only missing in the "informationally poor" countries (a term which not rightly covers countries lacking in education and countries with partial computerization), but also in the informationally developed communities, in which millions of adults are functionally and marginally illiterate.

And why do we say that each new interpretation of literacy is historically analogical and unjustified?

It is because literacy and the development of technical means follow the history of human development. In the primitive society, for example, the definition for "literacy" should cover the skill to "read" animal traces by imperceptible signs, knowledge and orientation in blood relationships, the degree of knowing, memorizing and a skill for telling the legends of the tribe. Nowadays the term "literacy" does not coincide in the least with reading and writing, which were enforced in the ancient times but involves evolved abilities, knowledge and skills acquired if not in university education, then at least in high school education. Of course if we are to follow this logic a computer engineer from the 21 st century would have looked functionally and practically illiterate if he had been dropped in the primitive age in all aspects, except for one -he will be able to tell myths and legends of the future.

Contemporary functional literacy cannot be divided from its historical determination: even nowadays people tell stories, read, write and watch materials, but on a much higher "technological" level. In other words, we cannot talk of a new typeautonomous, artificial literacy (even the artificial intellect will follow the functional connections of the "natural" human mind): the literacy, which is topical for the beginning of the 21 st century is a dialectical unity between language, written, audiovisual and computer literacy and consequently is neither "secondary" nor "new", but a new segment, a new determinate of literacy.

If we go back to the spiral of the cultural evolution, we will need to confess that "computer culture" rehabilitates at a higher technological level reading skills, which also involve the concept of "computer literacy". And the very concept of "literacy" has always been a "remarkable skill". In the ancient times if one had the skill to read they were definitely part of the circle of the "remarkable people". Saint Augustin, the intellectual of the 5 th century, mentions the uniqueness of his mentor Saint Ambrose, who apart from being the bishop of Milan, was the only one who could read non-verbally, without even moving his lips and because of this nonhuman skill earned himself the nickname "the smartest person in the world".

In the 19 th century literacy is gained by everybody who reads to be enlightened, to achieve the highest status in society for the reasons, which bulgarian writer Luiben Karavelov concisely and poetically generalizes: "Rich are the Clever Ones".

It seems to us as if nothing has changed in the requirements for literacy, prestige and remark-ability, when we have a closer look at the so topical for the beginning of 21 st century concepts of society of knowledge and economics of knowledge of Alvin Toffler, Lester Thurow, Daniel Bell, John Galbraith, Zygmunt Bauman, Jacques Delores, etc.

Generalizing and emblematic for all such theories is the argument provided by Lester Thurow in his research "Building of Welfare": The richest person in the world Bill Gates does not possess anything perceptible -neither land, nor gold, nor oil, nor factories, nor industrial processes nor armies. For the first time in the history the richest person in the world owns only knowledge (Thurow 1999).

A regularity of the 20 th century has been given in the following maxim: Reading is a method of acquiring knowledge and a cultural spending of the free time, used by people for the invention of the TV.

Actually all knowledge arises from books: the book is the "alpha and omega" (Stephen Zweig) of every social sphere, beginning of all knowledge and prime source of every science. And every technical system needs an intellectual engine, which to determine from the inside its external expansion.

Not every sort of knowledge today can be acquired by using alternative methods. If a person does not read there is no other way for him/her to receive the most recent and super specialized information, because such information cannot be achieved via television: television can expand and visualize cultural and scientific horizons, but cannot create them. The necessity for boosting and developing the culture of reading is neither a subjective concept nor an aim in itself. The contemporary "computer culture" as shown by the spiral of development of cultural practices is the foundation of the two traditional "live" and written cultures and can be developed only in their unbroken context. Breaking away from it means a threat of deformity to its own evolution. What we have is namely a "cultural pyramid", a whole massif, in which computer technologies are not only a superstructure but a new dimension in this massif -both to the foot and the peak.

If

The boosting of culture of reading needs to acquire a new dimension, a new sense: needs to be thought of as a care for the future, as literacy which is at the foundation of the culture of the new informational technologies. On the same grounds on which it was laid down in the foundations of the audio-visual culture: it was proved that the message of the written text is much more rich in meaning than the direct transmission of image and sound, that the images cannot replace the cognitive culture, the skills of the conceptual, discursive and abstract thinking and, on the contrary -the culture of images presupposes these skills. "A shot taken from an airplane would not mean anything to those who don't have at least some idea of archeology -argues Régis Debray from UNESCO. If we don't teach children to read, we won't teach them to see. If we value the conveying of messages more than the formation of the human mind, we will have the same effect as of "harnessing the horse at back of the cart" (Debray 1999).

CONCLUSIONS

The strategy of knowledge can be only one -there are no trends or retro-styles.

It has always been a successful one when it has involved traditional and new means for acquiring knowledge, when it has developed parallel spiritual-technical capacities.

Even today the cognitive culture triggers interest and access to the different sign realities -everyday, artistic, scientific, social realities, whereas the computer reality has its own place and time and should not be replacing any of them. In the world of knowledge of the 21 st century there is a place for both the virtual computer reality and the book, which will be existing as a source of different realities, as a polygraph product and an ergonomic interlocutor, as a source of fundamental knowledge and as grounds for written culture.

  no interest had been shown in the written information people would have lagged ten years behind and would have had only 30% of the newly acquired knowledge of the world and in 15 years would have run the risk of completely disqualifying themselves. If a person decides to use the whole wealth of computers and the Internet, he/she needs to read first a sufficient number of specialized and "navigational books". It is because, without applying the results of the current researches on the computer generation it is clear that only a person equipped with the culture of reading, only the qualified reader can become a qualified and competent user. The reading level determines to the highest extent the level of the informational development of people and influences the culture of acquiring the technical means for informational exchange.


Milena Tsvetkova
email: milenaic@uni-sofia.bg

THE IMPACT OF THE BOOK ON ASYMMETRIC CIVILIZATION

Keywords: literacy, reading, asymmetric information, book studies, asymmetry, reading habits, social separation, class distinction, literary reading

To what extend books and reading can be included in the project of the "asymmetrical civilization"? The point is, that the book by nature is politically active, because of the fact that along with many other functions the reforming

INTRODUCTION

"Book readers are optimists. However, do we have sound reasons to declare still that people should read books?" Those words were used at the opening of the Frankfurt's book fair 32 years ago (1974). Today I could begin the same way. The reason is that now we face once again the risk of wiping out books and reading as well. But I will say something else: to persist on defending the cause of books and book reading is only in the power of the winners, it is the cause of the successful and the lucky.

Even if there is only one reader left in the world, Life itself will call him for help.

A similar metaphor was used in the twice aired on the TV channel bTV * movie "Stream of consciousness" (from the TV series "The Outer Limits" -1997, aired on the 6 -th 2002 and on 23 -th march 2003). People live "plugged in" in the Information stream, created 50 years ago in order to allow everyone's access to the global network. In this apparently symmetrical society of working individuals with computer chips implanted in their brains, there is one that is "crippled" or more correctly "defective". Ryan, the one who creates the asymmetry in this world is the only one, who is surrounded by books, because he has no chip -on account of a trauma in his childhood. Everyone around him feels sorry for him because he is "struggling", because he is a remainder from the time when reading has bean a token of intelligence. Those with chips read * A private national Bulgarian television.

without their eyes directly from the Stream, and if one of them picks up one of Ryan's books he asks "How does it work?" Because all of the books in all the libraries are "poured" into the Stream at the time of its creation, the useless printed versions have bean destroyed in order to save space. On the other hand there were "dangerous" books, which were destroyed without being "honored" by digitalization. In one unfortunate moment, however, the Stream overloads, which causes "brain tsunami" in peoples' heads and one by one they begin to die, bombarded by all the data. In a way that is natural for us -by references in his familiar books, indexes and catalogs Ryan begins to search for the book, which contains the programming code for the Stream -in the deserted neighborhood of "Nothingness". There, in the ruins of the house of Jessie Koll, a bank manager and the smartest man in the world, who lived before the Stream, Ryan finds the "dangerous" book, which Koll forgot to return to the library, and which contains the schematics for the interruption of the Stream -and he shuts it down. Until civilization returns to normal, i.e. while the schools are being refilled with books, the hero of the story formulates the new principles of survival: "The only thing worse than burning books is not reading them."

CONCEPT THE "ASYMMETRICAL INFORMATION"

If today we can speak about a changing reality, which is far from the one in the movie but it also seams to be asymmetrical, how is it expressed? What can asymmetry mean in our civilization?

Let us take as initial concept the "asymmetrical information" phenomenon. The scientific interest towards it has been awarded the Nobel Prize for Economics three tomes -in 1996, 2001 and 2005. One of the Nobel Prize winners -Professor Joseph Stiglitz 1 explains the asymmetrical information thus: this is a situation of access to uneven, unequal amounts of information among two or more "players" and the winner is the one that is correctly informed, who knows more, better than the others, and the most important information for the moment. According to Stiglitz our society is under the power of "economics of information". According to this tendency the society restructures itself by the indicator "knowledge" and from an open and harmonious it becomes asymmetrical. The redistribution of power and influence in the social-economical environment is realized by inalienable resourceknowledge. Those who know much and have the necessary information gain a higher status than their "ignorant" colleagues and fellow-townsmen.

In other cases priority has the one, who has assured himself with the maximum amount of preliminary knowledge -when he knows what is happening before the others. Examples of the fatal outcome of the game for those, who don't have the informational superiority, can be derived not only from the pressing "asymmetrical war" with terrorism, but can be traced back to the victories of Attila (in the period 441-451 year against Byzantium and the Western Roman Empire), or even further back in time -to the "The Art of War" in Ancient China. The strategy of the commander of the Chi country (400 BC) for example is the possession of preliminary information: "If the educated ruler and the wise general defeat the enemy and their accomplishments exceed those of the ordinary man, the reason is in the preliminary knowledge." There is another rule -to have the right channels of information: "The preliminary information can not be gained from spirits, or from deities, analogies with past events or calculations. It has to be gained from people who are familiar with the state of the enemy." 2 Or in the current conditions, from the extensions of these people -written documents.

The contemporary consequences of the asymmetrical information can not be erased by someone`s capitulation. The reason is that they reflect on the whole civilization. And the battles are led on the "silent front" of education and literacy. Currently according to data from the statistical institute of UNESCO there are 771 million illiterate 3 people in the world, and only in Bulgaria there are 200 000 (according to "Mediana" -January 2005). And if we bear in mind that illiteracy now is defined as the inability to use reading in your line of work, although you received formal education. Even more, illiteracy now is considered a "slight mental retardation". In our country * for the first time illiteracy became the reason for unfitness for service in the army (with regulation № N-4 from 11 -th march 2005 for the military medical expertise of the army service in peaceful time). In the "medical standards" of the military the inability to read, write and speak in Bulgarian are included in chapter "nervous and psychological disorders", because they cause serious problems in the execution of orders. In addition to the actualization of the meaning of illiteracy in the 21. century UNESCO legitimized a definition for informational illiteracy: "Lack of skills abilities for critical perception, evaluation and usage of information in professional and private live." [START_REF]Information Literacy[END_REF] The new illiteracy 5 is not just not knowing anything, but: 1) knowing badly the things that everybody else knows; 2) not knowing what you should know; 3) not wanting to utilize the old and new forms of presentation of written information. And those are enough for new situations for asymmetry.

CONCEPT THE "ASYMMETRICAL CIVILIZATION"

To what extend, however, books and reading can be included in the project of the "asymmetrical civilization"? The point is, that the book by nature is politically active, because of the fact that along with many other functions the reforming function is inherent to the book. Often it has invisible, but definite role in the personal, public and global projects. In global aspect, for example, it turned out that reading will present the overall surprises. And this happened with the most impressive survey of the European Union (the grant political project of the old continent) about the "culture of reading", conducted in 2003 [START_REF] Gyaurov | Europeans and reading[END_REF] .

It reiterated an unbelievable asymmetry -the EU is divided into a reading majority in the North and a non-reading majority in the South. The northern * Bulgariatranslator` s note. countries (Sweden, Finland, UK) have more clearly expressed reading inclinations than the south ones (Greece, Spain, Portugal) and that is not because of higher incomes or cheaper books. It turns out that the reading resistance in the European South is routed in history. The countries that read most are those with protestant tradition, where liquidation of illiteracy of the population began the earliest -as a result of Reformation and Enlightenment.

The tragedy of the South and South-East countries (among which is Bulgaria) is, that liquidation of illiteracy began a hundred years later, and compared with Sweden (which liquidated in illiteracy in 18. century) began two hundred years later. And the reason is that in the south, neither the Catholic, nor the Orthodox Church was seriously threatened by the Reformation. The masses should read

The Bible? It would be politically incorrect.

If today we castigate ourselves in long lasting passive readers' mentality, we make a mistake. Simply for us -the peoples of the European South, it is harder to be readers. Before the EU, however, there lies a serious historical problem and it appears to be of an asymmetrical nature: instead of uniting, Europe is dividing.

The consecutive surprise was delivered in the beginning of last summer (June 15, 2005) by the marketing agency NOP World after it announced the results of its research of "readers` ratings" in 30 countries [START_REF]Uncovers Who's Tuning In, Logging On and Hitting the Books[END_REF] .

We face a new asymmetry and a new intrigue. The most reading country turned out to be India -the country with the biggest share in global illiteracy (34%) [START_REF]International Literacy Day[END_REF] . The lowest readers' ratings were registered in the USA (23 -th place), UK (26 -th place) and Japan (29 -th place). The question is how did the most developed countries manage to drop to the bottom of the chart for the time spent on reading? The answer is again in the field of asymmetry.

The people from the "reading three" -India, China and Thailand are politically motivated to say, that they read, because there now is the peak of interventions for liquidation of illiteracy. An Indian, who wishes to go to collage would answer the question how much time does he spend on reading with the maximum given answer. It is just because that both collage and reading are socially prestigious and represent his high self evaluation.

Exactly the opposite is valid for the West and the modern countries. Here you can't impress anybody with literacy. The man in the developed world hardly will put himself on airs with the time which he spends in routine reading of technical texts, reference books, textbooks and manuals. Hi will hardly calculate as specially spared time which he spent receiving information from the press, which he consumes silently all day long. The western citizen doesn't even count reading from the monitor, web-surfing which don't yet qualify as reading.

Subconsciously the modern man excludes anything mentioned above as "text noise", and about the question of reading he filters out only the time, which he spends on purpose for reading "prestigious genres", for books imposed on him by tradition or by bestsellers` charts. In other words, the foe of the rating of the traditionally reading nations, among which is Russia, is not at all a cause for worry. It is exactly the contrary. The downward movement in the charts of such surveys -on the quantity of reading, is in fact "rising" up to the level of the club of the chosen ones, where reading is not just courtesy, but it has cultural and economical cover.

Although Bulgaria is not included in this most recent research I think, that this tendency is valid for us too. The more "normal" country we become, the more we will consider books and reading as something routine and instrumental. If we report low levels of reading time and buying of books, this may grieve the statisticians, book publishers and book sellers, but as a whole it is not pessimistic.

The adult Bulgarian is busier and busier and it seams that he is more teased then happy when somebody asks him how much he reads, what he reads, when he reads and why he reads. The research of ASSA-M *9 , which had broad * Bulgarian private agency for research and analysis. -translator's note. response this year, showed in fact, that we may not want to read a lot of fiction books, but there is a rise in the target reading, reading out of necessity and reading for a career.

Shortly both we and the man from the West, now "use" books, wile in the undeveloped countries people are still learning to decipher them. And this is the latest paradox in the asymmetrical civilization. If we want to react to this new caprice of civilization in the most rational way, we have to forget several clichés and to admit several mistakes: about our vision of the future of the book, about the future of reading and about our fears about both.

First we have to admit, that about the worry we seam to be under some sort of autosuggestion. With refrains like "the end of the book", "the destruction of reading" and the "death of the reader", we press on our psychological space catastrophism, fatality, entropy and helplessness. It is true -the future has to be dangerous. But fears lower our sensitivity threshold, they cause rational blindness for the positive signals of the healing of society.

We have to admit secondly, that we created "book negativism" in the young people and thus we placed ourselves into a retrograde position. Some of the people who are engaged in the sphere of books probably look better in the luxury of despair, but in fact this is the luxury of another conflict between generations. Our moaning over the fate of the book is in a state of trench war against the generation which reads not necessarily paper books and not necessarily dictated by the "canon".

There has been a serious change in the perception of the book in the reading practices and the readers` profile.

If we don't want to find ourselves in the loosing illiterate side of our asymmetrical reality, we have to state that the future of the book already happened, but some of us hadn't reached it yet.

The book is leaving its new material "reincarnation", it's modifying, adapting to the new digital environment. In fact the electronic book is still just a book, which forms will never stop developing. The technical revolution changes neither the meaning, nor the mission of the "objects" of first necessity. The book, like the mason symbols the "angle" and the "compasses" today physically have technical analogs. But those analogs continue to respect the original form by just helping men to act, to own and to read better.

The wiser men already put an end to the requiems and dithyrambs about the fate of the books [START_REF] Darnton | The New Age of the Book[END_REF] . But still remains the curiosity about the word, with which it will be named, even if it is the expression "the next big thing in the exchange of ideas". It's more mature to say that the question "does the book have a future" is not highly convertible. When, for example, Astrid Lindgren was asked the same question she exclaimed: "And does bred have a future, does the rose have a future, does the lullaby have a future?" It would be more rational to concentrate over the question "what is the future of reading". It's painful and inconvenient for a lot of people in the outlining asymmetrical civilization. I will remind you the forecasts of two people with the biography of "committed world readers" -Julia Kristeva and Umberto Eco. According to Julia Kristeva [START_REF] Kristeva | In love with reading: Interview[END_REF] we already have two classes unevenly spread all over the planet -one of them, the minority, is reading and creates goods for the others, and the others -the dependent, hardly read and hardly see.

Umberto Eco also outlines our asymmetrical present, unbalanced and segmented into three sectors [START_REF] Eco | Eco's cybernetic library: Interview[END_REF] . In one of them is "the proletarian majority", like Orwell's prowls -the passive masses learning information only from television.

They either don't have access to the Network, or they do, but they don't know how to use it (without reading in Internet you are lost). In the second sector is the "lower middle-class" -user of the new media, but also a passive one (like an accountant). The minority in this asymmetrical triangle are "the game masters" the internal hackers of the city, as well as their rich employers. The similarity between them is the knowledge, gained by hard, selective and nonpublic reading -the knowledge that brings control [START_REF]the quick and the slow[END_REF] . I think that there is no need for much empirical evidence, that in "the society of the asymmetrical information" one of the players in "the game" knows more, better and earlier than the others because he reads more.

Because, what basically different is formed in us trough reading? Reading is a process of reduction of possibilities (this is the thesis of Frank Smith). The reason for this is that the more things we know the easier we can make a decision. The information from the "calmed" written exposition reduces in the maximum degree the doubts and uncertainty. For example, when children learn to read, it's difficult for them to distinguish between different letters. In a tense situation the more letters the child knows, the easier it can orient in the recognition of the given word.

Besides that the information is equal to the number of the alternatives, which have to be eliminated. If the one, who has to take the decision, can eliminate all possible answers except one, than the quantity of information is equivalent to the degree of uncertainty, which existed. Information diminishes the uncertainty trough the elimination of alternatives. But without understanding there can not be any reduction of alternatives. In this case, one of the most important features of reading as a skill is the presence of a "criteria".

The criteria is a term, which shows the quantity of information, which is necessary for the making of a particular decision. That's the reason why the more information the reader has, the less will be the volume of the so called criteria, which is necessary for the making of a decision or the perception of the text. A selection of the used criteria is made during the process of decision making. Every next "decision" depends on the previous ones and activates the analytical centers of the brain.

Reading is thinking, which is partly focused on the visual information on the list it is thinking, which is stimulated and led by written language. A huge advantage of reading over effective thinking in extreme and stress conditions is controlled, which it gives over the situations. Another good practical example gives again Umberto Eco. "There was a discussion about the last crash on Wall Street -says he -and most of all about why "the young stock lions" fell in the trap so foolishly. How was it possible for them not to know that there has been a similar crash, that the stock-market has its own dynamics, and a certain limit can not be surpassed? One of the answers was: but they don't read! Apparently they don't read. They didn't know the fact of "the black Thursday" on Wall Street in 1929. Those Yuppies -comments Umberto Eco -these sassy successful urban professionals, educate themselves vacantly, they have week memory and bad discipline of knowledge just because they don't read enough and the right things." [START_REF] Eco | The perfect bookstore[END_REF] Circumstantial evidence about the "guilt" of reading in the expansion of the asymmetrical reality can be found in every aspect of our "society of knowledge". One of the sides of every busyness, bargain, discussion, education knows more than the other and that is not necessarily the side of the power, the money or the higher stature. The dichotomy "informed -uninformed", "readnot read" multiplies the surprises and absurds.

For example an art critique, who doesn't know anything about visual perceptions; an intellectual, who clutches only to history and is ignorant to the last scientific ant technological achievements; a professor who knows less then his students about pressing issues in his field and so on. This is the wretchedness of the one who is convinced in his erudition a priori.

For the formulation of a core of people, who are always dissatisfied their erudition, of groups of highly educated and successful people, who have significant influence over the social, economical and political processes, we are convinced from a survey from the company for sociological research Roper ASW conducted in 2003. About 10% of the population of USA influence the opinion of the other 90%. This 10% consist of politician, journalists, business magnates, professors in universities, experts in different fields, leaders of big social organizations and so on. Roper ASW found out, that "the group that influences", prefers to get its information trough reading in Internet and not trough the mass media [START_REF]The net strengthens its influence[END_REF] . This sociological news gives us the opportunity to make the following conclusions. First, in the analytical field the two terms groups of influence and information can now be connected. Second, that the influential people restrain themselves from obtaining information trough the mass media.

Anyway Internet as a means of information and reading is a synonym of quickness, variety and a possibility to select.

We can search for foreign and local examples about how the status of the reader more and more merges with the status of the successful and the winning.

Or at last for his plans for successes. Let's remember the pre-election television clip of one of the potential winners of the elections for mayor of Sofia Milen Velchev from NDSV party * . With an open book in his hand and with a lot of books behind his back. The candidate suggested: "I know more then the others", or at least "I know how to know more than the others". We have a real example for a project of the type "how to get out of the bad side of asymmetry trough books". It's about practice "reading to get promotion" among the Mexican police officers, which was announced on BBC last spring (March 2005) [START_REF]Indians "world's biggest readers[END_REF] . In all the police departments in the Mexican capital there is an order: every employ must read at least one book a month, so he can hope for promotion. It's a fact that the level of crime in Mexico is higher than any other capitol, and the local police officers are accused not only of corruption, but of incompetence, illiteracy and laziness. According to the mayor whose idea was to issue the order, an educated employer of the low enforcement will be a better professional and a better person.

If we have to interfere resolutely in the orientation of the young Bulgarians toward "promotion", toward "win in the duel", toward "higher * A liberal political party in Bulgaria founded as a movement in 2001year.

income" or in general -toward the winning sector in the "society of asymmetrical information", it is necessary to create a new image of the book and reading and to make more adequate messages towards the modern people.

Something like: "Read, people -otherwise you are lost" (that was the motto of the Frankfurt's book fair). Or something simple like: Read for success in life! Books are for the leaders! Reading is for the champions! And so on.

It would be hard for us to deal with those, who will laugh at us: "There is no place for readers in the rotation of money!" That means there is no place for writers, poets, scientists and teachers, for doctors and engineers. Yes, but without them there is no rotation. The number of similar collisions -caused by the asymmetry in our everyday life will increase.

CONCLUSIONS

Not long ago came another proof of the asymmetrical reality. The new chess world champion, the Bulgarian Vesselin Topalov, has collided with people of a suspiciously uninformed type, some of those who, when they take a book, ask how it works. Their curiosity was sincere: "Do you use stimulants? Why there isn't doping control in chess?" Topalov answered, not without irony: "A doping for the brain has not yet been invented." That's right, champions keep their secrets. But we, if we wish trough wisest of sports to make an advertisement for reading, had better wait the end of mach between Topalov and the computer, in which the secret of the victory over the "chip" genius will be known to be "connected to books".

If the world has to stay the same, then readers are dangerous. But if we want more Bulgarian champions, there, where others have been comfortably situated, we need, as the teenagers say, lots of reading. I wish everyone a

  constructive day, worth to be read about! NOTES 1 Joseph E. Stiglitz was born in 1943, a professor in the economical faculty of the Columbian University in USA. He was chosen for professor of the Massachusetts' Institute of Technology (MIT) at the age of 26, but in condition that he starts wearing shoes and stops sleeping in the university. A chairman of the Committee of economical consultants of US president Bill Clinton and economical adviser of the president of Bulgaria Georgi Parvanov, vice-president of the World bank (1997 -1999). The author of "Globalization and its Discontent" (2002), "The roaring Nineties: a new history of World's most progressive decade" (2004) and others. In 2001 The Central Bank of Sweden awards him along with George A. Akerlof and Michael Spencer The Nobel Prizefor Economics for their "Analyses of markets with asymmetrical information". Their researches show, that practically the participants on the market don't have the same information, which excludes the possibility for just allocation and use of recourses. This fact changes radically the conclusions about the Balance theory. The asymmetry of information -a man applying for a job knows better the assets and liabilities of his employer than himself, the credited knows better than his creditor what are the perspectives of him paying back his loan, the manager knows better than the owner or the shareholders what is the real state of the company and so on -leads to an unavoidable market failure and to adverse selection, which imposes the intervention of the state for correcting the status quo. /www.library.ru/3/event/fact (28.11.2005); See also: Mexican policeman are charged to read "The little prince". In: Novinar, №56, 10.03.2005, p. 24.


Pierre Jehel
email: pierre.jehel@centralesupelec.fr

A MULTI-SCALE STOCHASTIC MODEL FOR CONCRETE IN UNIAXIAL CYCLIC LOADING WITH COUPLED MECHANISMS AT MESO-SCALE

Keywords: Concrete, multi-scale, stochastic vector random field, correlation, plasticity, damage

Concrete response at macro-scale results from numerous mechanisms at different scales. These latter cannot be all explicitly accounted for in numerical concrete models. In this paper, a multiscale stochastic model for predicting concrete response in compressive uniaxial cyclic loading is presented. Heterogeneous meso-structures are randomly generated; coupled plasticity-damage model represent local constitutive response. At macro-scale, a representative element can be recovered.

Introduction

This paper briefly presents the basic ingredients of a multi-scale stochastic model developed to represent the compressive cyclic response of a concrete specimen. Such a response is characterized by the following features (see Figure 1): a backbone curve (dashed line) that is a nonlinear strain hardening phase ( ) followed by a strain softening phase where strength degradation is observed; unloading-reloading cycles show that stiffness decreases while loading increases, hysteresis loops are generated. This typical response is observed at macro-scale and results from numerous mechanisms of different physical and chemical nature at many different scales. In concrete, there is a continuum of scales at which heterogeneities can be observed: at macro-scale, aggregates of different characteristic sizes are surrounded by a cement paste; at lower scales, the cement paste is in particular composed of water, voids, of the products of the complete or partial hydration of the clinker particles.

FIG. 1 -Strain-stress concrete experimental response in pseudo-static cyclic uniaxial compressive loading (adapted from [1]).

Two scales are explicitly considered in the model herein presented. At macro-scale -where the response of concrete specimen is observed as in Figure 1 -material is assumed to be homogeneous. At meso-scale, heterogeneities and uncertainties are explicitly represented. Response at meso-scale is not the same depending on which material the response corresponds to: an aggregate, the cement paste, a mix of aggregates and cement paste. At this meso-scale, the approach followed in the present work does not consist in explicitly generating a multi-phase medium with random distribution of aggregates of random geometry in a cement paste with known mechanical behavior for each phase. The path followed here consists in generating a random medium at each point of which the mechanical response 0  E  0.0027 obeys a prescribed behavior that has unknown parameters.

This prescribed behavior at meso-scale is assumed to represent what could be the response of an aggregate, of the cement paste, of a void or of any combination of these later three components of concrete. This behavior is presented in the next section and the set of unknown parameters is introduced. This set of parameters is modeled as correlated random fields over an area of concrete according to the method that is presented in section 3. Response at macros-scale is recovered according to the equations in section 4. Numerical applications are presented in section 5.

Behavior at meso-scale

Coupled damage-plasticity behavior is assumed at meso-scale. The model is developed with a set of internal variables that are the history of the material. The basic ingredients are as follows:

(1)

(2) (3)
Potential and criterion function are expressed with the stress at meso-scale , the damage and plastic deformations and , the damage compliance and the yield stress . The internal variables are and .

Then, we introduce the following damage-plasticity coupling relations: with , and

and the following equations can be derived within the framework of thermodynamics with internal variables (see e.g. [START_REF] Ibrahimbegovic | Nonlinear solid mechanics: theoretical formulations and finite element solution methods[END_REF] for the numerical aspects regarding this framework):

; ; and

(5)

Initially, previous to any damage, we set where is the elastic tensor.

FIG. 2 -1D behavior at meso-scale at two distinct positions and over a concrete area.

Model of the parameters heterogeneity and uncertainty

In a 1D setting, the model presented above is developed using 3 parameters: elastic modulus , yield stress and damage-plasticity ratio . Thereafter, we focus on a square material area and the spatial heterogeneity of these parameters over , along with their uncertain nature, has to be represented. Some correlation between the parameters is also expected. Suppose indeed that the material point of interest at meso-scale corresponds to an aggregate, then the elastic modulus is larger than at any other point, the yield stress is much larger too and there is no plasticity. Consequently, the 3 parameters , and should be correlated accordingly.

2-dimensional 3-variate homogeneous nonGaussian random vector fields are generated to model

✏ = ✏ d + ✏ p (✏, D, ✏ p ) = (✏ ✏ p ) 1 2 D ( ) = | | y  0 ✏ d ✏ p D y D ✏ p ˙ d + ˙ p = ˙ r ˙ = ˙ d (1 r) ˙ = ˙ p 0  r  1 ✏ d = D ˙ 0 ;  0 ; ˙ = 0 Ḋ = r ✏/ ✏p = (1 r) ✏ D = 1/C e C e 0 0 x 1 x 2 C e y r R = d ⇥ d R C e y r
these specific features at meso-scale. The method used is based on the so-called Spectral Representation Method with the following assumptions for material properties as introduced in [3]: (i) material properties possess quadrant symmetry, (ii) the cross-spectral density can be written as:

Where the correlation coefficients satisfy , and .

Then, considering three independent 2D homogeneous Gaussian random fields , , the homogeneous Gaussian vector field is calculated as:

(7)
where matrix is computed from the Cholesky decomposition . The Gaussian fields can then be translated to nonGaussian fields.

FIG. 3 -Yield stress field [MPa] generated over a unit area with two different correlation length:

[left] and [right].

Response at macro-scale

Macro-scale response is calculated assuming:

, and

Then, introducing the tangent moduli at both scales: and , it comes:

(9)

Both the stress and the tangent modulus at macro-scale are possibly random quantities because they are computed from a random meso-scale generated over material area .

Numerical application: Concrete uniaxial compressive cyclic response

The model developed in the 3 preceding sections is implemented in a computer program that can solve nonlinear problems. Material area is meshed by identical squares of size ; behavior law as presented in section 2 is assigned to the centroid of each of these squares. The random vector fields are generated with identical properties in both directions over ; all correlation coefficients are taken as equal to ; spectral density function is assumed to have Gaussian shape; log-normal distribution with mean 30 GPa and standard deviation 15 GPa is assumed for elastic modulus ; uniform distribution is assumed for both the yield stress and the damage-plasticity ratio with MPa and . The response of the material area in compressive loading obtained with this model is illustrated in Figure 4 for different Uniaxial compressive concrete responses are shown in figure 4. Top-left figure shows that the proposed model is capable of representing most of the salient features of concrete in uniaxial cyclic loading: nonlinear strain hardening, loss of stiffness as well as hysteresis observed in unloading-reloading cycles; the model is not capable of representing strength degradation (strain softening).

S(k) = S(k) 0 @ 1 ⇢ 12 ⇢ 13 ⇢ 12 1 ⇢ 23 ⇢ 13 ⇢ 23 1 1 A = S(k) s |⇢ 12 | < 1 |⇢ 13 | < 1 |⇢ 23 | < 1 g s (x) s = 1, 2, 3 f r (x) = r X s=1 h rs g s (x) h s = hh T 10 PIERRE JEHEL, GEORGE DEODATIS
At the end of the loading (E = 0.003), we can calculate the mean µ, standard deviation ν and coefficient of variation COV = ν/|µ|:

• Case 1: µ = -37.5 MPa, ν = 0.61 MPa, COV = 1.6%

• Case 2: µ = -37.5 MPa, ν = 1.84 MPa, COV = 4.9%

• Case 3: µ = -37.6 MPa, ν = 3.31 MPa, COV = 8.8% It can be observed that the mean response is not sensitive to the correlation length. In case 1, there is very little sensitivity of the system response to the correlation length. In this case, the full information available in the random field generated over a period is accounted for in the computation of the concrete response. Case

R = 1 ⇥ 1 b = 0.04 b = 0.17 E(X) = ✏(x) 8x 2 R ⌃(X) = h i(x) = 1 |R| Z R (x; X)dx ⌃ = D ef f E = D ✏ D ef f (X) = 1 |R| Z R D(x; X)dx R R = 1 ⇥ 1 64 ⇥ 64 x = 1/64 = 0.016 R ⇢ = 0.9 S(k) µ C e = ⌫ C e = C e

Conclusions and ongoing work

It is shown in Figure 4 that, for , a representative material area can be recovered in the sense that the response at macro-scale is almost independent of the realization of the meso-structure. Besides, for again, Figure 4 shows that the model is capable of representing salient features of concrete response in compressive uniaxial cyclic loading. Compared to the work presented in [START_REF] Jehel | On damping created by heterogeneous yielding in the numerical analysis of nonlinear reinforced concrete frame elements[END_REF], the model presented here can represent loss of stiffness. This comes from the fact that coupled damage and plasticity mechanisms have been introduced at meso-scale. Other methods to couple plasticity and damage at meso-scale, parametric analysis that further explores the potential of the model, investigation of the effects of the nonlinear translation of the pseudo spectral density function are among the points to be further investigated. Also, there is a need for experimental data from material scientists for identification purposes; the model presented here can show which data would be useful. 2 shows larger sensitivity (COV = 4.9% > 1.6%) and case 3 even more (COV = 8.8%). Nevertheless, this level of variability of the system response is much lesser than the level of variability in the parameters (COV E = 50%).

Conclusions

Figure 2 .

 2 Figure 2. Meso-structures generated over an area (x 1 , x2 ) ∈ [0, 1] 2 with different correlation lengths; [Left] Elastic modulus E [MPa]; [Right] Yield stress σ y [MPa]; [Top] b = 0.04; [Bottom] b = 0.17.

y r y 2

 2 FIG. 4 -[Top left], 1 realization of the meso-structure, uniaxial cyclic compressive loading. Mean response along with mean +/-standard deviation (dashed lines) for 200 realizations of the random meso-structure with [top right], [bottom left] and [bottom right].

bAFigure 3 .

 3 Figure 3. [Top left] Case 1, one realization of the meso-structure, uniaxial cyclic compressive loading; [Top right] Case 1; [Bottom left] Case 2; [Bottom right] Case 3. Statistical properties of the system response for all cases 1, 2 and 3 are computed with 200 realizations of the random meso-structure.

Acknowledgement

This research is supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme (proposal No. 275928).

Acknowledgement

This work is supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme (proposal No. 275928).