Catherine Audard

Kurt Almqvist

COSMOPOLITANISM Erik Wallrup

Margaret Ax

MULTICULTURALISM AND THE POLITICS OF RECOGNITION: THE CASE OF FRANCE 1

published or not. The documents may come

Multiculturalism and the politics of recognition: the case of France

The fairly recent opening of Western Europe in the last thirty years to North-South significant migratory fluxes, has clearly shown the deficiencies, or even the absence of, satisfactory immigration policies in the majority of European countries. A major political and social crisis is threatening, not least in France with the rise of the National Front, which gained 21% of the vote in the Presidential election last year, thanks to a campaign based on xenophobia and attacks on immigrants. These facts are well known. I would like to concentrate on conceptual questions and on the shortcomings of our democratic model. When we think about citizenship in this new social and cultural context, are the traditional notions of nationhood, Nation-State, and nationality still applicable? Especially, in the case of France, is the strongly assimilatory and universalistic Republican model justified? Don't we need to think differently in order to properly welcome and integrate populations who cannot or do not want to assimilate in the way previous waves of immigrants were able to? I will claim that immigration and its twin problem, integration, need different conceptual resources. We are confronted with a structural problem that questions our way of thinking, our social structures and our political values. This is no passing crisis due to a particular conjuncture. Immigrants are there to stay. They remain in the host country and have a deep influence on it. They bring with them distinctive social models, inherited, for instance, from colonial societies where stratification may be based not on social classes as in the 1 An earlier version of this essay has appeared in Cultural Identity and the Nation-State, C.Gould and P.Pasquino eds., Rowan and Littlefield, New York, 2001. classical Marxist model, but on ethnic identification. 2 This means, in particular, that immigration should be understood in collective terms. Thus abstract individualism and equality of the kind advocated by French Republicanism, and formulated first by Jean-Jacques Rousseau in On Social Contract, which were liberating for immigrants up to the Seventies because they tended on the whole to reject their original communities in the name of better lives, are no longer applicable to the new immigrant populations. As Charles Taylor has shown, assimilatory and "colour-blind" policies, based on anonymity and ignoring cultural attachments, have not had the desired impact because they do not include the recognition of historical disasters and of the humiliated and despised identities that ensued. 3 This demand for recognition has created a new normativity where notions of cultural identity, differentiation and recognition acquire a new positive value.

It is beyond the scope of this paper to examine the whole range of new conceptual challenges that will have to be met. I will limit myself to one question: what is the nature, and validity of arguments in favour of a "politics of recognition"? These arguments, in my view, are essentially moral arguments. They are not, contrary to what is usually maintained, based on the facts of cultural differentiation and they do not necessarily involve cultural relativism.

Following here Martha Nussbaum's argument in defence of universal values,4 I will argue that to meet the huge problems created by immigration and integration in a spirit of justice and pragmatism, we should rely not on a false toleration based on cultural relativism, but on a deeper understanding of moral individuality and of its needs, in the person of the immigrant as well as of the host citizen. We should look at the process as a two-way exchange. In the end, there is as much to be gained for the hosting party as for the migrant.

Integration or assimilation? Towards a new normativity.

Traditionally, the immigration process has met with two types of reactions. On the one hand, it may call for a logic of inclusion/exclusion, a logic of separation, where the immigrant population is contained and isolated, submitted to a kind of apartheid, even if a benevolent one. A separate list of rights and duties, distinct from those belonging to the dominant group, applies to them and prevents access to full nationality/citizenship. Roughly, this would be the case of Germany, before the major changes in the nationality laws voted in 2001, which have seen the move from jus sanguinis to jus soli in the access to nationality. On the other hand, there is a logic of majority/minority where progressively the minorities are called upon to dissolve and to disappear within the larger and more powerful dominant culture within two or three generations, thanks to its greater attractiveness for less well-off and underprivileged populations.

These two logics or discourses are contradicted by a new normativity, which has recently emerged. If we are to fight exclusion in the name of justice and equality, granting more rights, more security and respect to vulnerable populations, we should also abandon the very ambition of assimilation, of transforming them so that they become more "like us".

Equality does not mean uniformity. This is the major point. We have to learn to recognise differences as final or "incommensurable", to use Isaiah Berlin's expression. Public recognition of the importance of cultural identity is a moral requirement and it goes beyond the question of immigration. In the case of France, the movement equally concerns cultural minorities in the provinces: Corsica, Brittany, the Occitan lands, etc. But this seems impossible inasmuch as equality demands uniformity. In contrast, the demand for recognition is one based on differentiation.

In "Paix et proximité", Emmanuel Lévinas very lucidly describes the scope and nature of the intellectual revolution which is needed in order to think of differentiation as part of equality. He writes: "One has precisely to question the conception according to which, in the midst of human diversity, Ego can be reduced to a part of the Whole… whose unity is the cohesion of its members or of its global structure. One needs to ask… whether the otherness of the Other is not in fact absolute… whether peace, instead of being otherness absorbed or disappearing, would not, on the contrary, be some kind of brotherly closeness to the other." 5 This should lead to a reversal of our traditional view of toleration, which is based on disappearing differences and distinctions and on fusion between cultures and values.

The moral problem, which is at the basis of multicultural citizenship is then clearly formulated: how to create peace and solidarity within a fractured polis, between divided allegiances, fragmented identities, where daily fears of the otherness of the Other are obstacles in the quest for inclusion? This is a truly moral problem, not simply a political one.

No matter what social engineering arrangements, political institutions and funding may be provided, without the moral conviction that there is a duty to recognise and value the distinct cultural identity of the Other, the foreigner, the immigrant, the asylum seeker, immigration 5 Emmanuel Lévinas, Paix et proximité, Paris, 1996, p.165. policies will fail and civic peace will remain a distant dream. We have to understand, following Lévinas, that we are morally responsible for preserving these differences, as they are constitutive of our own global humanity. A failure to do so will dehumanise us further. This has been the horrifying lesson of the Shoah. The political meaning of Lévinas' reflection, when he talks about "fighting against annexing by the Essence" 6 is striking: we should aim at rethinking citizenship, equality and justice otherwise than on the basis of uniformity.

Let us now turn to the claims of multiculturalism and of the politics of recognition. Let us start with some clarifications.

'Multiculturalism' refers both to a state of affairs: the existence, in contemporary democratic and fairly "open" societies, of groups with fundamentally different cultures, some of them very much in a minority and very disadvantaged, and of competing sets of values within the one Nation-State; and to a social policy: a will to integrate these minority cultures and to recognise their distinct identities in an effort to make up for past discrimination in ways that go beyond mere toleration. 7 This policy is part of a broader liberal expectation: that, in the name of freedom, a democratic society should fully recognise the plurality of the conceptions of the Good that exist within it and not try to impose a single pattern of behaviour on its people, that the unity of the nation should not be bought at the expense of its heterogeneity.

Recognition of minority cultures, then, seems to go together with democratisation and the recognition of other minority categories based on sexual orientation, disabilities, etc. and, most importantly, with the recognition of women's rights. But, in fact, whether all these issues require the same arguments and strategies is highly questionable as it is unclear whether the terms 'groups' and 'cultures' can be aptly applied to women, gays, Blacks, Asians, etc.. What these sections of the population possibly have in common is their rejection as unfair of 'colour-blind' policies that pretend to treat everybody impartially in the abstract. This also signals the emergence of a new political normativity. It is not simply a question of new social trends or movements. It is the normative content, which is philosophically relevant. Here we have a positive awareness of ethnicity, of cultural differences, which did not exist in the past, and which is the result of failed assimilatory policies. One has to understand that this reversal of values, where it is what separates us, not what unites us, which is valuable, is the answer to centuries of discrimination and oppression in the name of unity; it tells us that separateness is reality. This is the common link between 6 Id., p.114. 7 See Charles Taylor in A.Gutmann ed., Multiculturalism, Princeton University Press 1994. otherwise extremely diverse movements, from the Civil Rights Movement in America or the "Black is beautiful" trend to the claims of British Muslims or French "beurs" and even feminist movements around the world. How to be equal and different?

The change in paradigm is considerable if we compare it to the Marxist conception of social justice in terms of a world proletariat where all differences are transcended by class membership. The claims for social justice, for redistribution, are now formulated in a new idiom where public recognition of cultural identities, protection for cultural rights are important. One major writer in this field, Nancy Fraser, writes: "Many actors appear to be moving away from a socialist political imaginary, in which the central problem of justice is redistribution, to a "post-socialist" political imaginary, in which the central problem of justice is recognition." 8 Already these policies have resulted in major changes in Europe and America in political representation, in membership of political parties and trade unions, in education programmes (affirmative action and positive discrimination programmes, the improved teaching of regional languages, the emphasis on "ethnicising" schools curriculum, etc) and in civil society: new family laws, new cultural rights, 9 etc. Since the beginning of the Nineties, the question of cultural, religious or other minorities has progressively been introduced in debates and legislation at the United Nations, UNESCO, the Council of Europe, in particular, claims concerning minority languages (1992).

The present debate on a European Union Charter of fundamental rights opposes those who would like to include in the list not only economic and social rights, but also new cultural rights, to the advocates of an undifferentiated European citizenship. Thus a "multicultural citizenship" 10 should express this new normativity and be based on arguments that go beyond a mere "right to difference".

Two main arguments provide the basis for these new claims: an epistemic and a moral one.

Let us start with the epistemic argument, based on the limits of reason. The twin myths of an integrated human being as well as that of a unified humanity have collapsed with the illusions of the Enlightenment and positivist philosophy. Mankind and its beliefs will not be 8 Nancy Fraser, Justice Interruptus, London, Routledge, 1997, p.2. See in particular chapter 1 "From Redistribution to Recognition". See also N.Fraser and A.Honneth, Redistribution or Recognition? A philosophical exchange, London, Verso, 1998. 9 P.Meyer-Bisch, Les droits culturels, Projet de declaration, Fribourg, Editions Universitaires, 1997. 10 Will Kymlicka Multicultural Citizenship, Oxford, Clarendon Press, 1995 and (ed.) The Rights of Minority Cultures, Oxford, OUP, 1995. progressively unified under the banner of science and rationality. This was already heralded in Max Weber 's 1917-1919 Vocation Lectures: "The ultimate possible attitudes towards life are irreconcilable and hence their struggle can never be brought to a final conclusion." 11 For Weber, this thesis was based on the divide between facts and values, and the contrast between the natural and social sciences. Human sciences deal with value judgements, which are highly individual and non-rational decisions. They should shy away from any attempt at explaining them and remain as far as possible neutral with respect to these decisions. The conflict that will inevitably result from these "free" choices lead to "the fracture of reason" and to the impossibility of any rational evaluation of values. Isaiah Berlin, in the same vein, but with less pathos, talked of the "incommensurability of values". 12 "The central assumption in the Western tradition, (with the exception of Hume, of course), was that problems of value were in principle soluble, and soluble with finality. Whether imperfect human beings could implement the solution is another question, a question, which did not affect the rationality of the universe. This is the keystone of the classical arch, which, after Herder, began to crumble." 13 Accepting the limits of rationality calls for a different basis for toleration of differences. Instead of hoping to reach eventually agreement and unity, we have to limit our ambitions to peaceful coexistence and to the recognition that what divides us is definitive and constitutive of our humanity. To be rational means to accept that the other may differ from me and still be reasonable.

The moral argument in favour of a new conceptualisation of the values of citizenship is based on the needs of moral individuality, not on the value of difference as such. If cultural identity has become a source of valid social, economic and political claims, it is because it is closely connected with moral identity. In Sources of the Self, Charles Taylor has brilliantly argued that inter-subjective identifications, those that involve "significant others" play a non causal, heuristic role in the moral construction of the Self. The construction of a person's identity and of the sense she has of her own worth, of what she owes herself, is linked with the recognition that she receives from members of the wider community for the values she shares and promotes. "A person or a group of people can suffer real damage, real distortion, if the people or society around them mirror back to them a confining or demeaning or 11 « Politics as Vocation » and « Science as Vocation » in From Max Weber : Essays in Sociology, ed ; and translated, and with an introduction by H.H. Gerth and C.Wright Mills (New York, OUP, 1948).

12 Isaiah Berlin, The Crooked Timber of Humanity, Princeton University Press, 1998. 13 I.Berlin, Herder and the Enlightenment, in Vico and Herder, Two Studies in the History of Ideas, London, Hogarth Press, 1976, p.206-7. contemptible picture of themselves." 14 My discovering my own identity does not mean that I work it out in isolation, but that I negotiate it through dialogue, partly internal, with others.

But for that recognition to be effective, "we are asked to recognise the unique identity of this individual or group, their distinctness from everyone else. The idea is that it is this distinctness that has been ignored, glossed over, assimilated to a dominant or majority identity." 15 This is a complex argument that mixes psychology, psychoanalysis, sociology and metaphysics. The historical and cultural characteristics that differentiate individuals and that have been bracketed in the French Republican conception of citizenship, are not peripheral, they are, according to Taylor and I would not follow him completely here, constitutive of the person, in the sense that they are not external conditions or circumstances, but elements that make the Self what it is. Thus, the individual is necessarily dependent for her selfconsciousness on the social contexts that recognise or dismiss the values that define her. To be a Christian or a Muslim is not simply a personal life choice. It implies supporting and maintaining a community where these values can be expressed and publicly shared. It is both a personal and collective identity. The separation between the public and the "private" spheres is in this sense irrelevant. This, however, is the basis for the French concept of citizenship: the separation, for instance, between Church and the State meaning that any public recognition of cultural and religious differences is illegal.

Presented in this way, however, the moral argument is probably not very convincing.

It merely reminds us of the social nature of our personal commitments and of our dependency on the wider context for the definition of our own identity. It gets more interesting when it redefines what makes a culture. A culture is made up of historical narratives, of traditions and forms of life, of beliefs, but all these are unified around ends, values and norms, that individuals share, protect and without which they could not define themselves, possess an identity. The communitarian discourse does not simply say that cultural diversity is a good we should protect because it allows for the socialisation process, but it goes further and maintains that without any attachment to values, we cease to be properly humans or rather fail to be humanised. Moral identity is only possible through the continued existence of respected traditions to which individuals can relate in a meaningful way and personal identity grows on top of that. "Selfhood and the good, or in another way, selfhood and morality, turn out to be 14 Charles Taylor, Multiculturalism and the Politics of Recognition, Princeton University Press, 1994, p.25 and 34.. 15 Id., p.38. inextricably intertwined themes." 16 The significance of the cultural context is that it allows for the regeneration of identification and recognition processes without which the Self is atomised or reified, looses any sense of self worth and dignity. To identify with devalued cultures is not only psychologically harmful; it is morally demeaning and destructive. We could invoke a Wittgensteinian argument here. Other language users mediate the relation to the Self through language games that cannot be "private", and that call for interpretations and understandings. To devalue or to destroy that language and the linguistic community that uses it, destroys the possibility for self-recognition, self-understanding and for developing the selfconfidence and self-respect that will make of us full cooperative members of society.

The experience of dehumanisation and self-hatred that has been described in cases of persecution or genocides, is exemplary here, when constantly, the alien, the Other are designated as scapegoats, as responsible for the ills, the pollution, the degradation of the community. The mental as well as physical spaces of the whole community are invaded and poisoned by this denial of the humanity of the other.

Justice and the Demand for Recognition

Should we then be scared by the demand for recognition? This demand is certainly unsettling as it opposes our more traditional conception of justice as impartiality.

It seems, first, to contradict the universalism conveyed in the idea of equal treatment for all, which on the face of it would seem to mean uniform treatment, no differences. It claims, in fact, that the very singularity, the uniqueness of a group, a culture or an individual, deserves respect and the protection of specific rights. Taylor is right to understand this quest as a result of modernity and of the loss of given identities, as part of the "ethics of authenticity". Even if we don't completely agree with him, we can see where this movement deviates from the traditional understanding of justice as equal respect. Respect is not enough, it is impersonal and abstract whereas historical and cultural situations are at stake: slavery, colonisation, discrimination, second-class citizenship, etc. But the difficulty now is how to make a distinction between identity politics and their dreadful corollaries: segregation, apartheid, ghettoisation, etc., on the one hand, and politics of recognition on the other. This is the main point. We must provide an argument that gives us a definite answer: the quest for recognition is not about separation and exclusion, it is not the mirror image of the sufferings and rejections that have been endured by cultural and ethnic minorities. If not, it will simply answer past injustices with new injustices and be animated by revenge.

The second difficulty is that the demand for recognition seems, at first, to be motivated not by justice, but by resentment and vengeance for past ills. It is seemingly not about justice, but retribution. Not only is its aim to preserve a reality which may well not be universally recognisable, whose values cannot be universally shared, but the justification for these values, this reality, is usually in the past, in dramas, exclusions, persecutions that have been aimed at specific groups. Differentialist ideology even thinks it possible to replace old inequalities with new ones: positive discrimination will allow students from minority groups to catch up and to access the best universities, in the name of redress, not merit, excluding by the same token more deserving students.

Last, the demand for recognition seems to oppose justice as it insists on the separation, the fragmentation between human groups instead of trying to welcome them into a "common human world" (Hannah Arendt). What is most important now for each of us is not what she can share with others, but what provides a specific narrative for identifying with a group, a history, a tradition, a culture, all unique and particular.

How should we answer these three objections? First, I would say that the quest for justice includes, besides its other dimensions, the demand for recognition. If recognition without impartiality is unjust, impartiality without recognition is equally unjust. I would add that a democratic and inclusive conception of justice, one that is non-hierarchical, should understand this demand for recognition instead of shying away from it and to favour an abstract universalism that has proved to be an equally unjust way of rejecting and segregating unfit minorities. Now, fighting against an abstract universality in the name of differentiation does not at all mean that we should renounce justice as the impartial treatment of persons and groups.

Here, I would like to recall the British philosopher Henry Sidgwick and his analysis of impartiality: "It cannot be just for A to adopt towards B a conduct that would be wrong if B adopted it towards A for the unique reason that they are two different individuals and without any difference existing, between the nature and the situation of these two individuals, that could be invoked as a reasonable motive for treating them differently." 17 In other words, justice is a complex issue that requires a similar treatment of similar cases, unless a justification for treating them differently is presented. Justice requires a justification process; it is not defined solely by sameness. The two dimensions of sameness and difference are inseparable and demand for recognition is a demand for impartial treatment that takes justified distinctions into account. Thus, the Rawlsian concept of justice as fairness is relevant here: fairness meaning the rejection of unjustified inequalities, but not of justified ones, as the second principle of justice shows. 18 It is obvious that impartiality is not enough and that justice has to take into account certain specificities of the historical, social and cultural facts that have fashioned claims and demands for retribution and redress.

One example here, might be the case of Francophone Canada and its desire to survive as a "distinct society" in an Anglophone continent. "Québec has passed a number of laws in the field of language. One regulates who can send their children to English-language schools (not francophones or immigrants); another requires that businesses with more than fifty employees be run in French; a third outlaws commercial signage in any language other than French. In other words, restrictions have been placed on Quebeckers by their (provincial) government in the name of their collective goal of survival, which in other Canadian communities might easily be disallowed by virtue of the Constitution, the Canadian Charter of Rights. Was this variation acceptable or not? The Supreme Court of Canada did strike down one of these provisions, the one on commercial signage. But the signage provisions are still in force in Québec because of a provision of the Charter that allows (provincial) legislatures to override judgements of the Court for a restricted period. Eventually the Meech constitutional amendment proposed to recognize Québec as a "distinct society", allowing a different interpretation of the constitution." 19 The demand for justice, in that specific historical and linguistic context, cannot be for simple abstract impartiality and equality of treatment. To abstractly treat similar cases in a similar way without taking into account the "historical" baggage of the peoples concerned would mean a negation of past wrongs and sufferings, of real threats to survival and to identities which are central to peoples' lives. Not to protect the French language or to blindly apply bilingual policies in Québec would be an injustice and deprive the population of a central right to identity and dignity.

As usual, abstraction is a way of avoiding complex conflicts, but it ends up leading to more injustices, favouring those who are already in a strong majority position: in this case, Anglophone Canadians. Positive discrimination, in such a case, is not simply a question of redress or retribution; it is a matter of survival and as such, justified. As I previously 18 John Rawls, A Theory of Justice, Harvard, 2 nd ed., 1999. 19 C. Taylor,Multiculturalism, mentioned, the question is one of determining what are reasonably justified exceptions to the principle of justice as impartiality. Is the demand for survival when a distinct society is threatened with extinction such a "good" reason? Another example would be the history of desegregation and the full access to their constitutional civil rights for the Black population in America. When one studies the history of desegregation, one is struck by the way in which inclusion and full citizenship have progressed more rapidly when the "colour-blind" attitude to equality (abstract, non-historical, neutral) has been abandoned in favour of positive recognition of the reality of differences and objective disadvantages. During the second half of the XXth century, the Supreme Court has oscillated between two views of the constitutional principle of equality of rights; on the one hand equality is linked to the status of a group, on the other hand it can only be conceived of as an individual right. For instance, thirty years ago, it was clear that Black schoolchildren, as a group, have a right not to be systematically excluded from schools attended by white schoolchildren. But recently, a majority in the Supreme Court has reverted to a different view where equality is a formal, not a real right and cultural and social aspects of equality are left aside in favour of the legal aspects. Now, fairness demands that we recognise that claims are never individual. One is never equal alone, but always in relation to one or more individuals. Undifferentiated citizenship would hide this social and cultural dimension and treat race, ethnicity, gender, etc. as if they were non-relevant factors, to be either ignored or kept "private".

Multicultural citizenship and the French context

I will now turn to the obstacles met by the idea of "multicultural" or "differentiated" citizenship in the French context.

Immigration has, over two centuries of colonialism and wars of independence produced a multi-ethnic state in France in a distinctive sense; this situation should not be confused with the American or Canadian cases. 20 France is a country whose borders were still changing at the turn of the century and which, all through the second half of the 19th century, had been integrating new populations, each with different languages, Italian dialects in the case of the Duchies of Savoy and Provence, German in the case of Alsace and Lorraine, and so on; a country which was integrating Polish and Italian miners before World War I, Jewish Eastern and Central European refugees between the wars, over one million French colonists and, after 1962, their Muslim partisans during the war in Algeria, the harkis, and 20 See, for useful comparisons, Will Kymlicka, Multicultural Citizenship, Oxford, OUP, 1995. which contains roughly three million immigrants without full citizenship living on its territory at the moment. It is said that one French citizen in four has one foreign grandparent. And still France does not see itself as a multicultural, multi-ethnic society in the way in which the United States and Canada see themselves and in which Britain has recently began to acknowledge itself. Why is that?

One main obstacle encountered to the formation of a modern Nation-State in France has been, as can be expected, the diversity of regional origins. Another obstacle has been the conflict between the Catholic Church and the emergent secular State from the time of the French Revolution and, in one way or another, ever since. In keeping with a long tradition of conflicts with the French "Gallic" monarchy, which would take too long to explain here, the Church has seen itself, with varying intensity, as the instrument of the unification of society around strictly Catholic values, of the creation of a'Jerusalem terrestre' and, consequently, as the only source of legitimate political power. Thus, the creation of a secular Sate has meant from the start a constant struggle against an alternative source of unity and legitimacy.

Therefore, especially during its beginnings at the time of the Third Republic, but still now if to a lesser degree, to be 'neutral' has meant for the French Republic a strong identification with its non-Catholic, non-religious denomination. In order to counteract the social and political influence of the Church, it has become, in a sense, its mirror image, and secularism can be read as a kind of 'secular faith' (foi laïque is Ferdinand Buisson's expression), which could explain, but not excuse, its strong anti-Muslim stance as part of its anti-religious ideology.

In that light, France appears to be significantly backwards and illiberal. This may be seen in the recent conflictual events surrounding the wearing of the hidjab (Islamic scarf) in State schools by young Muslim girls. First, this has been prohibited in the name of the neutrality of the State schools system (la laïcité). It has subsequently been authorized, but reluctantly and only to be banned again. The rulings of the Conseil d'Etat have been so carefully phrased that there seems to be no firm official view, leaving the local Boards of Governors and Schools administration responsible for giving or refusing the authorisation and thus creating confusions and uncertainties. Many young Muslim girls, at the present moment, are still excluded from schools and there is no alternative religious schooling system available for them. 21 What happened was that a limited incident, in a few secondary schools was transformed into a national issue because it touched on the very sense of what it is to be French, on the basis of national identity. 22 Multiculturalism, from the French point of view, is equivalent to the abandonment of the central tenets of the Republican egalitarian and assimilatory tradition that is so central to French identity, as we shall see later. The main question, then, is to see whether this tradition is illiberal by definition or if, as I shall try to show, there is room within it for change. One could give at least three different readings of the incident: it can be read

(1) as a conflict between a tolerant State and an illiberal religious minority, seen as "fundamentalist": this was the reading of those, in France, who advocated the interdiction of wearing of the scarf in the name of the emancipation of women from illiberal Islamic laws;

(2) as a conflict between an illiberal State and legitimate Muslim ways of life: this would be the favoured culturalist reading, based on cultural and moral contextualism; 23 (3) as a conflict between two illiberal cultures: this would be the reading of the liberal critique of the French Republican assimilationist policy. 24 In a sombre verdict, Fahrad Khosrokhavar writes: "In the name of the universal, the Republican ideology is in fact excluding the disadvantaged minorities." 25 The French model, then, appears to have failed the people all the more blatantly for having promised so much, perhaps too much. My view is that this is possibly a temporary failure and that the possibilities for moving on and becoming more welcoming to minorities have not all been completely exhausted.

I will now turn to some explanations, keeping in mind that to interpret what occurred as mere anti-Islamic prejudice and racism is not satisfactory.

One explanation of the specific problems raised by cultural diversity in France lies in the fact that, as a nation, -and here it is very similar to America -modern France is the result of a political project, the formation of a community based not on 'blood' or descent or on residence, but on citizenship as a reflective commitment: 'the nation as a community of for a detailed account of the events and their political significance. See also Tariq Modood, "Ethnic Difference and Racial Equality" in D.Millband ed. Reinventing the Left, Polity Press, 1994. 22 Similar conflicts erupted across Europe at the same time, but nowhere did they create difficulties and opposition on the same scale. In Britain, for instance, the importance of integrating young Muslim girls has been seen as paramount by most local Education Authorities and one pragmatic answer was to allow the hidjab as long as it had the school uniform's colours. This is not to say that there are no difficulties, but they do not carry the same political and ideological weight. 23 See Iris Marion Young, Justice and the Politics of Difference, Princeton University Press, 1990. 24 See Tariq Modood, op.cit. 25 F.Khoroskhavar, "L'universel abstrait, le politique et la construction de l'islamisme comme forme d'altérité", in M.Wieviorka ed., Une société fragmentée: Le multiculturalisme en débat, Paris, La Découverte, 1996. citizens '. 26 This emancipation project has been articulated most strongly by the French Revolution, but it has deeper roots, which I cannot explore here. What was most hated in the old regime, in the remains of the feudal system, around 1789, were the many particular interpersonal bonds between people, the particular so-called rights and obligations which, on the one hand, constituted the fabric of an organic society and of solidarity, but, on the other hand, were symbols of oppression and injustice. In fighting these traditional bonds, the language of equal rights and abstract universalism led to the ideal of the République une et universelle, an ideal which is still very central to French identity. To be or to become French was not simply to enter a particular ethnic, linguistic group or nation, but to become an actor in a wider drama, that of an emancipation process whose goal it was to lead eventually to a federation of democratic and peaceful nations, to universal reconciliation, to the dissolution of all particularities and differentiations, seen as sources of conflicts, to the recognition of a kind of universal brotherhood or world citizenship. The French Revolution had had the privilege of being the prime mover in this process by freeing the people from their particular roots and bonds and by 'recreating' them as the abstract bearers of rights: no more a Breton or an Auvergnat, a Jew or a Protestant, but a French citizen with equal rights and dignity. To be French, therefore, carried with it special responsibilities, very similar to those carried by the American notion of citizenship, those of enlightening the rest of the world as to the benefits of free and equal citizenship, beyond all differences of race, ethnic origins, language and religion. France had invented the notion of the 'civic nation' and, as such, constituted one particular instance of the 'universal Republic'.

In the creation of the civic nation, the State has had the primordial role. In France, nation building derives from the State, by contrast with the more usual move from the existence of a nation towards its recognition as an independent State. The State had a mission, that of creating a new type of human being, the Citizen in Rousseauist terms, by contrast with the Sujet 27 . No longer a particular individual, devoted to particular pursuits, he or she becomes a citizen devoted to the public good. But at the same stroke, he becomes a Frenchman, no longer an Alsatian, a Breton or a Provençal, attached to parochial communities. It is this confusion between selfish interests and particular identities, which was to sow the seeds of unease in the face of diversity. But this was the price to pay in order to foster a new sense of national unity. As Dominique Schnapper, among others, has shown in her book on French citizenship, this ambition has been successful. Far from being a disincarnate basis for membership in the new Nation-State, citizenship has a content, derived from a proper 'grand narrative' based on the French Revolution and the Declaration of Human Rights. It uniquely combines a political dimension, the allegiance to democratic ideals, with the very powerful attraction to a national tradition and a community of which one can be proud. This is shown in the emphasis in the school' curriculum on history as a particularly important subject matter. One learns how to become French through the study of history and literature; the great writers and figures of the past provide models both for how to think and write, and for membership of the French nation. This explains the emphasis on general knowledge, 'culture générale', rather than on personal experience and questioning, because the latter would be likely to lead to diversity, heterogeneity, anarchy perhaps, in any case to a challenge to the forces of unification. It says a lot about the ideology of emancipation according to the Republic that the Founding Fathers of the school system, the most famous of whom was Jules Ferry, should be disciples of the authoritarian Auguste Comte, not of the liberal John Stuart Mill! 28 This authoritarian tendency can lead to seeing the Republic as a totalitarian entity, the enemy of individual freedom and development. But this judgment should be qualified. Citizenship has been and still is a successful political instrument for integration in spite of its strong ideological content. To paraphrase Simone de Beauvoir, one is not born French, one becomes French. The birth of a democratic community and allegiance to it are made possible by a seemingly totalitarian ideology, where the individual seems to be crushed, when, in fact, it is his local parochial attachments that are dismissed.

The question, then, is this: can these attitudes change in view of the present new social conditions and can there be an allegiance based on a new recognition of these parochial attachments, in the sense indicated by Charles Taylor and 'the politics of recognition'? In my view, the notion of the civic nation, mentioned earlier, provides the pivot that not only explains the rejection of multiculturalism, but could also provide the ethical element for a recognition of the claims of diversity. 29 The very concept of a 'civic nation' is, in theory, the opposite of the concept of nationalism, but in reality it is still not completely free from it, as we have just seen. Because of its intrinsically artificial character and the fragility that goes with it, a different form of nationalism had to be invented. Doubts about French identity come 28 See Blandine Kriegel, "Liberté de conscience et citoyenneté" in F.Castro ed. L'identité française, Paris, Editions Tierce, 1985, p.84, and the reference book on the question by Claude Nicolet L'idée républicaine en France, Paris, Gallimard, 1982. 29 See Yael Tamir, Liberal Nationalism,Princeton University Press, 1993. As I will show later, my position would be close to that expressed by Yael Tamir when she says that "the non-normative content of the nation allows the development and the flourishing of numerous normative, sub-national communities of identification". In other words, the "civic nation" does not necessarily have to be homogeneous and assimilationist. See Tamir,90. from what is in principle the voluntary character of the national link, the fact that it supposes values and choices on the part of citizens, and not only reiteration and simple facts, as in the case of the German tradition based on jus sanguinis, where the ascription of citizenship is based only on descent. 30 Let us consider, first, the exact meaning of the 'civic nation', of the Republic as a community of citizens, united and integrated in spite of their different cultural origins. By contrast with the ethnic nation, the political project of the civic nation does not take political homogeneity to coincide with similar cultural origins: it is not 'given' as a kind of natural phenomenon, a second nature, as it were, but is the result of a voluntary and conscious allegiance. But this does not mean that the political superstructure is superimposed or, so to speak, forced upon a divided, fragmented civil society. The nation is not given as such by the past, by culture or by tradition, but is created at any given time by the tacit adhesion of the citizen to its political institutions and to its core values: the nation, as Ernest Renan famously said, is 'a daily plebiscite'. This is the best definition of the Republic as a voluntary political creation. It is neither given nor imposed, but is the result of an endlessly renewed social compact. But such an abstract ideal needs a very firm cultural basis to allow the durability of the nation.

There lies the deep, long-standing paradox of a universal political project, whose embodiment in the French State is necessarily particular; (the same paradox was encountered in the communist project, that of an international movement with national embodiments). To create modern social ties as strong as traditional commonality, the French nation had to become a sort of brotherhood and to implement a new common culture that would change the minds, the emotions and the allegiances of its people and this new culture, because of its fragility, could not tolerate diversity. Consequently, cultural pluralism has been, from the start, deeply threatening for such a project. This is why, if France is effectively a multi-ethnic society, it cannot take the risk of becoming a multicultural society.

Maintaining a balance between universality and particularity is or could be one of the merits of this model as long as universality is attributed only to the political institutions of the state and not to the cultural tradition within which they have emerged. But such a challenge is 30 France and Germany differ from Britain and the States in the sense that citizenship is ascribed to children of citizens, following jus sanguinis. But they differ between them in that French law automatically transforms second-generation immigrants into French citizens, incorporating some elements of jus soli or place of birth and residency; it is even the most common way to become French. Changing the law to bar certain categories of immigrants from becoming French would then make it impossible for children of French citizens to become French! See Brubaker,chapters 4 and 7. extremely difficult to meet. My point here, more modestly, is to say that at least there exists a possibility of using this ambiguity to open up another vision of the "civic nation", a polycentric one within which differentiated sub-national communities could flourish.

Secondly, the ideal of the civic nation is perhaps not as explicitly modelled on the past, on the organicist view of the Athenian City-State, as it seemed at first sight. Indeed, the historical reality is much more complex. Henry Michel, in 1901, views Republican democracy as "the city of autonomous consciences" and recognises the primacy of freedom of conscience. 31 Jules Ferry, the father of the public school system in France, insisted that the Republic stop where "conscience starts". The République has been influenced by liberals who evolved and became Republicans after the 1830s and the Monarchie de Juillet 32 . There has always been, within the Republican movement, a more liberal trend that has been influential in the field of education. There is not there just one single path. In politics as in educational policy, Republicans were divided between 'religious' sectarian hard-liners, willing to enforce a Republican catechism, and, on the other hand, more moderate defenders of freedom of conscience, like Célestin Bouglé or Ferdinand Buisson. 33 . For them, Condorcet, not Rousseau was the reference in their rejection of any kind of 'political religion'. It would be very interesting, of course, to draw a comparison between Mill's views on the need for a 'religion' to overcome the critical phase society was in, and, at the same time, the Republican view on laïcité, even if circumstances were extremely different in the two countries.

The conception of the free citizen of the République does not simply refer to a reflective and idealised freedom of thought, whereby the free use of reason leads to Truth, as the doctrine of laïcité would have it, but it incorporates another set of very different and more liberal views where the right to believe and to worship whatever you want in private is essential. The consequences are very different for the understanding of the civic virtues: commitment to Truth, as illustrated by the Dreyfus Affair, is constitutive of the former, but a certain relativism and a commitment to toleration of others and to the protection of a private sphere is essential for more liberal Republicans.

But the two versions share, in the end, a similar goal: autonomy and the self-respect that goes with it, in other words the moral standing implied by the possession of political power and the exercise of basic liberties and rights. I have tried, then, to show that the civic 31 Henry Michel, in Nicolet, op.cit., p.483. 32 See Lucien Jaume's recent book, L'individu effacé, Paris, Fayard, 1997, for a comprehensive history of the French liberals. See also Sudhir Hazareesingh, From Subject to Citizen, Princeton, Princeton University Press, 1998, 38, "Nineteenth-century Republicanism was already divided between revolutionists, radicals and opportunists". 33 Célestin Bouglé, Pour la liberté de conscience, Paris, 1906et Ferdinand Buisson, La foi laïque, Paris, 1912.. nation implies a range of freedoms necessary for a reflective allegiance to its political institutions which cannot be limited to positive freedom, the so-called 'freedom to', but which recognise the primacy of freedom of conscience and hence, the inevitability of diversity and individuality. The policy of laïcisation in the schools, the administration, etc., has not only aimed at assimilating the various cultural components of the larger society, but also at providing the necessary protections for such a central form of freedom, even if it has not always been successful. The protection of freedom of conscience is the entry to a French version of multiculturalism and that is where the argument should be most successful.

The root of the problem in the French context, lies, as we have seen, in the ambiguities in the conception of the Nation-State as well as in the religious conflicts, not in diversity as such. Therefore, the major imperative seems to me to be to change the meaning of citizenship: should it serve only the need of the State to control and assimilate the people or does it benefit the people as such? Has it as one of its central aims the defence of the individual's rights to security and fulfilment? This is the major ambiguity.

For instance, in the conflict between Republicans and 'differentialists' in France, concerning the issue of the 'hidjab, it is typical that no space has been available for voicing liberal arguments based on respect for a valuable minority culture and its significance for the development of the individual, such arguments being immediately dubbed 'individualistic' or 'multiculturalist'. The debate centres instead on the unity of the nation and its possible split into many ethnic groups or on the dangers of religious fundamentalism, and it invariably bypasses the individual's needs for recognition and moral development through cultural, religious, ethnic memberships. The truth of the matter is that the centralized State feels threatened by minority cultures and seeks to enforce their allegiance and their assimilation into the dominant culture in order for the nation to survive. What is at stake is the making of the French nation, of a French citizenry and, therefore, the nationalistic purposes of assimilation and the formation of 'good citizens' tend to override simple toleration and basic respect for individual rights. Against that, we have to show that recognition of diversity is a moral need that springs from the very nature of moral identity and the self and that this has to be acknowledged in a new and richer concept of citizenship.

We therefore have to re-examine the nature of individuality in our conception of citizenship.

The point that I want to make to conclude is that this reinterpretation of the civic nation as furnishing the individual with a rich context for his or her moral development provides the best argument by which to oppose a Jacobine conception of citizenship and its refusal of the value of cultural diversity. The claims of diversity should be met because they can be seen as giving a firmer foundation to the citizens' commitments and allegiance to democratic values.

Here we have an answer to one of the most powerful critiques of liberalism from the Republican point of view: namely, that liberal democracies are weakened by their individualistic basis, as shown by the lack of participation and commitment of their citizens.

A feature of liberal democracies is their appeal to the good of the individual as a basis for legitimacy and as an alternative to coercion, and, consequently, their vulnerability when faced not only with conflicts, but with the simple task of surviving the lack of individual commitment and participation in democratic politics. In other words, it is the individualistic dimension of democratic authority, which Pettit and Hamlin have aptly referred to as 'the principle of individual relevance', 34 that makes it so vulnerable and, sometimes, indefensible. This is the principle that brings moral individuality into the justification and stabilisation process of democratic institutions and practices in contrast to the appeal to authority, tradition or sheer coercion. What kind of citizens, then, should the members of the political association be to secure its survival, if no coercion is to be exerted, beyond that of the law? Should they not be some kind of angels? What is the source of their commitment to democratic institutions, especially when, as Rousseau said, the general will may quite often go against their particular wills and their particular interests?

Obviously the answers will differ according to the degree and kind of liberalism we are discussing. My argument runs as follows. The obvious vulnerability of democracies to individual preferences noted by Republicans can be overcome if these 'preferences' are not mere whims, but real moral commitments. Then, the recognition of diversity as a basis for moral development will strengthen allegiance to democratic institutions. Multicultural citizenship, in contrast with mono-cultural citizenship, is valuable both for the individual, for the flourishing of her moral individuality and the securing of her self-respect and dignity, and for the Republic as it strengthens the individual's attachment to democratic values at a time when no one conception of the good can any longer unite the nation.

Conclusion

The failure, for the moment, of both the Republican tradition and the liberal conception of justice to generate policies congenial to cultural diversity should not be seen as final. If we look at the historical process that leads from the Declaration of the Rights of Man and the Citizen, in 1789, through the 1848 Revolution in France, to the recognition of the economic and social rights of the worker in the 1948 Universal Declaration, there is no reason why new rights should not be added to the list, allowing for new social and historical conditions to be taken into account. Rights being both the condition and the result of political 'empowerment', we cannot expect that the process will be struggle-free. A first stage before new rights are identified and enacted is that of the socio-economical struggle. The quest for inclusion is, first, the search for better living conditions; this is where attachments and commitments to democracy are first created and where new bonds are forged. Integration through citizenship has been a powerful vector of social mobility and modernization in the case of France. In that sense, previous rights, to employment, education, culture, knowledge, can be given a new meaning and might open the way to the fulfilment of the needs of moral individuality.

For the time being, French legislation has been unable to recognize the need for the protection of minority cultures and the usefulness of such rights to strengthen the attachment of minorities to the Republic. But things are changing and the new government seems seriously committed to some kind of "devolution" in the case of Corsica and of the decentralisation of State power. But, even if multicultural citizenship were to become a reality in France, we should insist that group-differentiated rights should always be seen as rights of the individual; they should be conducive to integration in the long run and not a source of division and hostility. This is why the process cannot be hastened and existing rights should be used to their whole potential, while the argument of the needs of moral individuality presented here should be emphasised, rather than the differentialist claims as such.

Catherine Audard

Department of Philosophy

London School of Economics

D.Schnapper, The Relation to the Other, Paris, Gallimard, 1998, p.226: "Societies resulting from decolonisation maintain, even after independence, the social structures and representations inherited from the past."

Charles Taylor, Multiculturalism and the Politics of Recognition, Princeton, 1992.

Martha C.Nussbaum, Women and Human Development, Cambridge, CUP, 2000. See her criticism of cultural relativism in chapter 1, In Defense of Universal Values.

See, among others, A.E.Galeotti "Citizenship and Equality: The Place for Toleration" in Political Theory 21, n°4 (1993): 585-605, N.C.Moruzzi "A Problem with Headscarves" in Political Theory

22, n°4 (1994):653-672

Dominique Schnapper, La communauté des citoyens, Paris, Gallimard, 1994.


Sergio Andrés
email: sergio.ardila9@correo.uis.edu.co

Ardila Parra

Octavio Andrés González-Estrada

Jabid Quiroga

Damage Assessment of Spinal Bones Due to Prostate Cancer

Keywords: bone damage, bone segmentation, spinal, metastasis, FEA

The present research proposes a methodology to determine the strength of a spinal bone in patients who suffer from prostate cancer using diagnostic imaging, with the purpose of verifying if metastasis has occurred, and critical conditions have been reached. Advanced numerical methods allow the modelling of anisotropic materials for different applications in biomedical engineering. The computed tomography images (CAT) provide the information to create a 3D model of the bone, in this case, the lumbar vertebra L5. Using segmentation software, it is possible to identify the mechanical properties of the materials that form the bone and define anisotropic conditions. The 3D anisotropic model is evaluated using finite element analysis (FEA), considering the appropriate boundary conditions and its respective material properties, and compared with the reference case of a healthy bone in an initial stage to assess the damage. Indicators based on the changes in stiffness of the vertebra could provide evidence of the need for chirurgical intervention.

Introduction

Personalized medicine is one of the greatest challenges of engineering, once tools have been developed to investigate the complexity of biological systems. Medical imaging (MI), e.g. Computerized Axial Tomography (CAT) and Magnetic Resonance Imaging (MRI), are important since they represent a clear basis to promote the development of personalized medicine, based on the profile of the individual and not on the disease [START_REF] Layton | Examination of subchondral bone architecture in experimental osteoarthritis by microscopic computed axial tomography[END_REF], [START_REF] Avrahami | Early MR Demonstration of Spinal Metastases in Patients with Normal Radiographs and CT and Radionuclide Bone Scans[END_REF]. With MI, we can develop patient-specific models that allow realistic numerical simulations to obtain more information relative to the patient [START_REF] Schievano | Percutaneous Pulmonary Valve Implantation Based on Rapid Prototyping of Right Ventricular Outflow Tract and Pulmonary Trunk from MR Data[END_REF]- [START_REF] Soriano | Evaluación basada en el método del gradiente de las propiedades elásticas de tejidos humanos in vivo[END_REF]. These patient-specific models can be used for the mechanical characterization of the bone structure and to estimate the damage in scenarios such as, for example, implants, osteoporosis or bone loss by metastasis [START_REF] Vanel | MRI of bone metastases[END_REF], decreasing the risk of critical events for the patient, and allowing to schedule treatments or surgical interventions that seek to improve the quality of life of the patient.

As primary tumours are diagnosed earlier, the detection of metastasis becomes more important and more difficult [START_REF] Karr | Prostate Cancer in the United States and Japan[END_REF]. Clinically, even in the presence of known spinal metastases, more than 1/3 of the patients did not have back pain [START_REF] Schaberg | A Profile of Metastatic Carcinoma of the Spine[END_REF]. The principal cause of death is due to the spread of cancer to other sites. Patients with advanced breast and prostate cancers almost always develop bone metastases [START_REF] Mundy | Metastasis to bone: Causes, consequences and therapeutic opportunities[END_REF]. Current measurement techniques for bone metastases are not accurate and can be very expensive. Reports using bone scintigraphy (BS) show sensitives ranging between 62% and 89% [START_REF] Daldrup-Link | Whole-Body MR Imaging for Detection of Bone Metastases in Children and Young Adults[END_REF], however, recent research shows accuracy less than 50% [START_REF] Lecouvet | Magnetic resonance imaging of the axial skeleton for detecting bone metastases in patients with high-risk prostate cancer: Diagnostic and cost-effectiveness and comparison with current detection strategies[END_REF]. Magnetic resonance imaging (MRI) is the most accurate technique to detect bone metastases, sensitive has been evaluated around 90% [START_REF] Avrahami | Early MR Demonstration of Spinal Metastases in Patients with Normal Radiographs and CT and Radionuclide Bone Scans[END_REF], [START_REF] Vanel | MRI of bone metastases[END_REF], [START_REF] Lecouvet | Magnetic resonance imaging of the axial skeleton for detecting bone metastases in patients with high-risk prostate cancer: Diagnostic and cost-effectiveness and comparison with current detection strategies[END_REF]. Nevertheless, authors suggest the use of BS on the assumption that MRI would be costly, consumes a lot of time and would be clinically involved [START_REF] Schirrmeister | Early detection and accurate description of extent of metastatic bone disease in breast cancer with fluoride ion and positron emission tomography[END_REF].

Three-dimensional models can provide a lot of useful information that helps clinicians to determinate the state of a bone or even an organ [START_REF] Soriano | Evaluación basada en el método del gradiente de las propiedades elásticas de tejidos humanos in vivo[END_REF]. In the case of metastasis to vertebrae, based on stacks of sagittal, coronal and axial slices from a CAT, it is possible to obtain a 3D model of the bone structures using segmentation tools [START_REF] Schievano | Percutaneous Pulmonary Valve Implantation Based on Rapid Prototyping of Right Ventricular Outflow Tract and Pulmonary Trunk from MR Data[END_REF], [START_REF] Pham | Computer modeling and intraoperative navigation in maxillofacial surgery[END_REF]. Advances in software and hardware have made feasible to manipulate such data on personal computers [START_REF] Halazonetis | From 2-dimensional cephalograms to 3-dimensional computed tomography scans[END_REF]. Then, numerical methods can be used to detect changes in the bone and evaluate structural integrity [START_REF] Valencia | Desarrollo de una prótesis de rodilla para amputaciones transfemorales usando herramientas computacionales[END_REF], [START_REF] Lee | Finite element modeling of the contact interface between trans-tibial residual limb and prosthetic socket[END_REF]. This methodology allows finding structural changes in the vertebrae after the diagnosis of prostate cancer. These models would provide information to assess the risk of collapse of the vertebrae, which would contribute to anticipate the use of treatments that reduce the risk of suffering invalidating complications caused by fractures.

In this work, we use the segmentation software Mimics© to process the CAT image and generate the 3D model of a vertebra L5 affected by metastasis. Anisotropic material properties associated to the bone are extracted from the CAT data [START_REF] Rho | Relations of mechanical properties to density and CT numbers in human bone[END_REF]. Then, a finite element analysis (FEA) was performed with the software Ansys© to verify the mechanical response of the bone structure. The 3D finite element model can represent the irregular geometry and inhomogeneity of this tissue [START_REF] Keyak | Automated three-dimensional finite element modelling of bone: a new method[END_REF]. Physiological biomarkers are proposed to evaluate the risk of collapse of the vertebra as metastasis progresses.

Methods

Computed axial tomography images are used to build a 3D model, the stack of images collected are based on grey scale information (Hounsfield units). Two CATs of the L5 vertebra of a patient are analysed, corresponding to year 2009, with the healthy vertebra, and to year 2014, when the patient had developed, by metastasis, a lytic lesion. The segmentation is done for CAT images with a slice thickness of 2.50 mm and a slice increment of 2.00 mm. The CAT data is imported into Mimics software, where geometrical details are defined and, then, meshed in 3-Matic to generate volumetric mesh, Fig. 1. The maximum triangle edge length used is 1 mm, and flip threshold angle is 15. The volumetric mesh is imported into Mimics to map anisotropic properties. The relationship between the Hounsfield value 𝐻𝑈 and the material apparent density 𝜌 𝑎𝑝𝑝 is assumed linear [START_REF] Rho | Relations of mechanical properties to density and CT numbers in human bone[END_REF], the empirical expression reads:

𝜌 𝑎𝑝𝑝 = 1.22 • 𝐻𝑈 + 47 [𝑔/𝑐𝑚 3 ]. (1)
An empirical expression is selected to assign an average Young modulus 𝐸 to each element, relating apparent density with elasticity modulus. Validation of different expressions was studied in previous literature [START_REF] Schileo | Subject-specific finite element models can accurately predict strain levels in long bones[END_REF]. The relation used in this work reads:

𝐸 = 0.63 • 𝜌 𝑎𝑝𝑝 1.35 [𝑀𝑃𝑎]. (2)
The resulting volumetric and surface meshes are imported into Ansys to define the finite element model, where boundary conditions were incorporated based on the load real conditions generated by typical human body movements. The boundary conditions used in the FEA have been determined from [START_REF] Goel | A Combined Finite Element and Optimization Investigation of Lumbar Spine Mechanics With and Without Muscles[END_REF]. Lifting was the exercise taken as a reference to evaluate the different loads acting on the lumbar L5. A total of 5 loads, forces and moments, were used. One force, 𝐹 = [20; 1378; 405]𝑁, and one moment, 𝑀 = [6,4; -0, 05; -1,3]𝑁. 𝑚, due to the interaction with the intervertebral disc of a ligamentous motion segment and the other three forces related to muscles, 𝐹 12 = 84,85 𝑁, 𝐹 34 = 123 𝑁, as shown in Fig. 2. A static analysis is performed considering a fixed support in the lower zone of the bone. In structural health monitoring (SHM), a common indicator to assess damage is to evaluate changes in the eigenvalues and eigenvectors of the structure [START_REF] Sánchez Acevedo | Metodología para la detección de fallas en una estructura entramada metálica empleando las técnicas de análisis modal y PSO[END_REF]. We propose to extract information from the stiffness matrix, trying to define biomarkers for bone damage.

Results

To determine changes on the mechanical properties of the vertebra, we extracted the stiffness matrix of the domain generated with the mapped non-homogeneous properties. The sparse matrices are compared in terms of their eigenvalues and L2-norms. We evaluated the six largest eigenvalues for the two models and compare their percent difference, Table 1. We observe percent differences up to 13,43% for the second eigenvalue. The L2-norm for the CAT from 2009 was 5.08E+04 and for 2014 was 4.68E+04, for a percent difference of 7,92%. To verify changes in geometry and occurrence of metastasis, stress and strain fields were analysed. Different test points (Figs. 3,4) were evaluated in both models to find possible stress concentrators that could arise because of segmentation errors or because of bone degradation due to metastasis. Also, density decrease because part of a normal ageing process, after age 35, mass bone losing will be between 0,3% to 0,5% per year [START_REF] Tobin | Bone density changes in normal men: a 4-19 year longitudinal study[END_REF]. Regarding this, there is a zone were density could have decreased dramatically, as shows Table 2, on the second point tested a stress variation of 159% was found, which could be associated with a change in geometry due to mass bone loss or a degradation of mineral bone density. Figs. 3 and4 show changes in strain distribution between the two vertebrae, where the second test point, highlighted in red, is located where stress increases. This zone is called spinous process, and agrees with the clinical assessment for metastasis in that area. This is not an area where metastasis commonly begins, metastatic lesions had been found mostly in the vertebral frontal zone (body) [START_REF] Suzuki | Pattern of prostate cancer metastasis to the vertebral column[END_REF].

Strain fields shows significant changes, the location of critical points changed and the distribution, although similar in both cases, shows an increase of the strain values from 5,1E-3 to 5,8E-3. To verify these critical points where a metastatic lesion had occurred, the initial models are evaluated. We measure bone mineral density in different slices of the critical points. Where strain changes a density loss of 15% is found. For the spinous process, where a critical increase of stress was found, the loss of density was 25%. Density measures at random points indicate that the whole vertebra suffered metastasis. This is the most typical case, diagnosed in the 61% of the patients with prostate cancer [START_REF] Suzuki | Pattern of prostate cancer metastasis to the vertebral column[END_REF].

Conclusions

A methodology to evaluate metastasis due to prostate cancer on lumbar vertebrae was presented. Using 3D models and finite element analysis, we can evaluate the mechanical response of the model and detect changes on bone structure. CAT images are used to create reliable models for such analysis, however, a limited range of slice thickness must be used for this purpose [START_REF] Ford | Computed tomography slice thickness and its effects on threedimensional reconstruction of anatomical structures[END_REF]. A model with nonhomogeneous properties was implemented, each element of the mesh had a mean density and strength, and a static analysis with boundary conditions associated to typical loads was developed.

Results showed a vertebra with a degradation of its mechanical properties on the whole domain, this kind of lesions are the most typical due to prostate cancer.

Figure 1 .

 1 Figure 1. Sample of elements created with the parameters established for meshing.

Figure 2 .

 2 Figure 2. Loads applied over the lumbar L5.

Figure 3 .

 3 Figure 3. Equivalent strain field with test points for vertebra from 2009.

Figure 4 .

 4 Figure 4. Equivalent strain field with test points for vertebra from 2014.

Table 1 .

 1 Eigenvalues for the stiffness matrix for CAT models from 2009 and 2014.

	2009	2014	% difference
	50810,21	46783,04	-8,61
	48967,56	43168,24	-13,43
	44181,39	41838,73	-5,60
	42713,13	41740,76	-2,33
	42264,10	40350,57	-4,74
	40127,65	39693,13	-1,09

Table 2 .

 2 Equivalent stress on different test points.

	Equivalent stress 2009 [MPa]	Equivalent stress 2014 [MPa]	Location (x, y, z) [m]	% difference
	0,57	0,57	0.006129, 0.021090, -0.455290	0,12
	0,63	1,63	0.003925, 0.076280, -0.441867	159,47
	1,45	1,43	-0.035230, 0.041480, -0.437857	1,08
	1,34	1,32	0.045381, 0.039486, -0.434435	1,46
	6,54	5,92	-0.016158, 0.034375, -0.440238	9,41
	7,56	7,04	0.026612, 0.037148, -0.439232	6,97


O Bohórquez

S Ardila

A Pertuz
email: capertuzc@uis.edu.co

O A González-Estrada

Finite element analysis for palm oil bunches press shaft fractured in service

Keywords: fracture in service, FEM, fruit bunch press, shaft, failure mode

In this work, the behavior of a palm fruit bunch press shaft is investigated, which has presented early failure several times, not reaching its expected lifetime. The study developed allows determining the failure mode of the shaft by using the finite element method (FEM). In the model, was estimate the load produced by the fruit bunches over the worm screw and transferred to the shaft. Geometrical analysis of the shaft shape helps to determine failure mode. The stress and strain fields are obtained to determine the critical points of the design, allowing suggesting several forms to correct damage in the future. Moreover, after a short time of operation, the structure presented wear; the hexagonal shape in the shaft is fixed using a welding procedure. Is showed metallographic and hardness results obtained on surface and subsurface level of the affected area for the fractographic analysis. This is compared with a raw steel SAE AISI 4340 under tempered like original condition.

Introduction.

Colombia is the fourth palm oil producer in the world, palm oil industry represents in Colombia 4.2% in farming industry volume with half million of hectare in the country [START_REF]Entorno económico y desempeño del sector palmero en 2016 y perspectivas[END_REF], in this process, bunches of palm are impregnated with oil by sterilization cycle and fruit removal operation. the recovery of this oil represents until 2.11% of palm oil rate extraction [START_REF] González-Estrada | s s n en Palma de Aceite[END_REF], a strategy for this saving is take bunches and pass them for an additional pressing stage, this equipment for pressing has constituted by one motor, a gear reducer for speed reduction and torque increasing, coupling unit, and a unique body of press, that contains a drilled cage, three helical sections with rising diameter, and a principal shaft that support and distribute the force represented in torque to crush bunches [START_REF] Jorgensen | Treatment of empty fruit bunches for recovery of residual oil and additional steam production[END_REF]. A local manufacturer of this press, developed a new model applying a shape variation in shaft, bring on a hexagonal profile in the transversal section, the equipment showed a premature failure in service, giving an opportunity under FEM type review to analysis this geometry and his stresses and strains, while metallographic tests are applied with purpose to value real condition. A 3D model of this shaft configuration is showed in figure 1.

Fig. 1 Shaft CAD model in palm oil bunches press

This model presented a premature wear in support zone where hexagonal area in shaft convey torque to helical sections, specifically in the more restricted area zone, this let that these helical section slide above the shaft. After this failure mode, it was realized a welding procedure to reconstruct the shaft, hexagonal faces were not repair with a precision measures, causing a nucleation of crack to finally, obtain a fracture on shaft. Figure 2 shows images of shaft, with wear, and after of repair, and fracture final shaft.

Methodological Framework.

Structural analysis by finite elements method (FEM). An estimation is made of the field of stresses and deformations to which the shaft is subjected, taking as reference the energy consumption data provided by the process. These fields allow predicting the failure mode of the component, and in this way determining the causes that could produce this event characterized by a strong wear due to plastic deformation of the material that forms the hexagonal shape and that serves as support for the helical sections.

Problem statement. Numerical method was developed using 3D model from assembly, for problem solution was considered a AISI/SAE Steel 4340 bonified, with Young's modulus E=200GPa, and Poisson's ratio ν=0.3. Operational torque was calculated using voltage 220 (V) and current 244(amp), data collected in workplace and applying reduction due to mechanical mounting and motor efficiency. P shaft = P electrical *η motor *η mounting .

(

) 1
This power gives a reference about the torque value under power mechanics equation [4], taking the rotational speed directly on shaft 16 (rpm), and considering reduction ratio by gearbox, effective torque was calculated in 34893 (N*m). P shaft =T shaft * N shaft .

(

) 2
Boundary conditions. Shaft is supported by three rolling bearing, those preserve linearity and rotation on himself, due to working mode. This condition presents the model like a cylindrical support, giving restriction on moving in axial and radial direction. Figure 3 shows these conditions in the mounting system, where axial displacements are restricted by the cage and body of press. Finally a normal variable pressure was instaured in length of helical surface, this represents the force by bunches of palm oil compressing in the equipment. The pressure was calculated considering the energy consumption, obtaining in this mode the typical torques on working regimen of press [5]; to calculate the compacting pressure a numerical method was used, the input variable was the pressure in helical section, and output variable was operational torque on shaft, then making several iterations, a pressure profile was found as result by static equilibrium, applied on the helix above the shaft, this pressure flows from 0 to 9 (MPa) in x axis direction, Top value was located in the highest transversal area, a lineal simplified model on load distribution was assumed. This consideration represents a low friction model. These considerations are showed in figure 4. To analyzed the shaft was considered a Bonded type contact between helicoidal sections and shaft, reducing relative moves, and Frictionless type contact between final faces in helicoidal parts, this condition let tangential displacements con friction coefficient equal to zero [5]. Mesh type used in simulation is formed by quadratic tetraedrical elements SOLID187 type. In the beginning, level 2 adaptative meshing was used in strain concentrator, located in the sectional change area. Due to torque level, weight from elements was negligible, numerical tries showed low variations almost 0.4% of maximum stress with these values considerate.

Metallographic analysis.

Fracture zone was cut to obtained specimens to analyze under microscope, and verify conditions of hardness and grain formations at initial condition of shaft material and due to welding procedure affectations. These test were lined to ASTM E-3 and ASTM E-18, and finally ASTM E-407

Results.

Computational modelling. Von Mises strains are showed in figure 5. Can be observed that maximum strain is 823 (MPa), which is higher than elastic limit of material of shaft, 710 (MPa). This value let verify the plastics deformations showed in mechanical element [4]. This shape shows singularity conditions for hexagonal borders, these configuration presents several points where undefined load is located, additional to these models, the mechanical adjustment between helical sections and shaft, with hexagonal faces both of them, can to focus on this area, causing multiple stresses concentrator generation on depends of this adjustment. To obtain these results was realized located refining level 2 and adaptative refining on area of interest, with maximum range of 5% for this solution in displacements. Table 1 shows convergence values to independence of meshing.

Nodes.

Elements. Max. total displacements. % Variation. 68011 45278 8.85E-05 123180 85018 8.74E-05 -1.17 Table 1. Meshing convergence Metallographic results. Specimens preparation was based in ASTM E-3 and microstructural analysis was based in ASTM E-407; figure 6, shows microstructures of material previously to welding procedure to repair the shaft, martensitic tempered structure is predominant clearly. Under standard ASTM E18, hardness test were taken, a variation in this parameter was observed, this change was caused by heat exposure during welding process, these are auspicious conditions to nucleation of cracks, and this affectation produces a ferritic pearlitic structures, which are typical for hypoeutectoid steels [START_REF] Boyer | Failure Analysis and Prevention, Metal Handbook[END_REF], Conclusions. Failure mode in shaft was characterized by a reparation for welding process, due to premature wear on the hexagonal peripheral zone, this reparation persecuted to recover the support area to helical sections, after intervention, was evidenced a nucleation of crack, and propagation of fissure, that led to breaking off the shaft.

The strains analysis was realized for the main drive shaft with hexagonal section, used by to pressing bunches palm oil. To establish boundary conditions was realized a static analysis of loads using like reference the energy consumption, after was reviewed in detail contact conditions, the geometrical shape origins singularity points of stress (specifically hexagonal peripheral borders), to can analyzed high gradients of stress was necessary refining mesh in this area. Numerical results indicate that in these points a yield deformation is reached on these points, this causing plastic deformations and final failure of element.

2 .

 2 Weared off shaft (a), repaired shaft (b), fractured shaft (c).

Fig. 3

 3 Fig. 3 Boundary conditions in shaft.

Fig. 4 .

 4 Fig. 4. Pressure load profile in shaft.

Fig. 5 .

 5 Fig. 5. Von Mises stresses state on shaft.

Fig. 6 .

 6 Fig. 6. AISI Steel 4340 bonified, microstructure previous to repair procedure, microetching with nital 3%, martensitic tempered microstructure (a) 200X, (b) 500X

table 2

 2

	Data taken area	Rockwell C	Average
	Shaft with	Lenghtwise section	36 , 37 , 36	36.33
	original condition	Transversal section	36, 37, 37	36.66
	Shaft with welding process applied	Lengthwise section Transversal section	28, 28, 27, 30, 30, 30, 30, 31, 32, 31.5, 34, 35, 34, 33 28, 30, 31, 30, 31, 32, 32, 32, 33, 34	28.54 31.33

shows reduction in hardness in specific areas of interest.

Table 2 .

 2 Comparison values of hardness variation in areas of interest.

Maximum strength found was 823 (MPa), which overpass elastic limit for material of shaft 710 (MPa), indicates that this cause to lose original shape.

Catastrophic fracture on shaft occurs after welding process and it can be attributed to lose of resistance on repaired area. This was originate by heat affected zone (typical term in welding process), it led to nucleation of cracks and propagation of fissure.


Octavio Andrés González-Estrada

German Díaz
email: bgerman.diaz1@correo.uis.edu.co

Jabid Quiroga

Mechanical Response and Damage of Woven Composite Materials Reinforced with Fique

Keywords: composites, natural fibre, finite elements, woven fibres, mechanical properties

In this paper, we present the experimental and numerical modelling for the mechanical behaviour of woven composites reinforced with fique (furcraea selloa) fibre, for different fique fibre woven configurations embed in an R744 epoxy matrix. The woven configurations are taken from commercial models and their mechanical properties validated by experimental data. We perform experimental tests using ASTM D3039 for the tensile response. We obtain values for Young's modulus, ultimate strength, and deformation of unidirectional and woven reinforced composites. Scanning electron microscopy (SEM) is used for the fractographic analysis of the reinforced specimens. For the numerical model of the woven composite, we use the Texgen software to define the finite element voxel model and to estimate orthotropic mechanical parameters. Then, we determine the equivalent elastic properties of the composite, according to the materials and the fibrematrix relations. We compare and validate the numerical results with the experimental data. We obtain stress and strain fields for the yarns and the matrix. The objective of this work is to establish a baseline of the mechanical behaviour of these natural reinforced composites to propose applications for structural engineering.

Introduction

In recent decades, the use of natural fibres has emerged as a response to the need for sustainable composites materials. Composites reinforced with natural fibres have gained attention among the industrial an academic communities, and efforts to characterize and evaluate their mechanical behaviour have been done for several fibres, e.g., jute, sisal, fique, etc. [START_REF] Pickering | A review of recent developments in natural fibre composites and their mechanical performance[END_REF]- [START_REF] Gómez | Comparative study of the mechanical and vibratory properties of a composite reinforced with fique fibers versus a composite with E-glass fibers[END_REF], mostly for unidirectional laminates. Low environmental impact, low cost and a wide range of applications are some of their unique features [START_REF] Hidalgo-Salazar | Influence of Incorporation of Natural Fibers on the Physical, Mechanical, and Thermal Properties of Composites LDPE-Al Reinforced with Fique Fibers[END_REF], [START_REF] Posada-Correa | Estudio comparativo de negro de humo y alúmina como cargas reforzantes en mezclas de caucho natural[END_REF], [START_REF] Pickering | A review of recent developments in natural fibre composites and their mechanical performance[END_REF], [START_REF] Yan | A review of recent research on the use of cellulosic fibres, their fibre fabric reinforced cementitious, geo-polymer and polymer composites in civil engineering[END_REF]. To optimize the performance of natural fibre composites, we can improve the adhesion between the fibres and the polymer matrix, or develop appropriate geometries and configurations of the reinforcement phase, which contribute to increase the mechanical properties of the composite [START_REF] Zhou | Interface and bonding mechanisms of plant fibre composites: An overview[END_REF]- [START_REF] La Mantia | Green composites: A brief review[END_REF].

Composites materials reinforced with woven fibres are a good alternative in many applications, and they can be found in several configurations depending on the textile used, e.g., 2D laminated textile, 2D braided textile, etc. In this regard, Wang et al. [START_REF] Wang | Multi-scale Analyses of 3D Woven Composite Based On Periodicity Boundary Conditions[END_REF] have developed methods for woven fibres to use RVE with periodic boundary conditions for finite element analysis in micro and meso scales.

Reinforcement textiles can be recreated in different manners. Texgen software can reproduce the hierarchical structures and the geometric patterns of complex textiles [START_REF] Lin | Modelling and Simulating Textile Structures Using TexGen[END_REF], [START_REF] Sherburn | Geometric and Mechanical Modelling of Textiles[END_REF]. Numerical models using finite elements (FE) can be used to represent the mechanical response of composites with textiles [START_REF] Dai | Multi-scale damage modelling of 3D woven composites under uni-axial tension[END_REF]- [START_REF] González-Estrada | Análisis de integridad estructural de tuberías de material compuesto para el transporte de hidrocarburos por elementos finitos[END_REF]. The mesoscale modelling of textile composites is used to homogenize mechanical properties by evaluating the stress and strain fields inside a representative unit cell. The conditions for failure start and failure development, associated with damage properties of the materials, elastic properties and geometric characteristics may be proposed based on unit cells [START_REF] Lomov | Textile composites: Modelling strategies[END_REF], [START_REF] Lomov | Homogenisation of a sheared unit cell of textile composites[END_REF].

In this work, we investigate the mechanical response of a polymer-matrix composite reinforced with natural fibres of fique in the form of woven textile. The configuration of the natural textile was taken from commercial models and mechanical properties were obtained by ASTM tensile tests. Numerical models to predict the elastic constants are used, both considering the general rule of mixtures and finite element models, for different fibre configurations, showing good agreement with experimental results.

Materials and methods

The classical linear elasticity problem is considered, given by the internal equilibrium equation, and Dirichlet and Neumann boundary conditions. We assume materials with linear elastic behaviour, under the generalized Hooke's law for anisotropic materials [START_REF] Ansar | Modeling strategies of 3D woven composites: A review[END_REF]. The textile architecture is modelled using the TexGen software [START_REF] Sherburn | Geometric and Mechanical Modelling of Textiles[END_REF], in two different configurations. We assume that both the yarn and the matrix behave as isotropic bodies.

Fique natural fibres (furcraea andina), supplied by Coohilados del Fonce Ltd., were used. The fique fibre has a density of 0,72 g/cm 3 , for a linear density of 31,32 tex, with an average cross-section of 0,176 mm 2 and a diameter of 0,473 mm [START_REF] Mendez | Material compuesto de matriz polimerica reforzado con fibras naturales para la fabricacion de tenso-estructuras[END_REF]. Applying descriptive statistics, it was found that the yarn used is formed of approximately 29 fibres with an estimated diameter of 0.016 mm and an apparent thread diameter of 1.444 mm. Elastic modulus for fique is 22,06 GPa (measured with a fibre length of 250 mm), shear modulus 8,82 GPa and Poisson ratio 0,25, with an ultimate tensile stress of 780 MPa. These values were obtained experimentally for a single thread. The epoxy resin R744 was assumed as a homogeneous isotropic material, with an elastic modulus of 0,951 MPa. One of the textiles used is shown in Fig. 1. The dimensions of the models are 250x25x10 mm, the thread that forms the fabric is 1.44 mm in diameter.

Results

To determine the mechanical properties of the proposed composites, tensile tests were carried out on a universal MTS BIONIX testing machine with a load cell of 25 kN; 3 types of specimens were considered, unidirectional (UD), textile 1 and textile 2. The procedure and the size of the samples were made according to ASTM D3039, the specimens are shown in Fig. 2. In Table 1, we show the results of the tensile tests after the corresponding data treatment for each type of specimens. Note the effect of the reinforcement on the properties of the material, even for low volume fractions. Ultimate stress, σu, and Young's modulus, E 1 , increase with the number of threads, and the strain, εmax, decreases, which is consistent with the expected material response. For the samples with reinforced woven fibres, it is observed that Young's modulus and ultimate stress increase, and the strain decreases, compared with the epoxy specimen. For the fractographic analysis, images were obtained by scanning electron microscopy (SEM), using a Quanta FEG 650 microscope. Note in Fig. 3 that the failure mode for the tensile tests indicates a good adhesion between the fibre and the matrix, which improves the properties of the material [START_REF] Contreras | Fractografía De La Fibra Natural Extraida Del Fique Y De Un Material Compuesto Reforzado Con Tejido De Fibra[END_REF]. Impregnation of the matrix between the fibres of the threads of the textile is optimal, which indicates an appropriate process of casting and curing [START_REF] Tafur | Deformación y fractura de una resina epóxica reforzada con fibra de algodón[END_REF]. The fibre pull-out of the warp could be due to the lack of fibre preparation treatments, which are used to detach the layers of hemicellulose and lignin from its surface, to improve the adhesion between fibre and matrix. Also, small marks left by the weft are observed. Despite the minimal extraction, it can be observed that the material failed uniformly, little evidence of delamination is observed [START_REF] Monteiro | Natural lignocellulosic fibers as engineering materials-An overview[END_REF], [START_REF] Hughes | Deformation and fracture behaviour of flax fibre reinforced thermosetting polymer matrix composites[END_REF].

Finite element model.

A conventional Galerkin formulation is used for the finite element model of the linear elastic problem. For the topological model, a voxelized mesh was used, which was obtained using TexGen [START_REF] Doitrand | Experimental characterization and numerical modeling of damage at the mesoscopic scale of woven polymer matrix composites under quasi-static tensile loading[END_REF]. The boundary conditions are consistent with the ASTM tensile tests.

Elastic model of unidirectional and woven fibres. Initially, we obtained the elastic constants for the composite material with unidirectional fibres: orthotropic elastic moduli E 1 , E 2 , shear modulus G 12 , and Poisson coefficients ν 12 , ν 21 , Table 2. We use the rule of mixtures to estimate the elastic modulus for the different volume fractions. Table 3 shows the error between the experimental, E 1,exp , and the estimated value, E 1,RM . Then, the elastic modulus obtained by finite elements, E FE , was evaluated for each model, including the textiles. The error with respect to the values obtained experimentally is small, as shown in Table 3. With the voxelized FE model, a load of 8000 N was applied to obtain the stress distribution for each material. Fig. 4 shows the von Mises stress distribution for textile 1, displaying the reinforcement fabric and the epoxy matrix. As expected, the warp of the textile exhibits the highest stress, close to 500 MPa, while the transverse threads, weft, show compression stress close to the intersection with the warp. For the epoxy, the stress is high in the spaces between the longitudinal threads, which could cause separation of the matrix from the transverse threads. Considering that the cross-section of the model has an area of 250 mm 2 , the nominal stress is 32 MPa. Thus, the composite fails because the stress on the matrix exceeds the ultimate stress.

Conclusions

Tensile tests were done according to ASTM D3039 for different composite configurations. Epoxy R744 was reinforced with woven fique fibres and an increase in Young's modulus up to 66.8% was evidenced. Using voxel FE models, we could approximate the stress distributions for the textile and matrix. Longitudinal fibres show higher values of stress, as expected. The intersection with transverse fibres shows high stress values for the epoxy. According to FE results, the failure mechanism might be associated with the areas where the matrix exceeds the allowable stress. Numerical results using FE models presented differences below 6.8% with respect to the data obtained experimentally, for the elastic constants of the material. This indicates that the model has good agreement with experimental values, and could be used to study other composite configurations and volume fractions.

  (a) Original textile. (b) Geometric model. Figure 1. Model of the textile 2 × 1.

Figure 2 .

 2 Figure 2. Specimens for the tensile tests.

Figure 3 .

 3 Figure 3. SEM results for the textile 1 under tensile loads.

Figure 4 .

 4 Von Mises stress for the composite with textile 1.

Table 1 .

 1 Mechanical properties from tensile tests for epoxy and composite configurations.

	Specimen type	σu. [MPa]	εmax [mm/mm]	𝐄 𝟏 [GPa]
	Epoxy	25,237 ±1,218	7,470±0,316	0,951±2,044
	UD, 2 threads	28,803±1,135	2,975±0,022	1,417±1,440
	UD, 3 threads	28,137±2,517	2,617±0,126	1,528±0,727
	UD, 4 threads	30,477±1,518	2,783±0,015	1,658±1,181
	Textile 1	28,150±1,603	2,938±1,438	1,587±0,797
	Textile 2	30,254±1,155	3,420±0,285	1,509±0,561

Table 2 .

 2 Elastic constants for unidirectional fibres considering a different number of threads.

	Threads	𝐄 𝟏 [GPa]	𝐄 𝟐 [GPa]	𝐆 𝟏𝟐 [GPa]	𝛎 𝟏𝟐	𝛎 𝟐𝟏
	2	1,346	0,968	0,394	0,348	0,250
	3	1,544	0,977	0,401	0,347	0,220
	4	1,741	0,986	0,408	0,346	0,196

Table 3 .

 3 Comparison of elastic modulus for experimental, rule of mixtures and FE models.

	Specimen type	𝐄 𝟏,𝐞𝐱𝐩 [GPa] 𝐄 𝟏,𝐑𝐌 [GPa]	% error 𝐄 𝐅𝐄 [GPa] % error
	UD de 2 hilos	1,417	1,346	5,01	1,376	2,89
	UD de 3 hilos	1,527	1,544	1,11	1,461	4,36
	UD de 4 hilos	1,657	1,741	5,06	1,629	1,69
	Tejido 1	1,587	N/A	N/A	1,693	6,67
	Tejido 2	1,509	N/A	N/A	1,457	3,44

Acknowledgements

We acknowledge the collaboration of the Laboratory of Microscopy and Laboratory of Mechanical Testing, Universidad Industrial de Santander.