Claude Springer

SOCIAL STRATEGIES FOR COLLABORATIVE LEARNING AND WEB COLLABORATION

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The title of this communication is an acknowledgment of Rebecca Oxford's article "Vive la difference" (1988). It explicitly calls for a focus on collaborative learning and social networking and questions the notion of social strategies [START_REF] Oxford | Language learning strategies: What every teacher should know[END_REF].

Learning strategies are considered to be primarily cognitive and metacognitive (direct strategies) and concern the acquisition of linguistic contents. Social strategies, on the other hand, are considered to be indirect and related to communication. The CEFR (2001: 57) introduced a major change in the definition of strategy that has not really been taken into account. Mariani (2004: 35) explains that in an action-based perspective, in opposition to a knowledge-based perspective, strategies are related to the social context in which the action takes place and are not only related to language communication. This could imply a new way of considering Oxford's taxonomy. My main point is to adopt an activity-based theoretical perspective [START_REF] Lantolf | Sociocultural Theory and Second Language Learning[END_REF], moving away from the mainstream Input-Interaction-Output model that considers language learning as an individual cognitive process [START_REF] Block | The Social Turn in Second Language Acquisition[END_REF]. How can we then consider the social dimension in language acquisition and didactics [START_REF] Springer | La dimension sociale dans le CECR : pistes pour scénariser, évaluer et valoriser l'apprentissage collaboratif[END_REF][START_REF] Huver | L'évaluation en langues[END_REF]) and address the question of social strategies?

To begin with, I'll will present my personal ramblings on strategies; these general thoughts are intended to show different 'twists and turns' on strategies. I will then move on to focus on two different views on learning and on strategies. Finally, I will attempt to define social strategies in webcollaboration in a general way and propose to flip Oxford's taxonomy.

Personal ramblings on learning strategies

We love to tell stories that look like us, that look like our own lives, with the usual twists and turns that life reserves for us. I believe that the research projects we have chosen are inspired by stories of our lives, by stories that look like us, by ideas we have on teaching and learning. Unfortunately, mainstream research demands that we leave aside this storytelling that explains who we are and why we see the world and education the way we do. Mainstream research (the scientific doxa) demands neutrality and a so-called objectivity. It forces us to tell ourselves stories about 'rational and objective' methods in human sciences. I am taking the liberty to stray from this fixed scientific path and present the twists and turns that enlightened my reflections on the question of strategies. This part will outline three different ways of looking at the question of learning strategies. First, pictures of school models of teaching, then contemporary artists representing our world as constellations, and lastly a Greek way of looking at strategies with Ulysses.

Teaching past and present

In a traditional class, lessons are teacher-centred, teacher-led; pupils are expected to learn the teaching content, i.e. lesson input, by heart. In this first context, we can say that the educational culture does not expect what we now call learning strategies in an active and reflective way. In the modern way of teaching, the communicative classroom for example, pupils are expected to be more active but even though pupils and teacher interact, we can imagine that these interactions are also teacher-led (stimulus, response, evaluation). This modern context of teaching nevertheless allows for strategy-oriented teaching. The definition of learning strategies that we know can be easily applied here (cognitive and even metacognitive strategies). The third context can be described as collaborative learning enriched by ICT. In a collaborative class, the teacher stays in the background; he is the 'guide on the side' and not the 'sage on the stage' [START_REF] King | From Sage on the Stage to Guide on the Side[END_REF]. Thus, with the help of the teacher and with online communication artefacts (as it happens with webcollaboration), pupils can build together new knowledge and competencies. In this different cultural educational environment, social and metacognitive strategies are of primary importance. The concept of learning strategies has therefore to be carefully handled as it all depends on educative contexts and other parameters. This is probably why many researchers call it a 'fuzzy concept'.

Artists' representations of our new digital world

Modern artists like Miró and Calder, and many others, have a unique way of depicting our world in new representations. This summer I went to an exhibition of some of Miró's paintings in Sète, France. The paintings, called Constellations, give us a good idea of this new digital world and education. Everything is connected, there is no real beginning or end, no real linear interaction, but a multi dimensional interconnection.

Calder's mobile constellations are another way of depicting movement and the universe. He shows detached bodies with different shapes and colours floating and moving in space, some static and others moving. The world as movement and constellations can be compared to our web networks. We are now part of social networks; learning has become more and more socially interconnected. Everything we need is somewhere on the internet constellations. We develop different strategies to learn, and in this context social strategies are not indirect but direct, they are at the heart of the action we undertake on the internet. Larsen-Freeman and Cameron (2008: 29) tried to explain why applied linguists should take complexity into account: "In a complex and dynamic system, everything changes all the time." They add: "A system of human activity or development will be dynamic at each level of social or human organization, from the sociocultural, through the individual and down to the neural cellular". In this complex and dynamic constellation, "language, language use, and language development are continuously in action". This means that nothing is predetermined, nothing is stable. It therefore seems difficult to imagine and define stable and good learning strategies.

Mètis and Ulysses: dolos and kairos and polytropos

In my research story and scientific walk, I came across another important and new perspective: The story of Ulysses and Mètis. Intelligence and learning are not just a problem of logos, of rationality, of predefined and stable knowledge. Strategies in an action-based approach can be defined according to the CEFR as "a particular line of action in order to maximise effectiveness". Ulysses is clever and can use many tricks, he is polytropos and uses cunning, dolos, and knows how to adapt to difficult and new situations, kairos [START_REF] Detienne | Les ruses de l'intelligence : La mètis des Grecs[END_REF]. In an action-based approach, what matters is effectiveness, even if one has to lie and defraud! Mètis-like strategies are necessary when faced with complexity or chaos. They are dynamic and original. One cannot predict or define what strategy could be the best for everyone in a particular situation. Mètis-like strategies depend on each individual, on the story of his/her experience acquired over the years. Many students do not succeed at school because they don't give priority to logos-like strategies that are favoured by education. Ulysses, like many pupils, would have been miserable and would have cheated to succeed at school! Let me finish this part of my trip with Einstein's education and view on teaching.

Many things have been said on Einstein's education that are still controversial, but let's admit they are true! Einstein was a brilliant pupil but he resented the school's methods of teaching. He learned a lot on his own and preferred imagination and creativity to rote learning. In this sense he was a failure according to the school's standards. He was probably described as a medium learner who didn't fit in and adapt to school's prescription. He didn't use the good learner's strategies. For Einstein, the only source of knowledge is experience.

These different twists and turns show that the notion of strategy is difficult to handle if we consider learning as a complex and social dynamic activity. There are no universal learning strategies if we see learning as part of life experience. Mètis-like strategies seem to be more appropriate in an action-based perspective of human activities. We focus our attention mainly on individual strategies but what about social strategies? The social dimension is as important as the individual and cognitive dimension.

The social dimension: Two perspectives on social strategies

This second step is focusing on social strategies. I will quickly remind us of what is generally admitted as "Good language learner" and "Good practices". I thought that it would be interesting to present ecoethologists' views on social strategies. These two perspectives will then be compared.

Good Language Learner (GLL) and Good Practice (GP)

One of the main questions related to GLL and GP could be: What are the best attitudes to adopt to be efficient in general tasks and in language learning tasks? Literature on the GLL is mainly focused on the study of efficient attitudes in handling learning tasks and also on the description of the good learners' qualities and characteristics. Research therefore is on internal qualities of individual learners. It is a cognitive perspective related to the communicative methodology of the 80's. The underlying hypothesis is that teaching GLL strategies will help less efficient learners to be successful in language tasks.

In applied linguistics, we have this well known taxonomy [START_REF] Oxford | Vers une pédagogie du dialogue interculturel : agir ensemble à travers les nouveaux environnements numériques sociaux[END_REF] with cognitive strategies which are necessary to manipulate the language content; cognitive strategies are direct and primary strategies; they are considered to be the most necessary for the learner to be efficient. Metacognitive strategies, also called selfregulation strategies (see for example Gavriilidou and Psaltou-Joycey 2010) are triggered when managing the learning process. They have an important effect on the cognitive strategies. In a sense to be cognitively efficient one needs to be conscious and reflect on the learning process. The last category is called social strategies.

Obviously language learning has a lot to do with communication, with working with others and taking others' point of view into account, knowing the other. This obviously implies empathising and cooperating with peers, etc. This taxonomy therefore presents the attitudes learners need if they want to handle language learning tasks in an efficient way and be rewarded. For Oxford (2003: 14), social strategies are significant when pupils "work with others and understand the target culture as well as the language"; they have to ask questions for clarification and correction and communicate with proficient peers. This definition is therefore restricted to what is going on in a communicative language classroom.

Social strategies as seen by ecoethologists (Laland 2004)

Ecoethologists have a nice approach to our subject. They study animal behaviours, how they adapt and survive. Ecoethology is therefore the study of survival value of behaviours due to ecological pressure. Their main hypothesis is that animals (and humans?) cooperate with each other in order to increase their own fitness and efficiency; learning from others is inherently adaptive. The research question could be: Who do they copy and when. In a way this is not so far from what we have said on imitating GLL/GP strategies.

Ecoethologists [START_REF] Laland | Social learning strategies[END_REF]) distinguish social strategies, strategies that are culturally transmitted, from asocial strategies that are new and not socially transmitted.

Obviously developing new strategies can be very costly and risky for survival, but these scientists have been able to note such asocial strategies. We can say that most of the animals rely on social strategies because they are not risky and do not imply consuming a lot of energy. Individuals will therefore copy the majority, copy the successful individuals (what we could call the famous stars), copy their friends, etc.

They can of course create asocial or unlearned strategies when established strategies are unsatisfactory or unproductive. Facebook, Tweeter and other social networks). It is also important to stress that these strategies are necessary for reproduction and for survival. The pressure of the environment is an important factor. But even for animals, unlearned strategies, asocial strategies and innovation are possible.

The two perspectives compared: Individual cognitive perspective and collaborative ecological perspective

We can compare these two perspectives on social strategies in this way: The individual cognitive perspective is most of all devoted to the study of what being efficient at school means. As applied linguists, we are concerned with language and communication learning. We believe therefore that imitating the GLL strategies will help less efficient learners to succeed at school. Socialising remains on an individual level as SLA research and language didactics are seldom related to collaborative learning. On the opposite, the collaborative ecological perspective is concerned with social actions and attitudes in a community; it is more about how to behave, how to adapt in society. Language in this action-based perspective is considered as a medium and mediation, not as the ultimate aim. In a community, people imitate socially transmitted strategies that are supposed to help being efficient (most of the time transmitted by parents). They can also create new strategies when necessary or to be simply different. In real life, kids, and even adults, spend their time copying their favourite stars, the 'buzz' on Youtube or Facebook, etc. Are we any different from animals?

Collaborative Learning and Webcollaboration: strategies in an action-based perspective

SLA mainstream theory has recently been challenged by the necessity to take a 'social turn' and to open towards chaos and complexity approaches. The intrusion of technology and especially the social web has also questioned traditional ways of researching on language learning. Our interest in webcollaboration will give us the opportunity to re-question Oxford's taxonomy on strategies and make some proposals. [START_REF] Block | The Social Turn in Second Language Acquisition[END_REF] proposed an alternative approach to the input-interaction-output model of SLA that would take into account 'the social turn'. [START_REF] Van Lier | From input to affordance: Social-interactive learning from an ecological perspective[END_REF] also insisted on the necessity to abandon the computer metaphor (input/output) and to adopt an ecological perspective in SLA. Larsen-Freeman and Cameron (2008) designed a complex systems approach for SLA in coherence with chaos/complexity theories in other disciplines.

Complexity and sociocultural theory in applied linguistics

These contributions all agree that learning is a "non linear trajectory of development", "a sociocognitive process in which the learner and the context interact" (Larsen-Freeman and Cameron 2008: 254). This implies that we cannot disconnect the brain from the situated context where the educational activity takes place. Such terms as 'constellation' and 'networking' give us the idea that the ecological system is not stable and predetermined but dynamic: "A system roams across its landscape of possibility" (Larsen-Freeman and Cameron 2008: 253). [START_REF] Ellis | The Study of Second Language Acquisition[END_REF], in his analysis of sociocultural theory, highlights some points that are important for our action-based approach. Taking the learning situation in isolation does not seem to be a good idea as the learner is not like Robinson Crusoe, a lonely individual with a determined brain [START_REF] Springer | La dimension sociale dans le CECR : pistes pour scénariser, évaluer et valoriser l'apprentissage collaboratif[END_REF].

Ellis explained that learning and acquisition occur in a dialogical action-based situation. According to sociocultural theory, social participation in a community triggers regulation, regulation by others and also self-regulation since the meaning of the exchange is co-built during the collaborative dialogue. For Ellis (2008: 526), "Acquisition occurs 'in' rather than 'as a result of' interaction, language learning is dialogically based". Springer (2009: 518) stressed the importance of collaborative learning: "collaboration involves participation in group activities to accomplish a shared goal with others. It anchors the activity/learning in a social context of solidarity and understanding in a real communicative action. In a sociocultural perspective there is a real respect and concern for others as the construction of knowledge, of experience is shared. Learning is thus seen as participation in a social process of knowledge construction, social transformation of individuals and their environment. The community, as a whole, contributes to the achievement of the desired results".

Vicarious learning comes in naturally; copying the others (imitation) can be a kind of "creative, transformative activity" according to Vygotsky (Ellis, 2008: 534).

Imitation occurs in collaboration activities and enables learning to become development (internalisation). Learners develop with the mediation of others (and of technological artefacts) through language and action. As learning and acting are dynamic activities, teachers cannot define a task that would predetermine what learners will learn. Learners collaboratively negotiate the possible meanings of a task. "Tasks cannot predetermine what learners learn because learning depends heavily on the significance individuals assign to the various activities they participate in" (Ellis 2008: 547). [START_REF] Bandura | Self-efficacy: The exercise of control[END_REF] showed the importance of the belief in self-efficacy. Successes in social or individual experiences help building a strong self-efficacy belief. Vicarious experiences, seeing people, similar to oneself, succeed, also strengthen self-efficacy belief and motivation. Social learning therefore permits adaptive benefits for learners thanks to optimistic beliefs in self-esteem and self-efficacy. These sociocultural and ecological assumptions are similar to ecoethologists descriptions of adaptive behaviours.

Social Web and Webcollaboration: theoretical construct

We have seen that learning has a lot to do with participating and collaborating in social activities. Individual cognitive processes develop in a social environment. The media era has now been replaced by the social web era. Web 2.0 technologies are rapidly shaping our ways of learning, exchanging and acting. Young people are living in an open digital world; they are members of different social networks and have become familiar with new ways of thinking and writing; they engage themselves in different speech communities and learn different social norms, different web etiquettes. Social networking artefacts develop different forms of communication, of socialisation. The web is obviously a sociocultural and complex system, a complex constellation.

Computer supported collaborative learning (CSCL) has become an important part of computer mediated communication research in SLA. The notion of community, the relationship between the members of the community, the social participation of members to develop and reinforce the community, the shared tasks and projects are important elements for CSCL. [START_REF] Wenger | La théorie des communautés de pratique. Apprentissage, sens et identité[END_REF] defined what constitutes a community of practice: joint project, mutual engagement, shared repertoire and shared social practices.

In this new context, learning is action-based and collaborative: We learn with and thanks to the other members of the community. Learning is also distributed and in connection to others, intelligence is not only individual but also interconnected [START_REF] Downes | Connectivism and Connective Knowledge[END_REF]. Dialogic interactions (synchronic and asynchronic) enable learners to build a learning community, to take an active part in the project, to be responsible social actors. The focus is on collaborative dialogue, situated participation, self and coregulation, creative activity, not on predefined input, teacher controlled strategies and output. Collaboration implies that communication, action and learning are intimately linked and not separated (Dewey, learning by doing, 1916). Evaluation is also socially constructed, socially situated (not standardised).

Webcollaboration is based on this theoretical construct. For O'Dowd and Waire (2009), telecollaboration uses web communication tools to enable distant classes to develop linguistic skills and intercultural competence through a task-based approach.

Their definition therefore restricts learning to communicative and intercultural skills.

They do not take into account the importance of community, collaborative intelligence and joint construction of competencies. Springer (2014) offers another approach, which he calls webcollaboration, that is part of an educational project and aims to enable remote classes to collaboratively build a project (a complex social task, [START_REF] Springer | La dimension sociale dans le CECR : pistes pour scénariser, évaluer et valoriser l'apprentissage collaboratif[END_REF]. Students are social actors and together they create a 'masterpiece'; through this process in action, they learn how to act and live together an interdisciplinary learning experience. This experience allows them to develop transversal, social, personal, intercultural, and language competencies. Socialisation through different artefacts (not only language) is at the heart of webcollaboration and networking. Coste (2006: 45) explains clearly what the action-based approach of the CEFR means: "The action-based dynamic, related with the resources and capabilities of the actor, appears in the central articulation between tasks and strategies and manifests itself in the choice that consists in not reducing the notion of task to communicative task as well as the concept of strategy to communication strategy and learning strategy. It will also be noted that this extension implies that the strategic component, in this overall design, is somehow derived from the communicative competence to operate as a strategic execution of tasks, other than language, to a more general level action".

For webcollaboration, tasks are more than simply communicative activities; strategies are also of a more general nature than language learning strategies.

Webcollaboration: Strategies in an action-based perspective

To illustrate webcollaboration and strategies in an action-based perspective, I will rely on one of my doctorate students' thesis (Koenig-Wisnieska 2011). She nicely contrasts a learner-oriented communicative task to a co-learner-oriented collaborative social task. In an ecological action-based perspective, such as this webcollaboration project, the orientation is on the co-learners and on the community. They have to mobilise communicative resources to write and send a post, and for others to read, write and send a comment. What is important is how and what they are able to construct together. They do not only have to be linguistically efficient but also to be socially efficient if they want to solve a problem or realise their common task. Collaboration strategy is somehow similar to Oxford's definition of social strategies: asking questions, cooperating with others and empathising with others. But in an action-based perspective, collaboration strategies are at the heart of action; they cannot be indirect, second-hand. A collaborative interaction is not exactly a communicative interaction in the usual sense; we prefer to call it "collaborative dialogue" (Voloshinov 1929(Voloshinov /2010;;[START_REF] Swain | The output hypothesis and beyond: Mediating acquisition through collaborative dialogue[END_REF][START_REF] Longuet | L'impact des outils d'évaluation qualitative et du WEB 2.0 sur le développement et l'identification des compétences professionnelles des enseignants de langues[END_REF]) to stress the "task in process" (Ellis 2008: 547). This collaborative dialogue is also an "intercultural dialogue" (Springer 2008).

In a webcollaboration project, learners mobilise collaborative strategies we could call "interstrategies" (Koenig-Wisnieska 2011) to collaboratively accomplish a social task. Learning develops, in Koenig-Wisniewska's example, in the act of blogging; it is not reduced to a class learning activity based on a comprehensible input and on the reproduction of a written template. Learning and collaboration go hand in hand. What matters most is the design process and accomplishment of the social task, and the socialisation and development of oneself thanks to multiple and interconnected collaborative dialogues.

An open scenario is therefore necessary to avoid predetermined learning tasks where learners simply have to reproduce comprehensible input. Webcollaboration can therefore enable classes to participate in rich social learning experiences. It is through this type of social activity that learners develop cognitive and metacognitive strategies: "It is also through the diversity of learning experiences, provided they are not compartmentalised nor strictly repetitive, that the individual extends his/her ability to learn" (CEFR 2001: 13).

We can consider blogging as an interactive written discourse genre. It enhances open public writing in the form of a polylog. The main point is the social action not the correct use of language contents. Socialisation of the partners through the collaborative action and collaborative dialogue is a major factor. Learners as social actors participate in learning and collaboration experience online. If many learners are active and take full advantage of the experience, quite a lot are also passive and simple observers. But in this digital learning environment vicarious learning can develop even though it remains hidden. Vicarious learning is a basic way of learning and developing at the lowest cost as we have seen in the example of ecoethology. In this environment learners can use the action/cooperation/social strategies of their friends, of the majority, of the leaders, and when they feel more comfortable, they can take risks and contribute to the development of the project. For the CEFR (2001: 35), discourse competence is characteristic of advanced levels:

"This new degree of discourse competence shows itself in conversational management (co-operating strategies): give feedback on and follow up statements and inferences by other speakers and so help the development of the discussion; relate own contribution skilfully to those of other speakers".

But in fact, in an action-based perspective learners, very early, have to develop this type of discourse/dialogic competence.

Conclusion

We have shown that collaboration strategies come first and allow for the development of cognitive/metacognitive strategies. Therefore we propose to reverse/flip Oxford's taxonomy. The inter-or co-strategies we have described are as follows: Action based strategies, dialogic strategies and social strategies. Action-based strategies are at the most general level of activity; they are mètys-like strategies and are necessary to help the community to reach the joint objective. Dialogic strategies are more than interaction strategies or communication strategies; they constitute inter-mediation strategies necessary to jointly construct and develop the task in process; they also constitute inter-regulation/metacognitive strategies. Social strategies are not only necessary to develop an intercultural dialogue; they help to empower individual members, to give them a positive image of their self-efficacy; social strategies enable learners to observe and imitate other peers, to eventually take a calculated risk. In

Figure 1 :

 1 Figure 1: Animal social behavioural strategies (from Laland 2004)

Figure

  Figure The two perspectives compared: Individual cognitive perspective andCollaborative ecological perspective(Springer 2014)

Figure 3 :

 3 Figure 3: Learner orientation and Co-learner orientation (Koenig-Wisnieska 2011)

  Oxford's taxonomy, metacognitive and affective strategies are individual-oriented; in an action-based perspective they are collaboratively developed. Indirect strategies become therefore direct strategies in an action-based perspective.

Figure 4 :

 4 Figure 4: Strategies in an action-based perspective(Springer 2014)


Sylvain Haupert
email: sylvain.haupert@upmc.fr

Sandra Guérard

David Mitton

Françoise Peyrin

Pascal Laugier

Quantification of nonlinear elasticity for the evaluation of submillimeter crack length in cortical bone

Keywords: Cortical bone, crack, damage, elasticity, nonlinear acoustics, nonlinear resonant ultrasound spectroscopy, synchrotron radiation micro-computed tomography. HIGHLIGHTS

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

This study focuses on bone microdamage and particularly on the microcracks that are thought to play an important role in bone strength [START_REF] Burr | Does microdamage accumulation affect the mechanical properties of bone?[END_REF][START_REF] Diab | Effects of damage morphology on cortical bone fragility[END_REF][START_REF] Hernandez | Quantitative relationships between microdamage and cancellous bone strength and stiffness[END_REF][START_REF] Yeni | Fatigue damage-fracture mechanics interaction in cortical bone[END_REF], toughening mechanisms [START_REF] Diab | Effects of damage morphology on cortical bone fragility[END_REF][START_REF] Fletcher | Effects of fatigue induced damage on the longitudinal fracture resistance of cortical bone[END_REF][START_REF] Vashishth | Rising crack-growth-resistance behavior in cortical bone: implications for toughness measurements[END_REF][START_REF] Yeni | Fatigue damage-fracture mechanics interaction in cortical bone[END_REF] and remodeling [START_REF] Cardoso | Osteocyte apoptosis controls activation of intracortical resorption in response to bone fatigue[END_REF][START_REF] Verborgt | Loss of osteocyte integrity in association with microdamage and bone remodeling after fatigue in vivo[END_REF]. The link between microcracks and bone fracture is not fully elucidated yet [START_REF] Burr | Why bones bend but don't break[END_REF][START_REF] Chapurlat | Bone microdamage: a clinical perspective[END_REF][START_REF] Gupta | Fracture of bone tissue: The ' hows' and the ' whys[END_REF], though microdamage is suspected to be at the origin of some spontaneous fractures [START_REF] Shane | Atypical subtrochanteric and diaphyseal femoral fractures: report of a task force of the American Society for Bone and Mineral Research[END_REF].

The quantitative assessment of damage characteristics remains challenging. Histomorphometry is the gold standard, although providing only 2-D damage characterization [START_REF] Lee | Detecting microdamage in bone[END_REF][START_REF] O'brien | Bone as a composite material: The role of osteons as barriers to crack growth in compact bone[END_REF][START_REF] O'brien | An improved labelling technique for monitoring microcrack growth in compact bone[END_REF]. New techniques are emerging, such as synchrotron radiation micro-computed tomography (SR-µCT) [START_REF] Haupert | Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy[END_REF][START_REF] Larrue | Synchrotron Radiation Micro-CT at the Micrometer Scale for the Analysis of the Three-Dimensional Morphology of Microcracks in Human Trabecular Bone[END_REF][START_REF] Voide | Time-lapsed assessment of microcrack initiation and propagation in murine cortical bone at submicrometer resolution[END_REF]. However, none of these invasive techniques can be applied in vivo, nor is able to assess damage in a large bone volume. Consequently there is a clear need for alternative techniques to assess bone microdamage.

Nonlinear acoustics methods have been introduced recently for the investigation of bone microdamage. They include nonlinear resonant ultrasound spectroscopy (NRUS) [START_REF] Haupert | Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy[END_REF][START_REF] Muller | Nonlinear ultrasound can detect accumulated damage in human bone[END_REF], nonlinear wave modulation spectroscopy (NWMS) [START_REF] Ulrich | Application of nonlinear dynamics to monitoring progressive fatigue damage in human cortical bone[END_REF] and dynamic acousto-elastic testing (DAET) [START_REF] Moreschi | Monitoring trabecular bone microdamage using a dynamic acoustoelastic testing method[END_REF][START_REF] Renaud | Non-linear acoustic measurements to assess crack density in trabecular bone[END_REF]. These approaches, directly inspired from nonlinear elastic wave spectroscopy (NEWS) methods developed in the field of nondestructive testing of materials, have been reported to be sensitive to fatigue-induced damage in materials such as concrete [START_REF] Antonaci | Nonlinear ultrasonic evaluation of load effects on discontinuities in concrete[END_REF][START_REF] Chen | Rapid evaluation of alkali-silica reactivity of aggregates using a nonlinear resonance spectroscopy technique[END_REF][START_REF] Van Den Abeele | Damage assessment in reinforced concrete using spectral and temporal nonlinear vibration techniques[END_REF], metals [START_REF] Cantrell | Dependence of microelastic-plastic nonlinearity of martensitic stainless steel on fatigue damage accumulation[END_REF][START_REF] Cantrell | Nonlinear ultrasonic characterization of fatigue microstructures[END_REF][START_REF] Frouin | Ultrasonic linear and nonlinear behavior of fatigued Ti-6Al-4V[END_REF][START_REF] Kim | Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves[END_REF][START_REF] Kim | Surface acoustic wave modulation on a partially closed fatigue crack[END_REF][START_REF] Nagy | Fatigue damage assessment by nonlinear ultrasonic materials characterization[END_REF][START_REF] Sagar | Effect of microstructure on non-linear behavior of ultrasound during low cycle fatigue of pearlitic steels[END_REF][START_REF] Zagrai | Micro-and Macroscale Damage Detection Using the Nonlinear Acoustic Vibro-Modulation Technique[END_REF] or composites [START_REF] Aymerich | Experimental Study of Impact-Damage Detection in Composite Laminates using a Cross-Modulation Vibro-Acoustic Technique[END_REF][START_REF] Bentahar | Monitoring progressive damage in polymer-based composite using nonlinear dynamics and acoustic emission[END_REF][START_REF] Meo | Detecting damage in composite material using nonlinear elastic wave spectroscopy methods[END_REF][START_REF] Van Den Abeele | Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: Experimental and theoretical study[END_REF], 2001b). However, so far, few studies have attempted to quantify microdamage, using nonlinear acoustic methods [START_REF] Moreschi | Monitoring trabecular bone microdamage using a dynamic acoustoelastic testing method[END_REF][START_REF] Van Den Abeele | Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: Experimental and theoretical study[END_REF], 2001a). [START_REF] Haupert | Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy[END_REF] have investigated the relationship between the nonlinear elastic behavior measured by NRUS and fatigue-induced microdamage of cortical bone specimens, taking advantage of micrometer resolution imaging by SR-µCT. With this approach, the study evidenced a significant correlation between the variation of bone microcrack density and the variation of nonlinear elasticity. These findings not only revealed the sensitivity of NRUS to early bone microdamage, but also established the first quantitative relationship between the variation of nonlinear elasticity of bone and variation of a microcrack characteristic.

A complementary vision to the fatigue test is to produce damage locally by initiating and propagating a single crack in a controlled manner. In this study, calibrated specimens of human cortical bone undergoing a toughness test were measured by NRUS and then imaged by SR-µCT. Our main objective was to investigate whether the nonlinear elastic behavior or the elastic modulus are changed after propagation of a localized single crack and to specifically assess the relationship between the nonlinear elastic behavior and the length and the orientation of the crack. This was achieved by comparing NRUS measurements on native and cracked specimens in dry condition. An ancillary objective was to investigate the influence of hydration on the nonlinear response. . To this goal, NRUS testing were performed on cracked specimens in dry and wet conditions.

METHODS

Specimen preparation

Fourteen human cortical bone specimens were prepared from the femoral mid-diaphysis of four donors (age = 79.4±3.9). Ethical approval for the collection of samples was granted by the Human Ethics Committee of the Département Universitaire d'Anatomie de Rockfeller (Lyon, France). The tissue donors or their legal guardians provided informed written consent to give their tissue for investigation, in accord with legal clauses stated in the French Code of Public Health. Parallelepiped beamsshaped specimens (50x2x2mm 3 ) were wet machined (Isomet 4000, Buehler GmbH, Düsseldorf, Germany) oriented along the proximal to distal direction of the femur. Then they were notched by a diamond wire saw (ESCIL W3000, Chassieu, France) in their middle to form a notch of roughly a quarter of the specimen width (i.e. 500µm). The notch orientation was such that the nominal crack-growth direction for subsequent toughness testing was transverse to the long axis of the specimen, in a direction perpendicular to the osteon alignment. All specimens were defatted for 12 h in a chemical bath of diethylether and methanol (1:1) and stored at -20°C until experiments.

Apparent dry density (ρ dry ) was evaluated by measuring the specimen volume and weight. Bone specimens were dried at 37°C during 12h in a climate chamber (Memmert GmbH HCP 108, Schwabach, Germany) at relative humidity below 20% in the presence of desiccators. According to several authors, collagen molecular structure remains intact during drying and rewetting procedures, so that this protocol is believed not to affect bone properties [START_REF] Currey | The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone[END_REF][START_REF] Rho | Effects of drying on the mechanical properties of bovine femur measured by nanoindentation[END_REF].

Measurement protocol

The experimental protocol began with the NRUS measurements to determine the initial elastic nonlinearity of the dry notched specimens. Previous NRUS measurements on cortical bone [START_REF] Haupert | Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy[END_REF][START_REF] Haupert | High-accuracy acoustic detection of nonclassical component of material nonlinearity[END_REF][START_REF] Muller | Nonlinear ultrasound can detect accumulated damage in human bone[END_REF] were all performed on dry specimens. In the present study, we kept measuring bone specimens in dry condition in order to compare the results with previous reports. The specimens were then taken through a toughness test in wet conditions. Crack initiation and growing was carefully controlled to avoid the rupture of the specimens. NRUS measurements were repeated after the toughness test for all the cracked specimens in dry condition (i.e. relative humidity < 20%). Because some studies have evidenced that the nonlinear elastic response of materials such as concrete and rocks is influenced by the level of hydration [START_REF] Johnson | Dynamic measurements of the nonlinear elastic parameter alpha in rock under varying conditions[END_REF][START_REF] Payan | Effect of water saturation and porosity on the nonlinear elastic response of concrete[END_REF][START_REF] Van Den Abeele | Influence of water saturation on the nonlinear elastic mesoscopic response in Earth materials and the implications to the mechanism of nonlinearity[END_REF], NRUS measurements were repeated on the cracked specimens in wet condition (i.e. relative humidity > 80%). Finally, the crack length was estimated using SR-µCT. The sequence of measurement steps is illustrated on Fig. 1.

NRUS measurements

When damaged materials are subjected to a dynamic loading, the elastic modulus decreases as strain amplitude increases. A typical manifestation of this phenomenon, the so-called "softening effect", is the decreasing of the resonance frequency of the first compression modes [START_REF] Haupert | High-accuracy acoustic detection of nonclassical component of material nonlinearity[END_REF] when the excitation amplitude increases. In addition, the Q-factor of the resonance peak, defined as the ratio of the resonance frequency to the resonant peak width at half maximum, also decreases for increasing excitation amplitudes. This behavior, which is typical of the non-linear non-classical elastic behavior [START_REF] Guyer | Nonlinear Mesoscopic Elasticity: The Complex Behaviour of Rocks, Soil, Concrete[END_REF], also known as hysteretic elasticity, of damaged materials appears for strains above approximately 10 -5 [START_REF] Johnson | Slow dynamics and anomalous nonlinear fast dynamics in diverse solids[END_REF]. It conveys information about the amount of hysteretic nonlinear units representing the damaged zones in the material.

The principles of NRUS measurements have been extensively described elsewhere (Van den Abeele et al., 2000). The protocol was adapted to achieve high sensitivity to detect small variations of bone nonlinear parameters [START_REF] Haupert | High-accuracy acoustic detection of nonclassical component of material nonlinearity[END_REF]. Briefly, a piezoceramic emitter (Fuji Ceramics Corporation, Yamamiya, Japan) glued on a backload was bonded at one end of the specimen to ensure it is in free-fix boundary condition for NRUS measurements. Such boundary conditions impose a null displacement (i.e. maximum strain) at the fixed end of the specimen and a maximum displacement (i.e. null strain) at its free end. Each specimen was probed by a swept-sine (M2i.6612, Spectrum GmbH, Grosshansdorf, Germany) encompassing the first resonant mode of the cortical beam (assumed to be pure compression mode under asymmetric boundary conditions). The peak resonance frequency f and energy loss Q -1 were measured as a function of strain applying increasing voltage drive level. Two hysteretic nonlinear elastic (α f ) and dissipative (α Q ) parameters, related to the frequency shift Δf and to the energy loss variation (ΔQ -1 ) as a function of strain, respectively, were extracted as follows (Van den Abeele et al., 2000):

𝑓 -𝑓 0 𝑓 0 = ∆𝑓 𝑓 0 = 𝛼 𝑓 2 ∆𝜀 (1) 1 𝑄 - 1 𝑄 0 = 𝛼 𝑄 2 ∆𝜀 (2)
where f and Q are the resonance frequency and Q-factor at increased strain level, f 0 and Q 0 are the reference values (assumed to be linear) at the lowest drive amplitude, Δε is the maximal dynamic strain level over a period. The dynamic strain amplitude ε was calculated from the longitudinal particle displacement U at the free end of the specimen measured by a laser vibrometer (LSV 1MHz, SIOS, Ilmenau, Germany):

𝜀 = 𝛿𝑈 𝛿𝑥 = 𝑈 * 𝑘 = 𝑈 * 2𝜋 4𝐿 ( 3
)
where k is the wave number and L is the specimen length.

Both nonlinear elastic α f and dissipative α Q parameters were evaluated on intact and cracked specimens in dry condition. During NRUS measurements, specimens were kept at fixed temperature (37°C ±0.1°C).

Given the free-fix boundary conditions for NRUS measurements, the resonance mode is such that the length of the specimen L equals a quarter of the wavelength at the corresponding resonance frequency (λ = 4L). Thus, the sound velocity c 0 can be estimated by:

𝑐 0 = 4𝐿 * 𝑓 0 (4)
As the wavelength λ is much larger than the characteristic dimension of the cross section of the specimens, the wave propagates in the specimens according to the bar mode. Thus, the ultrasonic Young's modulus (E us ) can be estimated by [START_REF] Achenbach | Wave Propagation in Elastic Solids[END_REF][START_REF] Grimal | Assessment of cortical bone elasticity and strength: Mechanical testing and ultrasound provide complementary data[END_REF]:

𝐸 𝑢𝑠 = 𝜌 𝑑𝑟𝑦 * 𝑐 0 2 (5)

Toughness testing

The piezoceramic emitter attached to the specimen was removed before mechanical testing. To be closer to realistic in-vivo cracking conditions, the notched specimens were hydrated into saline during 12 hours. The wet specimens were monotonically loaded at a displacement rate of 0.05 mm/s with a preload of -4N, using a crack opening (mode I) four-point bending setup. The test was stopped before failure at different crack lengths. The test was conducted on wet specimens in the air, at ambient temperature, using a hydraulic testing machine (INSTRON, 8802, High Wycombe, England) with a 1kN loading cell (accuracy 0.5%) and the internal displacement transducer (accuracy 1%). The specific four-point bending assembly is composed of 6.35 mm diameter roller-bearings with a 40 mm outer span and a pivoting 20 mm inner span. In this configuration, the formation of grooves under the rollers is minimized [START_REF] Griffin | Artifactual nonlinearity due to wear grooves and friction in four-point bending experiments of cortical bone[END_REF].

3-D synchrotron radiation µCT (SR-µCT)

After NRUS measurements and mechanical testing, the samples were measured by SR-µCT at the European Synchrotron Radiation Facility (Grenoble, France) on beam-line ID19 following the data acquisition protocol extensively presented in previous studies [START_REF] Haupert | Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy[END_REF][START_REF] Larrue | Synchrotron Radiation Micro-CT at the Micrometer Scale for the Analysis of the Three-Dimensional Morphology of Microcracks in Human Trabecular Bone[END_REF]. The photon energy was 25 KeV and the size of the measured volume was 2.8x2.8x1.96mm 3 with a voxel size of 1.4 µm 3 .

For crack characterization, a sub volume of interest (VOI) of 2.15x1.75x1.75mm 3 , encompassing the notch and the crack over the entire width of the sample, was analyzed.

The VOI was sampled by 2-D longitudinal crosssections regularly spaced with an interval of 350µm (Fig. 2). Each cross-section was obtained by averaging a stack of 10 adjacent 1.4µm-thick slices in order to decrease the noise level and improve the contrast between the crack and the bone matrix (Fig. 2).

For crack length determination, only the main crack starting at the notch was considered, while all peripheral microcracks that were not connected to the main crack were removed to avoid including bias in the analysis. Crack length was manually determined by approximating the main crack as a succession of line segments. The total crack length was estimated by summing the length of the line segments. A line segment n was represented by a vector of length L n and angle θ n . The total mean crack length (Cr.Le [µm]) was the average of the total crack lengths measured on six different longitudinal sections regularly sampling the VOI. The mean crack angle θ is estimated in a coordinate system composed by the osteon direction (x-axis) and the notch direction (y-axis). It corresponds to the vector orientation delimited by both extremities of the main crack. Lengths (L n ) and angles (θ n ) were measured using the software ImageJ (NIH, USA) with the plugin NeuronJ [START_REF] Meijering | Neuron Tracing in Perspective[END_REF]. The length of the cracks projected in the notch direction, i.e. perpendicular to the ultrasound wave propagation, is Cr.LeProj. (Fig. 3). Cr.Le.Proj is the sum of the length projected on y-axis of all the line segments of the crack at 90° (L n .proj = L n *sin (θ n )) (Fig. 3).

The bone surface was computed as the total area of bone section, including the pores (Harversian and Volkmann canals, and resorption cavities) [START_REF] Lee | The nature of fatigue damage in bone[END_REF][START_REF] Zioupos | Accumulation of in-vivo fatigue microdamage and its relation to biomechanical properties in ageing human cortical bone[END_REF]. The apparent bone porosity corresponds to pores appearing as dark pixels on SR-µCT cross-section images. The pores, visible as dark regions, were segmented using a low threshold value chosen heuristically, following by an opening on the binary image to remove isolated pixels. Cortical porosity was derived as the ratio of the summed area of all pores to the total bone area, including pores.

Data analysis

Matlab 7.8 with statistics toolbox 7.6 (Mathworks, Natick, MA, USA) was used for statistical analyses. The difference between measurements (α f and α Q ) before and after the mechanical testing, hydrated or dry, were assessed with a non-parametric Wilcoxon signed rank test on nonlinear parameters (α f and α Q ). The relationship between nonlinear parameters (α f and α Q ) and crack length (total Cr.Le and projected Cr.Le.Proj) was assessed using the Pearson correlation coefficient after checking for the normality of the parameters distributions. (Shapiro-Wilk test). The significance level was measured using a p-value p<0.05.

RESULTS

Evaluation of the crack length

The characteristics measured for all the specimens are displayed in Table I. The total length of the cracks varies from 6µm to 2277µm while the mean angle of the cracks (θ) varies from θ =13° 81° (0° means an alignment with osteon direction) with a mean value of 27±19°. The projected length (Cr.Le.Proj) of the cracks varies from 6µm to 664µm.

Note that two specimens (#2 and #5) were fractured during the toughness test therefore data analysis was performed with twelve specimens.

Figure 3: (a) Decomposition of the main crack into 5 vectors with lengths L n and angles θ n . The crack length Cr.Le = L 1 + L 2 + L 3 + L 4 + L 5 . The mean crack angle is estimated in a coordinate system composed by the osteon direction (x axis) and the notch direction (y axis). It corresponds to the vector orientation between both extremities of the main crack. (b)

The orthogonal projection of the main crack on the transverse axis corresponds to the sum of the 5 vectors projected on the same axis. Cr.Le.Proj= L 1 .proj+ L 2 .proj+ L 3 .proj + L 4 .proj+ L 5 .proj (with L n .proj = L n *sin (θ n )).

NRUS

We remind that the measurement precision of NRUS was found to be 16.2% for α f and 14.2% for α Q in previously reported results [START_REF] Haupert | High-accuracy acoustic detection of nonclassical component of material nonlinearity[END_REF]. The initial values of α f and α Q were remarkably similar for all the specimens and vary within a relatively narrow range: α f =-5.5±1.5 (min: -4.4; max: -10.0) and α Q =1.8±0.6 (min: 0.7; max: 3.1). After crack propagation, the nonlinear elastic coefficient α f has increased significantly (p<0.006), with α f values ranging from -4.0 to -296.7 (Fig. 4a). Two specimens manifested a huge increase of α f (#1: α f varies from -4.9 to -296.7; #8: α f varies from -5.8 to -120.5). Two specimens (#3, #11) showed an insignificant change of α f , compared to the technique precision, In contrast, the values of α Q after crack propagation, ranging between 1.1 to 3.5, remained close to the initial values and the variation did not reach a significant level . (Fig. 4b). The dissipative nonlinear α Q could not be extracted for two specimens (#1 and #8). Indeed, in these two cases, there was no linear dependence between the strain level ε and the energy loss variation ΔQ -1 as expected from Eq. 2. For high strain level above ε = 10 -4 , the variation ΔQ -1 saturated. For these reasons, these two specimens were removed from the statistical analysis.

Finally, a statistically significant difference was found between both nonlinear coefficients (α f p=0.002; α Q p=0.01) between measurements achieved on cracked specimens under hydrated or dehydrated conditions, suggesting that hydration has an effect on nonlinear Corresponding author: sylvain.haupert@upmc.fr elasticity. Nonlinearity was higher under hydrated condition.

Both nonlinear hysteretic parameters measured after crack propagation, in dry and wet conditions, were significantly correlated (hydrated specimens: R=0.78 p=0.007; dehydrated specimens R=0.85, p=0.002) (Fig. 5).

The nonlinear elastic parameter α f was significantly correlated to Cr.Le (dehydrated R= 0.79 p<0.01: hydrated R= 0.84 p<0.005) and to Cr.Le.Proj (dehydrated R= 0.88 p<10 -3 ; hydrated R= 0.94 p<10 -4 ) (Fig. 6). Similarly, the nonlinear dissipative parameter α Q was significantly correlated to Cr.Le (dehydrated R= 0.71 p=0.02: hydrated R= 0.79 p<0.005) and to Cr.Le.Proj (dehydrated R= 0.76 p=0.01; hydrated R= 0.76 p=0.01).

There was no significant difference between the values of the Young's modulus (E us ) measured before or after crack propagation

DISCUSSION

To our best knowledge, this study represents the first investigation of the variations of linear (E us ) and nonlinear hysteretic elastic parameters (α f , α Q ) of human cortical bone specimens after a crack initiation and propagation experiment. Similar studies have been reported, but in metal or in concrete [START_REF] Courtney | Factors affecting the ultrasonic intermodulation crack detection technique using bispectral analysis[END_REF][START_REF] Donskoy | Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing[END_REF][START_REF] Duffour | A study of the vibro-acoustic modulation technique for the detection of cracks in metals[END_REF][START_REF] Straka | Detection of structural damage of aluminum alloy 6082 using elastic wave modulation spectroscopy[END_REF][START_REF] Zardan | Effect of the presence and size of a localized nonlinear source in concrete[END_REF]. Linear and nonlinear measurements of elastic properties were achieved on each specimen before and after crack propagation, so that each specimen was its own control. The results evidence an increase of the nonlinear hysteretic elastic coefficient α f of the bone specimens after crack propagation in agreement with the results reported on different materials [START_REF] Courtney | Factors affecting the ultrasonic intermodulation crack detection technique using bispectral analysis[END_REF][START_REF] Duffour | A study of the vibro-acoustic modulation technique for the detection of cracks in metals[END_REF]. Furthermore, we found a significant correlation between crack length and the nonlinear parameters α f and α Q , which is consistent with the recent results reported by Zardan et al. [START_REF] Zardan | Effect of the presence and size of a localized nonlinear source in concrete[END_REF] in concrete and Donskoy et al. in steel [START_REF] Donskoy | Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing[END_REF].

In contrast, the crack propagation has no measureable effect on the elastic modulus E us . This suggests that the nonlinear hysteretic elastic behavior is more sensitive to the presence of a single crack than linear elasticity corroborating the result found in concrete by Zardan et al. [START_REF] Zardan | Effect of the presence and size of a localized nonlinear source in concrete[END_REF]. The values of α f and α Q measured in the specimens before crack initiation and propagation are in agreement with those observed in previous experiments conducted on human or bovine dry cortical bone [START_REF] Haupert | Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy[END_REF][START_REF] Haupert | High-accuracy acoustic detection of nonclassical component of material nonlinearity[END_REF]. However, the damaged specimens of the present study, with a single crack, exhibit values of α f that are far higher than those measured in damaged specimens with an accumulation of non-localized microcracks occurring after a fatigue test [START_REF] Haupert | Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy[END_REF]. During the fatigue test conducted in our previous study, the damage remained at an early stage of development resulting in the accumulation of tiny microcracks with a lower nonlinear responses compared to the current specimens. We hypothesize that the total volume of the accumulated microcracks, within which the nonlinear mechanisms may occur, is probably much less extended than the volume of a region damaged with a large crack. Future studies are required to gain insight into the role played by the volume occupied by cracks on the nonlinear elastic behavior.

We assume that the activation of the nonlinear elastic behavior by crack opening/closing processes is larger when the crack is perpendicular to the direction of propagation of the compression wave. As a consequence, the correlation of the nonlinear elastic behavior is expected to be stronger with the length of crack portions perpendicular to the wave direction than with the total crack length. Although our data showed a trend to a higher correlation of α f with Cr.Le.Proj than with Cr.Le, the difference did not reach a statistically significant level (Z<1.65, Steiger's Z-test for correlated correlations [START_REF] Meng | Comparing correlated correlation coefficients[END_REF]), probably because of the weak statistical power of the test due to the limited number of specimens included in the study. A larger sample size is needed to confirm this assumption.

The nonlinear elastic behavior was investigated under different hydration conditions upon the same set of cracked specimens. Both nonlinear hysteretic parameters increase after bone hydration (Fig. 4). The influence of hydration was also studied in rocks [START_REF] Johnson | Dynamic measurements of the nonlinear elastic parameter alpha in rock under varying conditions[END_REF][START_REF] Tutuncu | Nonlinear viscoelastic behavior of sedimentary rocks, Part II: Hysteresis effects and influence of type of fluid on elastic moduli[END_REF][START_REF] Van Den Abeele | Influence of water saturation on the nonlinear elastic mesoscopic response in Earth materials and the implications to the mechanism of nonlinearity[END_REF][START_REF] Zinszner | Influence of change in physical state on elastic nonlinear response in rock: Significance of effective pressure and water saturation[END_REF], woods [START_REF] Derome | Hysteretic swelling of wood at cellular scale probed by phase-contrast X-ray tomography[END_REF] and concrete (Payan et al., 2010). In rocks, the nonlinear elastic behavior increases as the water content increases [START_REF] Johnson | Dynamic measurements of the nonlinear elastic parameter alpha in rock under varying conditions[END_REF] contrary to concrete [START_REF] Payan | Effect of water saturation and porosity on the nonlinear elastic response of concrete[END_REF]. These observations are interpreted based on different mechanisms, such as 1) capillarity forces due to water (non-viscous) (Van den [START_REF] Van Den Abeele | Influence of water saturation on the nonlinear elastic mesoscopic response in Earth materials and the implications to the mechanism of nonlinearity[END_REF], 2) adhesion forces due to a viscous liquid between grain boundaries or cracks lips [START_REF] Nazarov | Acoustic nonlinearity of cracks partially filled with liquid: Cubic approximation[END_REF], or 3) fluid flow that modify the diameter of tubes where the fluid moves [START_REF] Nazarov | Acoustic nonlinearity of water-like materials with partially liquid-filled capillaries[END_REF]. Whether such mechanisms may exist in cortical bone which can be considered as a matrix pervaded by a porous network filled with viscous fluids, in the specific case of bone, collagen with hydration-dependent elastic properties [START_REF] Rho | Effects of drying on the mechanical properties of bovine femur measured by nanoindentation[END_REF]) may be another factor that has to considered. From an experimental point of view, this result has important consequence as it suggests that humidity must be strictly controlled during measurement.

The nonlinear dissipative parameter α Q was measured concurrently with the nonlinear elastic parameter α f . We found a significant correlation between α f and α Q in the damaged specimens when they were measured in dry or in wet conditions. Such a correlation between α f and α Q has already been described in various damaged material [START_REF] Van Den Abeele | Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: Experimental and theoretical study[END_REF], 2001a;[START_REF] Van Den Abeele | Damage assessment in reinforced concrete using spectral and temporal nonlinear vibration techniques[END_REF]. Like Van Den Abeele et al [START_REF] Van Den Abeele | Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: Experimental and theoretical study[END_REF], we report a lower sensitivity of α Q to crack length, in comparison to α f . Nonlinear resonant ultrasound spectroscopy is suitable for a multimodal approach [START_REF] Rivière | Nonlinear acoustic resonances to probe a threaded interface[END_REF] as each resonant mode generates a different strain field. In this report, we focus the analysis on the first compression mode. But other resonant modes can be measured. For example, we measured also the second and third compression modes. The results obtained with these modes were similar to the results obtained by processing the first compression mode (data not shown). These results are consistent with the theory [START_REF] Liu | Localization of material defects using nonlinear resonant ultrasound spectroscopy under asymmetric boundary conditions[END_REF][START_REF] Van Den Abeele | Multi-mode nonlinear resonance ultrasound spectroscopy for defect imaging: An analytical approach for the one-dimensional case[END_REF]. Indeed, the value of the measured nonlinear parameter depends on the local strain field: if the crack is located in a node of the strain field, the crack would not be excited by opening/closing and no nonlinear hysteretic behavior would be measured. In fixed-free boundary conditions, the strain field is identical for the three modes in the center of the specimens where the crack is localized. It means that the value of the nonlinear parameter must be the same for the three modes. Different nonlinear elastic behavior would be expected under symmetric boundary conditions (free-free or fixed-fixed) as the local strain fields may vary depending on the mode [START_REF] Liu | Localization of material defects using nonlinear resonant ultrasound spectroscopy under asymmetric boundary conditions[END_REF][START_REF] Van Den Abeele | Multi-mode nonlinear resonance ultrasound spectroscopy for defect imaging: An analytical approach for the one-dimensional case[END_REF][START_REF] Van Den Abeele | Resonant bar simulations in media with localized damage[END_REF].

Although NRUS most often exploits the first compression mode (or Pochammer-Chree mode for cylinder), other modes have also been exploited, such as flexural mode [START_REF] Van Den Abeele | Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: Experimental and theoretical study[END_REF], 2001b). In this study, the nonlinear hysteretic behavior of our specimens has also been investigated using the flexural mode (data not shown). The nonlinear hysteretic parameters extracted from this mode were similar to those derived from the compression mode. Indeed, in case of flexural modes, shear stresses exist but remain weak such that they are generally neglected. This may explain why the nonlinear elastic parameters measured in compression and flexural modes are similar, as we observed it in this study. They reflect mostly the nonlinear longitudinal elastic behavior of the specimens. For both compression and flexural modes, the activation of the nonlinear hysteretic behavior is mainly controlled by opening/closing mechanism due to the longitudinal traveling wave, while the friction mechanisms due to shear stresses remaining too small. In order to investigate selectively the sensitivity of shear elastic coefficients to the nonlinear hysteretic behavior, one would have to perform NRUS measurements with torsion resonant modes for instance.

CONCLUSION

The results described in this study provide new insights into the nonlinear elastic behavior of human cortical bone. The proposed experimental protocol allowed the concurrent assessment of acoustic nonlinear parameters reflecting hysteretic elasticity of human cortical bone specimens subject to a crack initiation and propagation. SR-µCT was used to assess crack lengths and orientations at the end of the toughness test. Results showed a significant correlation between the nonlinear hysteretic elasticity of bone and crack length. NRUS is a promising minimally invasive approach for assessing microdamage in situ. Although the results relate primarily to the characterization of bone, they can be useful for other materials such as metals, composites or concrete.

Figure 1 :

 1 Figure 1: Diagram illustrating the measurement protocol

Figure 2 :

 2 Figure 2: Diagram illustrating the process leading to an equivalent histomorphometric 2-D transverse cross-section image from 3-D reconstructed bone volumes acquired by SR-µCT.

Figure 4 :

 4 Figure 4 : Nonlinear elastic α f (a) and dissipative α Q (b) before and after crack propagation, measured in dry and wet conditions. For the sake of clarity, the two outliers (#1 and #8) are not represented.

Figure 5 :

 5 Figure 5: Correlation between the nonlinear elastic coefficient α f and the nonlinear dissipative coefficient α Q measured in dry and wet cortical bone specimens.

Figure 6 :

 6 Figure 6: Correlation between the crack length (total Cr.Le (a) or projected Cr.Le.Proj (b)) and the nonlinear elastic coefficient α f measured in dry and wet cortical bone specimens.

Table I :

 I Apparent density (ρ dry ), porosity, Young's modulus E US , total mean crack length Cr.Le, mean angle, projected mean crack length Cr.Le.Proj, nonlinear elastic α f and dissipative α Q parameters before and after the toughness test and in dry and wet conditions.

	specimen	ρ dry [g/cm 3 ]	Porosity [%]	Initial E US [GPa]	Final E US [GPa]	Cr.Le [µm]	angle [°]	Cr.Le. Proj [µm]	Initial dry α f	Final dry α f	Final wet α f	Initial dry α Q	Final dry α Q	Final wet α Q
	#1	1909	6.2	22.6	21.4	2277	17	664 -4.9 -296.7 -217.6 1.8	-	-
	#2	1987		22.8			failure		-4.4	failure	1.6	failure
	#3	1778	11.0	18.8	19.8	65	14	16	-5.5 -4.0 -6.2 2.1	2.0	1.5
	#4	1867	7.8	21.6	22.2	208	33	112 -6.3 -10.8 -19.7 2.2	2.7	3.7
	#5	1856		21.0			failure		-5.0	failure	1.4	failure
	#6	1886	7.1	22.3	22.2	341	38	209 -4.1 -21.3 -21.5 1.5	2.7	4.0
	#7	1847	8.5	21.0	20.6	738	26	318 -4.4 -20.2 -37.0 1.7	3.5	6.7
	#8	1759	11.7	20.6	19.7	917	20	315 -5.8 -120.5 -119.1 0.7	-	-
	#9	1744	12.2	19.9	19.8	104	21	37	-4.5 -6.3 -14.6 1.6	1.9	4.3
	#10	1635	16.2	17.4	17.5	192	42	128 -7.1 -11.5 -17.5 1.5	2.4	2.0
	#11	1762	11.6	20.8	21.0	6	81	6	-5.0 -5.6 -7.4 2.6	1.1	2.8
	#12	1744	12.2	20.4	20.4	475	25	203 -4.4 -11.8 -28.7 1.6	1.8	4.5
	#13	1877	7.4	21.5	21.3	547	13	126 -5.3 -16.0 -23.0 2.2	2.6	4.3
	#14	1871	7.6	21.9	21.5	618	14	147 -10.0 -14.5 -17.8 3.1	2.6	4.3

ACKNOWLEDGEMENTS

The authors are grateful to G. Renaud and J. Rivière for their helpful comments and suggestions during the preparation of the experiments, as well as P.A. Johnson, Los Alamos National Laboratory, NM, USA for fruitful discussions and E. Boller, M. Zuluaga and M. Langer for help during the ESRF experiment performed in the framework of LTP MD431. This research was supported by the Agence Nationale pour la Recherche (ANR), France (Grant BONUS_07BLAN0197).


Henning Jensen
email: sussehen@outlook.dk

Dankort The Danish National Debit Card System from the early 1980s

Keywords: Dankort, payment card, debit card, electronic payment, encryption

In the mid-1970s the Danish banks saw problems in controlling national payments. The use of checks had increased dramatically, as had the cost of check clearing. The national postal giro system was a cheap and popular payment system across a large part of the population, and foreign payment card companies were interested in the Danish market. Facing these challenges, the Danish banks and savings banks agreed to establish a shared national electronic debit card system (Dankort), the first in the world. The Dankort project faced much public and political attention, which produced a parliament act on payment card systems. The Dankort project encompassed development of new hardware and software and a new payment procedure in the Danish retail. Dankort now covers more than 80 % of all retail payments in Denmark (2014).

Introduction

The Danish financial market of the 1960s and 1970s was fragmented. Many banks and many savings banks were operating. No single bank or savings bank dominated the market and no foreign bank was established in the Danish retail market. Businesses primarily used the banks, and private people mainly used the savings banks. Savingsbanks were by regulation restricted in their business opportunities. Traditionally all banks and savings banks cooperated, and checks were accepted all over the country and could be cashed at the branch office of any bank and savings bank. The branch office was responsible for storing all cashed checks. They were not sent to the issuing sent to the issuing bank. Bookkeeping and clearing was done electronically on a daily basis. All medium size and small banks and saving banks were members of one of about 15 IT-centers, and each large bank had its own computer center.

All Danish employees were by a parliament act required to have an account in a bank or savings bank within the Danish income tax system. The employers delivered salary and income tax information electronically to the banks. For this end the banks and savings banks had produced a common IT-salary system and offered it to the employers. They also introduced an IT based common monthly payment service.

The costs of handling the rapidly increasing number of checks led to studies and negotiations in the Association of Danish Banks and the Association of Danish Saving Banks. During several years they both had tried to agree upon a fee for each issued check, but this had met great resistance from private customers as well as retailers. The customers would not pay a fee to the banks and savings banks for using their own money. A new payment solution had to be found.

A new Payment Solution

The two financial associations established a task force, in 1975, to come up with ideas for an electronic solution. The existing international card systems, e.g. Eurocard, were brought into consideration. After about two years of discussions the common "payment systems committee" agreed to suggest that banks and savings banks developed a common Danish debit card, to be called "Dankort", and banks and savings banks concurred. In this process two key questions emerged: paper based or electronic processing and how to pay the costs of the system and its operation.

Analyses had shown that the cost of cash payments was DKK 7.50 per transaction. Cost for a check was DKK 5.00, and cost for an electronic transaction would be DKK 1.25. But the committee reasoned that two Dankort transactions would be needed to replace a check transaction. The committee suggested that the costs for the new Dankort should be split between the retailers and the consumers. The retailers should pay DKK 1.50 and the consumers DKK 0.50 per transaction

The publication of this suggestion nearly started a "revolution" because neither retailers nor consumers would pay anything for a new payment system. Signs with "Reject the Dankort" were posted in many retail shops, and consumers asked why they should pay money for paying for goods in a shops? So far using cash has been free of charge.

Although the retailers could see benefits from the suggested electronic system, they were not willing to make the needed investments and to pay transaction fee. So they took the "say no" attitude. However later in the development phase there was a fair and professional cooperation between the Dankort development group and the retailers IT-departments.

The basic idea of the payment system was to introduce a standard plastic card and a four-digit PIN-code (not to be chosen by the user) plus electronic terminals in the shops and encrypted communication to a central computer. There was no balance control against the consumer's bank or savings bank account. Like in the check system, book-keeping would take place every night in the banks' computer centers.

The banks and savings banks stuck to their proposal and a new shared company was established on September 3, 1979. It was named the Financial Institutions' Debit and Credit Card Company (Pengeinstitutternes Købe-og Kreditkort Selskab, abridged PKK). The first CEO was recruited from retail. Two years later he was replaced by a person from the banks' association.

Act on Payment Card (Lov om betalingskort) of June 6, 1984

The public reaction to the proposal caused a debate in parliament. The responsible minister was confronted especially by the left wing parties. They were worried about the possible registration of data about where and for what each consumer was spending money. They were worried about the system's security, e.g. during the communication process. They asked about consequences of possible breakdowns of an electronic system, about responsibility when a card was stolen and used by the burglar etc. Several members of parliament found that such an important system should not be established and controlled by private companies. It should be controlled by government. There were also discussions about the information on the receipt issued to the customer. It was argued that the receipt should contain no information about the single items bought, and no name of the shop, only a shop number, a date and the total amount. (Today you wonder.)

In June 1984 an act was adopted to operate starting on January 1, 1985. Banks and savings banks were not allowed to charge transaction fees from consumer or retailer. The act decided the distribution of responsibility between the card issuer and the consumer. It regulated security and registration of data and readable information on the plastic card.

During the political discussions and the parliament's readings of the new act, a technical project group from retailers, banks and savings banks worked on developing a technical solution, which could benefit both parties.

However, despite the original idea of a completely electronic system, the Dankort system was first introduced as a note based for political reasons. Notes were embossed in the shops and signed by the customer.

The Technical Solution

In addition to the plastic card, the elements in the system were a payment terminal in the shop, a communication system between the shop and the central Dankort computer system, a central Dankort computer system and a communication system to the ITcenters of the banks and savings banks. For the complete system, PKK demanded high security both against break downs and fraud, quick response time and simple to use. Further, the retailers demanded that the response time for a transaction should be no more than one second. This was an extreme demand in 1984.

4.1

The Plastic Card At first it would seem an easy job to make the specifications for the Dankort. The content of the magnetic strip would follow international standards, but what about the visible information on the card? Banks and savings bank found that their name and logo was the most important information. The developers in PKK had the Dankort logo as the most important visible information. The compromise was to have the bank or savings bank's logo on one side and the Dankort logo on the other side. There was also a discussion about having a portrait photo and the social security number on the card. The credit card act banned the social security number from the card. Since 1985 the card's layout has changed 4 or 5 times. A few years ago all cards were replaced by chip cards, mainly for security reasons which involved introduction of terminals with a chip reader.

Terminals for the Shop

Early in the development phase the technical project group in PKK saw that a complete new terminal had to be designed, primarily because of need for encryption. Transmission would be based on landline telephones, because even the smallest retailer had a telephone, and the PKK development team established cooperation with the telephone companies. At that time Denmark had four regional telephone companies each covering a "telephone region". The four telephone companies and PKK established a common project group to design standards for transmission. A technical description including an encryption module was written. A completely new design by Henning Andreasen, a well-known Danish designer, was agreed upon by PKK and the retailers. It included a two part terminal, one part to be used by the customer and one part to be used by the shop. (Some years later the functions of the latter could be performed by an electronic cash register). A Danish telephone manufacturer, GNT, was selected. GNT demanded an order for minimum 10,000 terminals before starting production. In addition PKK had to issue a warranty for the production.

The first terminals were simple. They could only read the Dankort -no other payment cards could be used. The receipt to the customer printed on the shop-part of the terminal was a small one with a minimum of information. However, this reduced the transaction time.

The Communications System

At that time telephone communication was one technical system and another was data communication. The maximum speed for telephone communication was 300 baud. Anything higher was called data communication, and it was only available on leased lines supplied by the Danish Post and Telegraph (PTT). Leased lines were expensive. The telephone line communication protocol was analog. The telephone companies offered to double the communication speed to 600 baud. To speed transmission, communication was routed to leased digital data transmission lines at selected telephone exchanges across the country. At the exchanges, concentrators converted the signal from analog to digital form and communicated with the central computer system at a higher speed. A modified CCITT protocol (X21) was used for this communication. At the Dankort computer centre, a front end computer entered the communication from the network into the central processor.

4.4

The Central Processor

The central processor had to support that 95 % of the transactions should be processed in less than 1 second (including decryption and encryption). It should operate non-stop 24 hours a day. It encompassed end-to-end control with any transaction to secure no loss of data and handling access from up to 50,000 terminals creating up to 600 transactions per second. These demands were overwhelming at that time and maybe also a little too exaggerated. There were no off the shelf computer systems available in the market. Therefore, PKK negotiated with several suppliers, including IBM, NCR, Burroughs, Tandem and CRAS. CRAS, Christian Rovsing limited, was a Danish computer manufacturer and had success producing high performance systems and. CRAS just had achieved orders for a ticket reservation system to be used by an American and a Canadian airline. In PKK's negotiations with CRAS, the company suggested an extendable system based upon a standard microprocessor, which could process up to 40 transactions per second. CRAS also designed a front end processor, a processor for encryption and a virtual disk storage system. This was a perfect drawing board system, but a nonstandard system with many completely new elements. PKK contracted with CRAS, they established a project group, CRAS manufactured hardware and software. But three months before start of production CRAS went bankrupt.

Luckily CRAS had produced most of the hardware and software for the Dankort central processor. PKK bought the whole project group (about 15 persons), and they became employed by PKK. Thus the development process did not stop and processing of Dankort payments (called "production" at PKK) started in November 1984 with a very low number of daily transactions. The system was expanded over the next couple of years and ran production until the mid-1990s. By this time the processing capacity was about 100 transactions per second and the CRAS system was replaced by an IBM system. At that time the system had to be expanded to handle other kinds of debit and credit cards.

Encryption and Security

In the beginning of the 1980s encryption was exclusively used for military purposes. Nobody within banks and savings banks had any knowledge about encryption. The project group had to read public information, establish communication with technical universities, foreign specialists-etc. A DES-encryption based upon a 64 bit key was chosen. In theory the encryption key could be broken, but the encryption/decryption process was very fast and demanded little processor power. This was very important for the development of the terminal for the retailers. The specification of the encryption box was set up in cooperation with National Physical Laboratory in UK. A Dutch company made the security control of the box. Each encryption box was loaded with a unique encryption key. CRAS developed a front-end processor for decryption/encryption. This machine had a processing capacity second to none at the time.

A very Slow Start

The first Dankort transaction took place on September 1, 1983. It was a paper or note based transaction. The customer signed a note with the card information, shop information and the amount. The signature had to be compared with the signature on the plastic card. Exactly as the well know procedure used for other payment card systems, like Master Card, Diners and American Express. Many retailers had experience with this procedure and during the first year after introduction, about 14,000 shops contracted for Dankort payment with PKK. Still consumers were negative, and the last four months of 1983 only saw about 78,000 transactions. In 1984 the number increased to about 580,000. In 1992 the number of Dankort transactions was higher than the number of check transactions (more than 200 million.). Today (2014) the yearly number of Dankort transactions have passed one billion. In addition a raising number of transactions are based on buying and selling on the Internet. In 2013 there were 74.3 million Dankort payments on the Internet. About 4.5 million Danes (nearly the total number of grown-ups) have a Dankort, and more than 80 % of the turnover at the Danish retailers is paid by Dankort. Some retailers would prefer only to accept payments by Dankort or other cards in order to avoid handling cash money.

ATM Cash Machines Spread over the Country

However back in 1984 something had to be done to change the population's negative attitude to the new payment system. The means was outdoor ATM machines, which were not known in Denmark at that time. Some banks and saving banks have had indoor ATMs for self-service. As an effort to teach the consumers to use the Dankort and remember their PIN-code, PKK decided to install 150 outdoor ATMs with the same design at highly crowded places in Denmark. They should for competitive reasons not be installed close to a bank or savings bank, but at so called neutral places such as railway and bus stations, shopping centers and market squares. The ATMs were called "Kontanten" ("The cash"). They were supplied by NCR. The ATMs provided customers of banks and savings banks access to cash money during nonopening ours. Many branch offices have very limited opening hours and only one weekly late opening until 19:00.

It is a little strange that a system introduced to minimize the use of cash money had to be helped getting started by a system which gave quick access to cash money. The 150 ATMs became very popular, and they were in operation for about 15 years. Today every bank has its own ATM-system.

The Dankort System and the Impact on the Danish Society

In 1983 even employees at banks and savings banks had a negative feeling about the proposed electronic payment system. They feared for their employment. The customers' need for cash money would be reduced, which meant fewer employees in the banks. The handling and counting of the daily deliveries of checks and cash money from the retailers would be reduced. They did not understand that their work would be changed towards counseling, investment handling and other kinds of customer services.

Around the year 1980 the number of branch offices for banks and savings banks were much higher in Denmark than in other countries, and the numbers of customers per branch office were very low. A reduction was needed, which was aggravated by the economic crisis in 2008 and the following reduction of business and income for the banks. Simultaneously, the number of banks and branch offices and the number of bank employees have been reduced dramatically.

It was expected that a break-through in technology caused by the Dankort system would create export possibilities for Danish hardware and software companies. This did not happen despite strong efforts. The bankruptcy of the hardware manufacturer and the fact that a payment system similar to Dankort is difficult to introduce in countries with different financial marked and another infrastructure might be among the reasons. In many countries one or two dominating bank are operating with great market shares. They will not involve themselves in shared systems, which gives even their smallest competitor the same business opportunity in the payment market as they have.

The Dankort system has proved that Denmark can be proud of having probably the most effective and cheapest payments system in the world. The total cost for an elec-tronic Dankort transaction is about €0.10 or $0.15. The price for cash payments and credit card payments are at least 10 times higher.

Despite the great success of the electronic Dankort system there has been no reduction in the number of coins and notes in Denmark. Especially the number of the highest denomination (DKK 1,000) has risen.

The extensive use of Dankort also means that a break down has tremendous impact on the consumer business in Denmark. On January 20, 2014 the system was down from 05:00 a.m. until about 04:00 p.m. No electronic payments could be processed. A note based back-up system is only available in shops with a very low number of transactions. Today no Danes are using checks and many do not even carry cash money. Luckily many of the new terminals in the shops can store data from the Dankort and print an extra receipt, which the customer can sign if a break down occurs. In general system availability is very high, approximately 99,9 % uptime in average for a system running 24 hours, 365 days. Fraud is very low. In 2013 it was 0,015% of the total turnover.

What`s to Come?

In April 2014 the Dankort operator, Nets, was sold to two US-located investment companies (Bain Capital and Advent International) and the Danish national pension fund ATP. The previous owners were Danish banks and savings banks plus the Danish National Bank. Many Danes felt unsafe having an American owner of a system with such an importance for society. How would the security about the enormous amount of privately related and sensitive data be handled? Would a foreign government be able to demand access to Danish data? Would the new owners go for a higher return on investment and thus higher prices for use of the system?

The current agreement between Nets and the Danish organization for retailers is running from 2013 to 2020. Within this agreement retailers will gradually cover more and more of the costs for the system. By 2020 the retailers will have to pay all costs.

It might be expected that payments by the use of smart phones could be a severe competitor to Dankort payments. If the security will be approved and the price per transaction is acceptable, we probably will see Dankort transactions replaced by phone payments, especially from young people who have their smart phone on-line 24 hours a day.

But the Dankort will also be "upgraded". Mid-2014, NETS decided that from mid-2015 all issued Dankort will successively be replaced with cards having the NFC (Near Field Communication) technology.

Fig. 1 .

 1 Fig. 1. Early Dankort. Name of bank or savings bank on one side; Dankort logo on the other side.

Fig. 2 .

 2 Fig. 2. The Dankort terminal. To the left the shop cashier's terminal, where she entered the amount and printed the receipt. To the right the customer terminal with card reader and key-board for the PIN-code.

Acknowledgements. Thanks to my previous colleagues and friends at PKK, PBS and CRAS. Finn Hagen, Poul Bernt Jensen, Torben Jespersen, Ole Lachmann, Poul Bøgh Nielsen, Mogens Munk Rasmussen, Ole Stampe Rasmussen and Preben Rathgen.

Also thanks to Benedicte Federspiel, Association of Danish Consumers (Forbrugerrådet), Niels Henrik Jørgensen, associate professor, RUC, Ole Mørk Lauridsen, former technical manager at GNT Automatic (Dankort terminal producer) and Søren Winge, manager of communications, Nets.