Andreas Abildtrup Hansen

Yanis Aeschlimann

Samuel Deslauriers-Gauthier

Anna Calissano

Yanis

Permutation equivariant structure-function mapping

Why structure-function mapping?

Brain structure-function mapping addresses the problem of predicting the brain's functional connectivity measured through (rs-fMRI) from the structural connectivity measured through (dMRI). The modelling procedure is built on two main assumptions:

1. Given the structure of a subject, it should be possible, at least partially, to predict his function.

2. The structure and function of specific sub-regions of the brain are matched across all subjects.

Permutation equivariant structurefunction mapping Andreas A. Hansen¹, Yanis Aeschlimann², Samuel Deslauriers-Gauthier², Anna Callissano² A PE-GNN achieves performance similar to a naive mean-estimator even though information on parcel-ordering is discarded during the modelling procedure.

The PE-GNN is compared, using 10-fold cross-validation, to the mean functional connectivity matrix, which is used as a reference estimator of the functional connectivity¹. We compute this predictor on both the training data (M-FC) and a second version of the training data where the rows and columns have been randomly permuted (PM-FC).

Why a permutation equivariant model?

Assume that is a matrix and P is an arbitrary permutation matrix. Then a function is permutation equivariant if Modelling the relation between structure and function by incorporating permutation equivariance ensures that the model behaves similarly for all parcel-orderings, and therefore relaxes the second assumption.

Predicting the brain's function given its structure (structure-function mapping¹²) is no easy task. In this work, we observe the problem through the lens of a permutation equivariant graph neural network (PE-GNN).

  of 3 equivariant modules. The most important components in each module are the linear equivariant layers (L)⁵, and the 2D convolution with a kernel size (F) as seen below. MLLS CRONOS Key finding: https://www.nmr.mgh.harvard.edu/neurorecovery/technology.htm Methods This work considers dMRI and rs-fMRI of 1050 young and healthy adults from the Human Connectome Project³. For each subject, we derived a pair of structural and functional connectivity matrices. Two parcellations of the brain are considered; one containing 68 parcels (Desikan-Killiany), and one containing 200 parcels (Gallardo⁴).

Acknowledgments

The research leading to this poster was funded by the Independent Research Fund Denmark (project no. 1032-00349A), and supported in part by the Novo Nordisk Foundation through the Center for Basic Machine Learning Research in Life Science (grant no. NNF20OC0062606)


L Franzoni

Prediction of fire-exposed CLT floors deflection using an advanced modeling and calibration of the Reduced Cross Section Method

Keywords: Fire design, Reduced Cross-Section Method, CLT panels, Deflection, Fire testing

Introduction

During last decades, the timber structures construction field has sharply increased, covering also modern residential and commercial buildings within the city agglomerates. This development takes benefits from the parallel development of the new massive timber construction method based on Cross Laminated Timber (CLT) panels (or crosslam). These prefabricated thick panels are composed by an uneven number of lumber layers stacked crosswise and glued on their upper and lower faces. The orthogonal lay-up ensures uniform mechanical and hygroscopic properties along both directions and allows the use of CLT as full-size floor, wall or roof element. The enhanced properties of crosslam compared to solid wood make this product competitive with respect to traditional mineral-based construction materials (concrete, masonry) which have a higher environmental impact than wood.

The development of timber structures has to be followed by a progressive increasing in knowledge about their fire safety. This assumes significant importance when dealing with relatively recent products such as CLT panels. Indeed, the current version of the Eurocode 5 -1-2 (2004) includes a fire design method for timber structures derived in the '80s and originally developed for simply supported Glued Laminated Timber (GLT). Such design method, called the Reduced Cross Section Method (RCSM), was originally derived by [START_REF] Shaffer | Structural fire design: wood[END_REF] for GLT by means of an extensive experimen-tal campaign. The principle is to use normal properties of wood at ambient conditions combined with a reduced cross section of the timber member due to the fire exposure. The reduction of the cross section is computed with two steps: (i) a first reduction due to a uniform charring rate and (ii) an additional reduction of a layer having no mechanical properties (also called zero strength layer -ZSTL) in order to take into account the reduced properties of wood in the region close to the char front. In the current version of the Eurocode, such additional layer is set to 7 mm according to [START_REF] Shaffer | Structural fire design: wood[END_REF], independently from any parameter such as the panel's geometry or time exposure. The main advantage of the RCSM compared to more advanced calculation methods lies in using normal properties of wood instead of reduced properties. This hypothesis can be successfully applied to timber structures for two main reasons: (i) wood has a very low thermal conductivity and (ii) charred wood acts as an insulating material that protects the intact wood after the char front. Therefore the temperature and reduced properties gradient ends not so distant from the char front (35 mm to 40 mm according to [START_REF] Shaffer | Structural fire design: wood[END_REF].

The simple approach of the RCSM makes this method useful for practical applications by engineers. However, recent studies [START_REF] Schmid | The Reduced Cross Section Method for the design of timber structures exposed to fire -Background, Limitations and new Developments[END_REF](Schmid , 2014a(Schmid , 2014b) ) showed that the predicted behavior of timber members exposed to fire using the RCSM is not always on the safe side, and the the "exact" value of the ZSTL is difficult to predict since it depends on a multitude of parameters like for instance the boundary conditions, the panel's geometry and the kind of acting stresses. Moreover, dealing with innovative timber products like CLT having an orthogonal lay-up, the ZSTL can be superimposed to transverse layers that do not contribute to load-carrying capacity. Additional complex phenomena can occur for the presence of glued interfaces between layers. Indeed, the presence of glue at CLT layers interfaces can influence the fire behavior because of the difference of thermal properties between glue and timber. When the char front is not yet at the glued interface, the temperature gradient can decrease glue mechanical properties and therefore can lead to premature falling-off of layers and an increasing in the charring rate. This phenomenon has been observed in CLT floors exposed to fire by [START_REF] Frangi | Experimental analysis of cross laminated timber panels in fire[END_REF], and the proposed approach of Eurocode for initially protected surfaces seemed to well reproduce this delamination phenomenon. However, other studies found very few falling-off of layers [START_REF] Craft | Investigation of the behaviour of CLT panels exposed to fire[END_REF][START_REF] Osborne | Preliminary CLT Fire Resistance Testing Report[END_REF] or a falling-off phenomenon that has low influence on fire design [START_REF] Klippel | Fire tests on loaded Cross Laminated Timber wall and floor elements. 11 th international symposium on Fire Safety Science[END_REF]. This discrepancy between test results derives from the multitude of parameters influencing the falling-off effect, like the glue thickness between layers, the type of glue, the presence of small gaps between boards of each layer, the panel's lay-up and so on.

Fire tests on loaded timber elements are useful to understand the actual thermalmechanical behavior of the specimen, but they are expensive, time-consuming and sometimes it is not straightforward to obtain reliable information on the actual mechanical response of the specimen. This is also due to the fact that, in most of the cases, the test is stopped before the failure of the specimen for the safety of people and equipments.

The basic principle of this paper is to use the deflection of fire-exposed CLT floors as mechanical information on the elastic properties distribution within the panel during fire exposure, in order to estimate the zero stiffness layer -ZSSL during the fire test. The deflection is predicted with both advanced modeling based on reduced properties and the simplified RCSM. The comparison with the experimental deflection of fire exposed crosslam floors shows that the RCSM of Eurocode can be improved when considering a ZSSL as a function of time exposure.

First, in Section 2, the available experimental data of bending tests on fire exposed crosslam floors is presented. The following Section 3 presents both advanced and simplified modeling in order to reproduce the experimental deflection. The comparison between the predicted and experimental behavior is showed in Section 4, while Section 5 includes a discussion on obtained results.

2 Fire tests on CLT floors 2.1 Description of fire tests on CLT floors Three CLT floors from three different producers were submitted to bending and exposed to ISO fire on their lower face in tension. The out-of-plane load remained constant during fire exposure and the panels were simply supported on two sides. Thermocouples were placed in several sections and over the thickness in order to measure the temperature profiles. The deflection was measured with LVDTs at panel midspan and the displacement rate was constantly monitored. The end of tests was determined when reaching the safety criterion of maximal displacement rate, when rupture occurred or when reaching an established time exposure without satisfying any safety criterion. Table 2.1 shows the main properties of the fire tests on CLT floors. All panels were made of Norway spruce lamellas of strength class C24 and glued with one-component polyurethane glue. Suddenly after the end of fire test, the specimen was removed to fire exposure and the fire on its exposed side extinguished with water. Figure 2.1 presents a typical residual cross section after removing the exceeding charcoal. .1 shows that there were no alteration of panels' supports geometry due to fire exposure, allowing therefore the hypothesis of respected simple supported boundary condition for the subsequent modeling step.

Temperature profiles

The temperature evolution within the panels during fire exposure has been measured by means of thermocouples along the cross section. Figure 2.2 presents the position of thermocouples over the thickness for the three tested floors.

Figure 2.2 Position of thermocouples across the thickness of tested crosslam floors. Dimensions in mm

Due to its high number of thermocouples (9 sections along the span and 9 thermocouples per section), Test-1 has the most certain documentation on temperature profiles over the CLT thickness. In Figure 2.3 are plotted the registrations of Test-1 thermocouples placed at 84 mm from the bottom exposed side during the test. The solid black line is the considered mean temperature at 84 mm thickness between the nine sections along the panel's span. The same mean temperatures between sections are considered in Test-3, while the specimen of Test-2 had only one section of thermocouples over the thickness. The significant difference between measured temperatures from different sections derives from the local falling-off of timber pieces that yields a local sharp increase of temperatures.

2.3

Charring rates Starting from the temperature profiles registered by the thermocouples during the test and assuming 300 °C to be the wood charring temperature, one can simply derive the charring rates β over the CLT thickness. Table 2.2 presents the computed charring rates for several layers of Test-1 during the fire exposure, considering mean temperatures from the 9 sections (Fig. 2.3). The great increase in the charring rate when passing from the first to the second layer clearly shows that a falling-off of layers occurred. Moreover, the charring rate within layer 2, directly exposed to fire after the falling-off of layer 1, is the double of the previous charring rate, exactly as established by the design approach of initially protected surfaces of Eurocode 5. Concerning the interfaces layers 2/3 and layers 3/4, the charring rate of solid wood (0.65 mm/min in Eurocode 5) is in average respected and therefore no significant falling-off phenomena should be occurred.

Dealing with Test-2 and Test-3, charring rate variations similar to the rates presented in Table 2.2 have been found, showing that also during the two other considered tests, the falling-off phenomenon occurred.

2.4

Evolution of deflection during fire tests During the fire test on loaded crosslam floors, the mid-span, deflection was constantly measured by means of Linear Variable Displacement Transducers (LVDT) placed on the upper side in compression. Figure 2.4 plots the evolution of mid-span deflection during fire exposure of the three tested CLT.

Figure 2.3 Evolution of the mid-span deflection during the three fire tests on CLT floors

Test-1 reached the safety criterion of maximum displacement rate at 150 minutes, highlighted by the sharp increase of its mid-span displacement curve versus time. This means also that the specimen was close to the failure point at that time of exposure. The specimen of Test-2 failed brittely on the tension side at 86 min of fire test, as the respective displacement curve shows. Finally, Test-3 was stopped after 90 minutes without reaching any safety criterion. 3 Modeling

In this section the modeling procedure to reproduce the deflection of tested CLT floors is presented, as well as the compared design approaches based on the RCSM.

Advanced modeling based on reduced properties

The advanced modeling is based on temperature prediction with Safir software and mid-span deflection prediction using a plate theory combined with reduced properties by means of the Eurocode laws.

Prediction of temperature profiles

The temperature evolution over the panels' thickness during fire exposure was predicted with Safir software. Crosslam panels were modeled as solid wood, with perfect connections between layers. According to EN 338, C24 solid wood was modeled with a mean density of 420 Kg/m 3 , while the initial relative humidity of the panel was set to 12%. The emissivity (ε) of the modeled wood was set to 0.8, while the coefficients of convection of heated (h h ) and unheated (h c ) surfaces were assumed to be respectively 25 W/m 2 K and 4 W/m 2 K. Parameter studies not reported in this paper showed that the density and relative humidity are the parameters that most influence the predicted temperatures, while the variation of the remaining coefficients has a negligible influence.

One dimensional constant mesh of 1 mm was applied as a discretization over the panel thickness for the temperature prediction. Figure 3.1 plots the comparison between predicted and experimental temperature profiles during Test-1 across the specimen thickness.

Thermo-mechanical coupling

Dealing with the mechanical properties of panels, no characterization of the raw material has been done. Hence, elastic moduli of wood according to strength class C24 of EN 338 and a rolling shear modulus of 50 Mpa were considered. Once the temperature profile is established for each considered time exposure, the CLT floor is considered as a "multilayer" panel having all thicknesses of 1mm with different values of elastic moduli. Such elastic moduli are defined as a function of temperature using the reduction coefficient k θ given by the Eurocode 5 laws (Figure 3.2). Different reductions of Young's modulus for the upper or lower part of the crosslam floor have been taken into account. Since no reduction diagrams are present in Eurocode, the same law of compressive Young's modulus has been adopted for shear moduli. Finally, with the reduced properties for each 1mm layer, the mid-span deflection is computed with a plate theory for thick layered plates (Lebée and Sab, 2011). This theory is an extension to laminated plates of the well-known Reissner-Mindlin plate theory. Therefore transverse shear effects, which sometimes play a crucial role in CLT panels in bending, can be well predicted with this approach.

RCSM modeling

The simplified design approach of the RCSM implemented in the Eurocode considers reduction of panel's geometry instead of properties during fire exposure. The cross section of the timber member is reduced by the charring rate during fire exposure and by an additional zero strength layer -ZSTL in order to take into account the reduced properties of wood close to the char front. In the actual version of the Eurocode 5, the ZSTL is set to 7 mm and recent studies pointed out that such approach is not always conservative [START_REF] Schmid | Review and analysis of fire resistance tests of timber members in bending, tension and compression with respect to the Reduced Cross Section Method[END_REF]. However, several attempts to improve the RCSM without changing its simple principle have been done. In the next paragraphs, three methods to determine the geometry of the effective cross section are presented. Once the effective geometry is established, normal properties of C24 timber from EN 338 are combined with the plate theory in order to predict the mid-span deflection according to the RCSM.

Existing approaches

-RCSM-1. The first existing RCSM approach has been derived by [START_REF] Schmid | The Reduced Cross Section Method for the design of timber structures exposed to fire -Background, Limitations and new Developments[END_REF] fitting results of advanced numerical simulations on timber members in bending and exposed to fire on their tension side. According to this method, the charring rate is uniform and as prescribed in the Eurocode 5 (0.65 mm/min), while the ZSTL is derived as a function of panel's total thickness by means of a logarithmic relationship. Applying this approach to the three tested panels leads to the following ZSTLs: Panel-1 = 11 mm; Panel-2 = 10.7 mm; Panel-3 = 10.8 mm. -RCSM-2. The second simplified design model [START_REF] Frangi | Experimental analysis of cross laminated timber panels in fire[END_REF] is based on the initially protected surfaces approach of the Eurocode, in order to take into account the falling-off phenomenon discussed in the previous section. Hence, a double charring rate (1.3 mm/min) is considered suddenly after a glued interface between layers and until 25 mm of charring depth. After 25 mm of charring depth after a glued interface, the charring rate returns at 0.65 mm/min. Within this method, the ZSTL is taken as in the Eurocode (constant at 7 mm).

Calibration of the RCSM

More than the two presented existing models, a new simplified approach based on the RCSM is suggested by the authors (RCSM-3). The principle is to use the reduction coefficient for material properties k θ found within the advanced modeling to reduce the cross section geometry. The basic hypothesis is that, for each discretized mesh within the advanced modeling, the value (1-k θ ) multiplied by the thickness of each mesh (1 mm) returns the thickness of wood that has no mechanical properties (Figure 3.3). The sum of each reduced thickness finally leads to the ZSSL for each considered time of fire exposure. The suggested derivation of the ZSSL is therefore based on the hypothesis that at established reduction of stiffnesses corresponds the same reduction of geometry (or "loss of material"). The studies of [START_REF] Franzoni | Advanced modeling for design helping of heterogeneous CLT panels in bending[END_REF][START_REF] Franzoni | Bending behavior of regularly spaced CLT panels[END_REF] showed that this hypothesis is valid when dealing with the bending deflection, without contribution of transverse shear. On the contrary, such hypothesis is not anymore valid concerning the transverse shear deflection. However, since the geometry and the lay-up of the considered panels yield a low contribution of transverse shear to global deflection (in the range of 10%-12%), the principle showed on Figure 3.3 can be applied to the tested panels with a low margin of error. When plotting the estimated ZSSL versus the time of fire exposure, a plot like the one showed in Figure 3.4 can be found. From Figure 3.4 it is clear that the ZSSL increases during time exposure, reaching values much higher than the constant 7 mm prescribed in the Eurocode 5. On the basis of Figure 3.3, values of ZSSL as a function of time are therefore suggested, in order to take into account the increasing heat flux received by the CLT panel during fire exposure. Finally, a simplified design approach can be obtained setting four values of zero stiffness layer for four ranges of time as in Table 3.1. The same principle can be applied to strength using the Eurocode 5 laws for tensile, compressive and shear strengths reduction factors k θ . With this approach, ZSTL for fire exposed members in tension, compression or submitted to shear as a function of time like the values presented in Table 3.2 can be derived.

Comparison of predicted deflection

The comparison between the predicted and experimental mid-span deflection for the three fire tests on CLT are showed from The advanced modeling based on reduced properties returns the mid-span deflection that less deviates from experimental results for the three tests. Moreover, contrary to RCSM approaches, it does not show plateau corresponding to the noncontribution of cross layers to global stiffness. This confirms that the actual phenomenon is a progressive reduction of properties and not a reduction of geometry. The RCSM-1 approach underestimates the deflection of the three fire tests. Despite of the falling-off effect in Test-1 highlighted in section 2.3, the RCSM-2 (derived to take into account such phenomenon) overestimates the Test-1 deflection. The deflection of Test-2 is underestimated by RCSM-2 due to the charring of almost only the first layer. Dealing with Test-3, the final part of the deflection evolution in Figure 4.3 clearly shows an increase of deflection when the char front passes from first to second layer and then the slope returns smooth, highlighting the falling-off phenomenon. Hence in this case the delamination phenomenon has an influence on global elastic response, contrary to Test-1 results. Therefore the reduced properties method, based on temperature prediction of solid wood without delamination, cannot correctly predict the deflection. In this case, the RCSM-2 and RCSM-3 seem to well reproduce the sharp increase of deflection, even if in a quite conservative way.

In the final parts of Figure 4.1 and Figure 4.2, all methods underestimate the deflection. This is because both of specimens were close to failure at those times exposure and hence the increasing non-linear contributions to deflection cannot be taken into account by the plate theory.

Discussion and Conclusion

In the present paper, the deflection of fire exposed CLT floors has been used to obtain information on the mechanical response during fire exposure. The experimental results have been compared to advanced modeling based on reduced properties and to the simplified RCSM of Eurocode 5. The advanced modeling globally returned a better agreement with test results than two existing RCSM approaches. However, the predicted results can be affected by the variation of material properties such as wood density, relative humidity and density. Unfortunately, the raw material of crosslam has not been tested and the input parameters for the modeling are based on mean properties given by C24 strength class in EN 338. Being the predicted deflection based on a linear elastic plate model, for a given variation of wood stiffness, the same variation of global deflection occurs. Dealing with the reduced properties modeling, further parameter studies not reported in this paper showed that the predicted temperature profiles by Safir software, and consequently the reduced stiffnesses, are strongly influenced by input wood density and RH. For instance, for a variation of 10% of wood density, a variation between 20% and 50% of the predicted deflection occurs, depending on the exposure time.

However, it is clear from section 4 that the RCSM based on reduced geometry deviates from experimental results. This is also due to the reduced properties after the char front taken into account by a constant value of zero stiffness layer. Such limitation can be improved when considering a ZSSL that varies during fire exposure, as showed in section 4.

The phenomenon of layers falling-off is a complex mechanism influenced by a multitude of parameters and therefore very difficult to predict. It can occur locally, with delamination of small pieces of wood, or with a complete falling-off of layer. The charring rate estimation with thermocouples registration presented in section 2.3 pointed out falling-off phenomena for the three considered test. However, only Test-3 showed an influence of such effect on the mid-span deflection evolution, while the other two tests showed no increase on deflection evolution. Hence, more research on influencing parameters on delamination phenomenon is needed.

The suggested improvement of RCSM is based on zero stiffness layer estimation as a function of time exposure. The fire design of timber members is often governed by ULS and therefore the determination of zero strength layer instead of zero stiffness layer has a great importance. However, dealing with panels' strength and loadcarrying capacity, a direct comparison with experimental results is not as simple as in the case of mid-span deflection. A starting point for future studies may be assuming a zero strength layer as a function of time derived as the zero stiffness layer in this paper. Therefore, values similar to those presented in Table 3.2 can be obtained. Of course, this approach needs further validation with advanced modeling and available experimental data, but it may be a research path to follow, considering also the ongoing revision process of the Eurocode 5.

Figure 2 . 1

 21 Figure 2.1 Residual cross section of the Test-1 floor

Figure 2

 2 Figure2.1 shows that there were no alteration of panels' supports geometry due to fire exposure, allowing therefore the hypothesis of respected simple supported boundary condition for the subsequent modeling step.

Figure 2 . 3

 23 Figure 2.3 Evolution of the measured temperature in Test-1 at 84mm from the bottom side for each of the nine sections and considered mean temperature (solid black line)

Figure 3 . 1

 31 Figure 3.1 Evolution of the predicted and measured temperatures within the floor of Test-1

Figure 3 . 2

 32 Figure 3.2 Eurocode 5 laws for the determination of reduction coefficient k θ for softwood stiffness

Figure 3 . 3

 33 Figure 3.3 Principle of the suggested derivation of the zero stiffness layer. θ = temperature

Figure 3 . 4

 34 Figure 3.4 Variation of the ZSSL during time exposure of Panel-1

  Figure 4.1 to Figure 4.3. As already introduced in 3.2, the RCSM-1 method is according to Schmid, 2012, the RCSM-2 is according to Frangi, 2009 and RCSM-3 considers the ZSSL as a function of time (Table3.1). For the three approaches based on reduced cross section, the ZSSL is computed as in the EC 5: ZSSL = k 0 •ZSSL, where k 0 = time/20 for time < 20 minutes and k 0 = 1 for time > 20 minutes.

Figure 4 . 1

 41 Figure 4.1 Comparison between predicted and experimental deflection of Test-1

  Figures 4.1 to 4.3 show that the RCSM of the Eurocode can be improved when considering a ZSSL as a function of time exposure.

Table 2 .

 2 1 Properties of the tested specimens of CLT floors

	Test number:	1	2	3
	Span L [m]	4.2	4.5	4.6
	Thickness H [mm]	195	160	182
	Load [kN]	40	40	60
	Kind of load	4-points	4-points Uniform
	N° of sections	9	1	4
	N° of thermocouples per section	9	4	10
	Time exposure [min]	150	86	90
	Safety criterion reached	Displacement rate	Failure	None

Table 2 .

 2 2 Charring rates of Test-1 during the fire test for the first four layers

		1100 1000 900		TC no. A05 TC no. B05 TC no. C05
	(°C) Temperature	300 400 500 600 800 700		TC no.D05 TC no.E05 TC no. F05 TC no. G05 TC no. H05 TC no.I05 Tmean-84mm
		200
		100
		0
		0	20	40	60	80	100	120	140	160
					Time (min)

Table 3

 3

		.1 Suggested values of ZSSL as a function of time exposure
	Time t (min)	0<t<20	20<t<40	40<t<60	> 60
	ZSSL (mm)	10	14	17	20

Table 3

 3

	.2 Variation of ZSTL as a function of time exposure for timber members in compression, ten-
			sion and shear
	ZSTL | Time	25 min	50 min	75 min	100 min
	Tension [mm]	9.6	12	13.5	14.5
	Compression [mm]	16	19.5	22	23
	Shear [mm]	13.5	17	19.5	20.5


Quelle autonomie dans le travail ? Par les marges ou par le centre, saisir l'aliéna8on et l'émancipa8on aujourd'hui Proposi8on de communica8on Autrice : Madeleine Sallus8o (CNRS, SciencesPo) Titre : L'autonomie comme privilège. Retour sur les enjeux d'émancipa8on du travail utopique en collec8f néo-paysan (France, Italie, Espagne) Résumé De nombreuses études en sciences sociales font aujourd'hui état de la volonté de « réinventer le travail » portée par les protagonistes du phénomène d'installa8on en communautés inten8onnelles en monde rural [START_REF] Lallement | Un désir d'égalité. Vivre et travailler dans des communautés utopiques[END_REF][START_REF] Pruvost | Chantiers participatifs, autogérés, collectifs : la politisation du moindre geste[END_REF][START_REF] Pruvost | L'alternative écologique. Vivre et travailler autrement[END_REF]Sallus8o, 2020 ;[START_REF] Samak | La politisation variable des alternatives agricoles[END_REF]. Ce phénomène social n'est pas spécifiquement récent. Déjà au XIXe et au XXe siècle, la campagne du nord de la France avait vu l'arrivée d'ac8vistes anarchistes fa8gués des luaes urbaines et désireux de construire des communautés exemplaires où la liberté et l'égalité entre les individus seraient effec8ves "ici et maintenant" [START_REF] Antony | Les communautés utopiques sont-elles toujours condamnées à disparaître ? Cahiers d'histoire[END_REF][START_REF] Baubérot | Aux sources de l'écologisme anarchiste : Louis Rimbault et les communautés végétaliennes en France dans la première moitié du XXe siècle[END_REF][START_REF] Legendre | Expériences de vie communautaire anarchiste en France[END_REF]Pe8gils, 2011 ;[START_REF] Steiner | Vivre l'anarchie ici et maintenant : milieux libres et colonies libertaires à la Belle Époque[END_REF]. En France, ce sont cependant les mouvements communautaires post-Mai 68 qui ont eu le plus d'impact sur l'opinion publique et la sphère scien8fique [START_REF] Chevalier | Les phénomènes néo-ruraux[END_REF][START_REF] Léger | Des communautés pour les temps difficiles. Néo-ruraux ou nouveaux moines[END_REF][START_REF] Léger | Le retour à la nature[END_REF][START_REF] Stuppia | La révolution dans le jardin. Utopies communautaires et expériences néorurales françaises après Mai 68[END_REF].

Aujourd'hui, les mouvements visant à créer des collectifs agricoles à la campagne continuent de se développer, mais cette fois-ci ils sont motivés par des préoccupations liées à la crise climatique, à la méfiance envers l'État et aux luttes de pouvoir organisées [START_REF] Verdier | Éditorial : L'autonomie-en-commun au XXIème siècle[END_REF], ainsi que par une préoccupation pour l'autonomisation à travers une remise en question de la valeur du travail et du salariat. En créant des collectifs autogérés, ils cherchent à gagner en autonomie, c'est-à-dire non seulement dans l'idée de 1) produire une grande partie de leurs besoins quotidiens (alimentation, logement, mécanique automobile), mais aussi 2) développer des compétences qui dépassent la logique de la spécialisation du travail ou 3) vivre et travailler selon des "temps choisis" (Grossin, 1996 : 246-247). Ensemble, ces personnes cherchent à mutualiser, à subvertir la propriété privée et à s'organiser de manière horizontale, non autoritaire et en permanente discussion.

Cette contribution est basée sur un terrain multi-situé en France, en Italie et en Espagne, réalisé en observation participante au sein de collectifs néo-paysans autogérés. La conférence proposée sera organisée en deux parties. Tout d'abord, je discuterai de la critique de l'organisation du travail et de la valeur du travail qui anime ces installations. Nous verrons comment ces acteurs refusent d'utiliser le terme "travail" pour parler de leur projet de jardinage, d'élevage, de construction, de transformation de produits ou d'artisanat en tout genre. Ce terme est en effet lié à une conception intrinsèquement douloureuse et aliénante. Inspirés par le mode de vie présumé de la paysannerie traditionnelle, ces personnes cherchent à vivre "l'unité du travail et de la vie" (Gorz, 1988 : 97), donnant ainsi un sens à toutes les actions qu'elles accomplissent au quotidien [START_REF] Arnsperger | Éthique de l'existence post-capitaliste[END_REF][START_REF] Pruvost | Chantiers participatifs, autogérés, collectifs : la politisation du moindre geste[END_REF].

Ensuite, je détaillerai la confrontation de ces idéaux avec la réalité du travail agricole et de la vie collective quotidienne. À partir d'exemples ethnographiques, je démontrerai comment réapparaissent des normes qui valorisent la proactivité au travail, même si elles étaient destinées à être déconstruites [START_REF] Boulier | Autogestion et réalisation utopiques[END_REF][START_REF] Cingolani | Un travail sans limites? subordination, tensions, résistances, Clinique du travail[END_REF][START_REF] Samak | Travail et emploi ruraux » -Le prix du « retour » chez les agriculteurs[END_REF]. Nous verrons en particulier comment ces normes entachent la légitimité des acteurs au sein des groupes, en particulier les femmes avec des enfants. La valorisation de la présence et de la proactivité au sein du groupe, du travail physique, de l'effort et du manque de confort contribue en effet parfois à établir une valorisation d'une relation virile à la vie et au travail [START_REF] Fourment | Femmes en noir. Stéréotypes de genre dans les black blocs[END_REF]. Comme c'est courant dans le secteur associatif [START_REF] Hély | Splendeurs et misères du travail associatif[END_REF], nous verrons également comment le refus de considérer les activités réalisées comme du "travail" a une influence sur l'épuisement et les conditions de travail générales des acteurs ainsi que sur la sécurité économique que peuvent garantir ces espaces. Cela conduit à une grande instabilité des populations au sein de ces groupes, à la reproduction de rapports de genre inégalitaires, à une désertion des habitants plus âgés et l'absence de classe moyenne ascendante au sein de ces groupes. Nous conclurons sur l'intérêt d'étudier ces expériences sociales, bien que marginales, pour réfléchir à la réconciliation des luttes sociales liées à l'émancipation au travail.


Théophile Kurtz
email: theophile.kurtz@univ-eiffel.fr

Y Godio-Raboutet
email: yves.godio-raboutet@univ-eiffel.fr

J.-L Tailhan
email: jean-louis.tailhan@univ-eiffel.fr

"Propagation de fissure sur tronçon d'os long rainuré" [1] Crack propagation in grooved long bone segment

Keywords: Mechanical test, Crack propagation, Three-point bending, Cortical bone

come

Introduction

The skeleton is the framework that ensures the physical integrity of the human body. It is subjected to different loads during the daily life and can fracture. This quasi-fragile biological tissue has a hierarchical and multi-scale internal structure, as well as a high degree of heterogeneity. It is also characterized by a significant variability between subjects [START_REF] Rho | Mechanical properties and the hierarchical structure of bone[END_REF] and within subjects. The study of fracture properties, particularly through tests on the initiation and propagation of cracks in human bone tissue, represents a vast area of study within the field of biomechanics. These tests serve, on one hand, to illustrate and understand the physical mechanisms [START_REF] Behiri | Fracture mechanics of bone-The effects of density, specimen thickness and crack velocity on longitudinal fracture[END_REF][START_REF] Zioupos | The extent of microcracking and the morphology of microcracks in damaged bone[END_REF][START_REF] Nalla | On the origin of the toughness of mineralized tissue: microcracking or crack bridging?[END_REF][START_REF] Granke | Prevalent role of porosity and osteonal area over mineralization heterogeneity in the fracture toughness of human cortical bone[END_REF][START_REF] Phelps | Microstructural heterogeneity and the fracture toughness of bone[END_REF], and on the other hand, to determine mechanical properties such as strength and toughness [START_REF] Behiri | Fracture mechanics of bone-The effects of density, specimen thickness and crack velocity on longitudinal fracture[END_REF][START_REF] Vashishth | Crack growth resistance in cortical bone: Concept of microcrack toughening[END_REF][START_REF] Li | Silberschmidt. Analysis of fracture processes in cortical bone tissue[END_REF][START_REF] Zioupos | Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure[END_REF][START_REF] Giner | Calculation of the critical energy release rate Gc of the cement line in cortical bone combining experimental tests and finite element models[END_REF][START_REF] Morais | The double cantilever beam test applied to mode I fracture characterization of cortical bone tissue[END_REF]. These data are essential for the development of cracking models. However, the majority of them are conducted on machined specimens with controlled and small dimensions, thus not taking into account the unique morphology of the bone.

The test presented, whose initial developments were published in [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF], focuses on the study of the propagation of a macrocrack in a section of a long human bone segment. Working at this scale has the advantage of not requiring specific tooling for specimen fabrication and simplifying their realization. However, the major drawbacks include: (i) the control of the boundary conditions of a specimen with irregular geometry and (ii) the post-processing of results for the determination of mechanical parameters with the 3D reconstruction of a biofidelic numerical model of the test.

The test involves a three-point bending on a bone segment, pre-notched at mid-span. Fine control of crack propagation is ensured by indirect control of the press cylinder using the measurement of the notch opening. Furthermore, a modification to the original test [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF] is proposed to maintain a transverse propagation of the macrocrack. To achieve this, it is necessary to modify the stress field with two possible choices: either orthoradially prestrain1 the specimen or locally reduce its central section. The latter option was chosen for its technical simplicity, involving machining a hemispherical groove around the outer surface of the bone in the notch section. Simultaneously, significant improvements in the reproducibility and repeatability of the test have also been made. The primary goal of interpreting the obtained results is to better understand the physical mechanisms involved in the transverse fracture of bone.

Materials and methods

Sampling and preservation

The femurs are harvested from Post-Mortem Human Subjects (PMHS), initially embalmed by injecting a solution of zinc chloride, except for specimen 150-17D, embalmed with formaldehyde. Tissue manipulations are carried out under the ethical supervision of the Faculty of Medicine of Marseille. Data related to the subjects are summarized in table 1.

The tissues are cleaned and degreased manually, removing connective tissues with hot water, without the use of chemicals. The femoral bone is then cut in the diaphysis to obtain a 180 mm section. For the sake of simplification, the study focuses on cortical tissue (future work will focus on the fracture behavior of trabecular bone). Trabecular bone and marrow are manually removed by scraping.

The bones are stored in a freezer at a controlled temperature of -18°C. On the day before a test, the specimen is stored in a refrigerator at 4°C. The preparation, instrumentation, and adjustment phases are carried out at room temperature (20°C). After the test, the broken specimen is once again stored at -18°C.

Preparation of a sample

On the day of the test, the specimen, which has been thawed the day before, is positioned on the test rig. To ensure reproducibility of the test, each bone is tested in the same orientation relative to common anatomical features. The load is applied on the rough line (linea aspera) of the femoral section, at the level of the central cross-sectional area. The anterior face of the bone is oriented towards the supports. This sample position is chosen because it is naturally the most stable.

Due to the irregular and variable geometry of the samples, small parallelepipedic metal prisms (7mm x 5mm x 20mm) are bonded with cyanoacrylate adhesive to locally distribute the stresses to the supports and prevent tilting of the specimen. The bonding is carried out under the press directly, with a load of 30 N, to ensure they remain tangent to the anterior face of the bone. Their positioning and longitudinal alignment are ensured by a 3D-printed guide with reference to the loading head. To avoid any detrimental friction at the supports and ensure proper functioning in simple bending of the bone, it should be noted that one of the prisms is designed to be "sliding." It is actually composed of two half-blocks (sliding relative to each other). The contact surfaces of the two half-blocks are machined, polished, and lubricated2 . The assembly is held in place by an elastic membrane, which also ensures elastic return to the initial position during unloading of the specimen.

Once the supports are glued, a notch with a thickness of 200 µm is machined in the central section of the bone using a scroll saw. The bone is positioned on a carriage guided on the saw table. Its position on this carriage is adjusted using a 3D-printed piece simulating, identically, the positions of the press supports and the loading head. A 7.5 mm slip gauge is used to set the stops of the carriage on the saw table and fix the depth of the notch machining.

To guide the macrocrack in the transverse direction, a semi-circular section groove is milled around the external surface at the notch section. It is crucial to ensure a constant depth of 2 mm. The tool used is a tungsten carbide spherical cutter, Dremel 225. A 3D-printed cap is screwed onto the manual support of the cutter and slightly protrudes. The depth is calibrated with a 2 mm standard shim. The particularity of the cap is its semi-spherical shape, ensuring a constant machining depth on the bone despite the irregular geometry of its external surface. This step is carried out under a water jet to avoid necrosing the bone tissue and risking excessive alteration of its properties.

The sensor measuring the notch opening must be attached to aluminum supports bonded to the bone. A new guide, also 3D-printed, holds these sensor supports in the bonding position and adjusts their alignment with respect to the metal supports. A point of cyanoacrylate adhesive is deposited on the surface of the supports. The anterior face of the bone section is then placed on the guide so that the supports are positioned on either side of the notch and aligned with the supports. This crucial step ensures proper positioning of the assembly for all tests.

Once all these steps are completed, the specimen is finally positioned on the test rig.

Mechanical test

The three-point bending mechanical test is conducted on an MTS Landmark 370.10 hydraulic press equipped with a 15 kN force sensor. The span between the supports of the press is 155 mm. A KA-MAN KD-2300 inductive displacement sensor, with a measurement range of 0-2 mm, measures the Notch Opening Displacement (NOD). This sensor measures the relative distance between its support and a target glued to the opposing support. Both supports are made of aluminum to avoid creating electromagnetic disturbances that could affect the measurement. Figure 1 shows the test setup.

The quantities measured during the test are:

• The applied load in N

• The NOD in mm

The experimental procedure follows the steps defined in [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF]. It involves loading the specimen at its center and applying ten cycles of unloading-reloading during the test. The loading is driven via the notch opening at a speed of 36 µm/min, considered quasi-static. The effects of loading speed are not evaluated in this study and should be part of a separate investigation. The cycles step is 200 µm from 0 up to 2 mm. The unloading is force-driven to reach 15 N within 5 minutes.

Analysis of the results

The results are processed and analyzed in the same manner as in [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF] to compare notched tests with non-notched tests. The study focuses on the following elements:

• The overall shape of the curve,

• The evolution of the stiffness of the specimen,

• The evolution of the residual notch opening,

• The shape of the imposed cycles.

For a complete analysis methodology, we invite the reader to refer to the details provided in [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF]. However, we emphasize that the evolution of stiffness during loading can be obtained through an analysis of the slopes of the different cycles imposed during a test. It has been chosen, and justified in [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF], to consider the measurement of the slope of the reloading path of a cycle to evaluate the structural stiffness of the bone, relative to the considered cycle. The evolution of stiffness is studied through the evolution of the relative stiffness reduction coefficient (W) defined in [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF] as the relative difference in stiffness compared to the initial stiffness. Its expression is recalled below:

W = 1 - K K 0 (1)
We also remind that the measurement of the residual notch opening is obtained for each cycle by extrapolating (linearly) to 0 the unloading path of the considered cycle.

Finally, the shape of the cycles is analyzed in relation to the evolution of their widths during the test.

The width of a cycle is calculated as the quotient of its area by the amplitude of the imposed force [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF].

Results

The raw results are expressed in terms of overall Force (P ) versus Notch Opening (ω) curves, as shown in figure 2. Table 2 provides the maximum force values for each bone.

Figure 3 compiles the final crack paths for each conducted test. The views were captured using magnifying cameras (Dynolite USB microscopes) positioned on the lateral and medial sides of the bones. It is worth noting that, given the quasi-cylindrical shape of the bones, the cracking process initially localizes at the notch tip during the test and then propagates simultaneously in the lateral and medial portions before eventually converging towards the rough line. Although there are initially two cracks, lateral and medial, they are considered as a single cracking process, and the results are analyzed accordingly.

Discussion

Analysis of load vs notch opening (NOD) curves

The examination of the curves in figure 2 reveals that they all have similar shapes. Three phases can be distinguished:

• In their pre-peak regions, the obtained curves show evident nonlinearities. However, these are relatively weak from 0 to approximately 70% of the maximum force (see table 2). Subsequently, around 80 to 85% of the maximum force, these nonlinearities intensify more markedly, leading to the peak. These nonlinearities are indicative of physical processes corresponding to the formation of the Fracture Process Zone (FPZ) at the notch tip [START_REF] Willett | The microdamage process zone during transverse cortical bone fracture: No ears at crack growth initiation[END_REF][START_REF] Behiri | Fracture mechanics of bone-The effects of density, specimen thickness and crack velocity on longitudinal fracture[END_REF][START_REF] Vashishth | Crack growth resistance in cortical bone: Concept of microcrack toughening[END_REF][START_REF] Piekarski | Fracture of Bone[END_REF][START_REF] Bonfield | Advances in the fracture mechanics of cortical bone[END_REF][START_REF] Parsamian | Diffuse damage accumulation in the fracture process zone of human cortical bone specimens and its influence on fracture toughness[END_REF], where stresses are concentrated. The literature has extensively detailed their potential origins, all related to phenomena affecting each scale of the material's microstructure [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF]. We will mainly highlight that microcracks (in the range of 10 to 200 µm) appear at the notch tip, and this zone grows as the loading progresses.

• Around the loading peak, the densification and coalescence of these microcracks generate a macrocrack. At this stage, larger microstructural elements (porosity: Haversian and Volkmann canals, resorption cavity/interlamellar zone/cement lines, and osteonal structures) come into play and influence the crack propagation path [START_REF] Willett | The microdamage process zone during transverse cortical bone fracture: No ears at crack growth initiation[END_REF][START_REF] Zioupos | The extent of microcracking and the morphology of microcracks in damaged bone[END_REF][START_REF] Li | Silberschmidt. Analysis of fracture processes in cortical bone tissue[END_REF][START_REF] Parsamian | Diffuse damage accumulation in the fracture process zone of human cortical bone specimens and its influence on fracture toughness[END_REF].

• In the post-peak region, the localized macrocrack propagates with its associated FPZ. The FPZ reaches its maximum size in this post-peak phase, sometimes slightly after the peak, and maintains a constant shape if not influenced by the proximity of boundary conditions. In this softening phase, the propagation of the macrocrack results in the gradual loss of load-bearing capacity of the bone [START_REF] Behiri | Fracture mechanics of bone-The effects of density, specimen thickness and crack velocity on longitudinal fracture[END_REF][START_REF] Bonfield | Advances in the fracture mechanics of cortical bone[END_REF][START_REF] Parsamian | Diffuse damage accumulation in the fracture process zone of human cortical bone specimens and its influence on fracture toughness[END_REF].

In conclusion, two regimes can be considered in the cracking processes. In the pre-peak phase, these processes are dominated by the progressive diffusion of micro-damages (microcracking leading to material damage) at the notch tip. In the post-peak phase, they are dominated by the propagation of the macrocrack and its associated FPZ, leading to structural weakening.

It is also important to note that the observed dispersion in the overall curves, especially concerning their peaks and post-peaks, is related both to the different bone geometries and differences in internal microstructures [START_REF] Rho | Mechanical properties and the hierarchical structure of bone[END_REF][START_REF] Granke | Prevalent role of porosity and osteonal area over mineralization heterogeneity in the fracture toughness of human cortical bone[END_REF][START_REF] Martin | Fatigue and Fracture Resistance of Bone[END_REF].

Crack paths analysis

Figure 3 shows the macrocrack propagation paths obtained for different conducted tests (notched and non-notched). The best result on notched bone is in the case of specimen 15017D, where the macrocrack remains entirely confined within the notch. In other samples, the macrocrack exits the notch but still maintains a predominant orientation in the vertical direction (see sample 9021D in figure 3). No mechanism showing the influence of this exit from the groove is particularly visible on the experimental curves in figure 2. There is also no notable difference between the crack paths on the lateral and medial sides: the macrocrack can exit on either side, but it consistently tends to go slightly in the distal direction (towards the knee). This trend was already present in non-notched bones, where the crack consistently propagated in this direction. It is also noteworthy that the crack exits the groove always after traveling a minimum distance of 5 to 10 mm inside the groove. In the case of non-notched tests (like sample 5320D in figure 3), the bifurcation of the macrocrack almost systematically occurred at the notch origin. The exit of the macrocrack is likely related to the fact that the notches may not be deep enough to sufficiently concentrate stresses and guide the crack. However, the choice of a depth of approximately 2 mm is a good compromise between providing sufficient action to keep the crack in a transverse orientation and having a minimal impact on the overall behavior of the bone.

Determination of the initial stiffnesses

As mentioned earlier, the overall curves in figure 2 start with a quasi-linear portion, and it is possible to calculate the slope of this section. The measurement of this slope provides the initial stiffness of the bone. The values obtained for each tested bone are indicated in table 2. The initial stiffness primarily depends on the microstructure and geometry of each specimen.

Evolution of the stiffnesses

Figure 4 represents the evolution of the stiffness reduction coefficient (W) as a function of the imposed notch opening in the considered cycle. The average value of W reached at the peaks of the tests is 0.36. It can also be observed that these curves reach their asymptote W=1 more quickly than that in [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF]. This is clearly related to the presence of the notch, which forces transverse crack propagation and promotes a greater reduction in section than when the crack is deviated.

Evolution of the residual notch openings

The evolution of residual notch openings is plotted in figure 5 as a function of the imposed notch opening in the considered cycle. The curves show that nonlinear mechanisms lead to residual deformations after unloading. It should be noted that it has been demonstrated in [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF] that these phenomena are visible for a notch opening of approximately 0.1 mm and negligible below that value. It is also noticeable that the results are relatively similar between the two types of tests (notched and non-notched). This indicates that the mechanisms inducing natural deformation are of the same nature and magnitude.

Figure 6 presents the evolution of residual notch opening as a function of W. Similarly to [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF], the extrapolation to the origin of the curves indicates that residual notch openings are negligible for W=0.

It is inferred that the cracking processes are the main cause of residual deformations. The observed differences with non-notched tests are primarily due to a different evolution of W for the two types of tests.

Cycle's shape

The unloading/reloading cycles exhibit a characteristic closed-loop shape. This particular form indicates the involvement of dissipative phenomena, primarily attributed to blockages related to crack interlocking and friction between the lips of the macrocrack and within the microcracks of the FPZ [START_REF] Acker | On the importance of initial stresses in concrete and of the resulting mechanical effects[END_REF]. It is also noted that the reloading path does not pass through the unloading point that initiated the cycle.

Figure 7 shows the evolution of the cycle width as a function of the imposed notch opening in the considered cycle. It is observed that the obtained curves are very close to the envelope of those in [START_REF] Tailhan | Macrocrack propagation in a notched shaft segment of human long bone: Experimental results and mechanical aspects[END_REF], indicating similar mechanisms of the same magnitude.

Physical mechanisms

The obtained results are attributed to crack-related phenomena. Crack formation induces a progressive structural weakening (W increases, cf. figure 4) of the bone segments during loading. These phenomena are also responsible for residual deformations, as there is a concurrent evolution of residual deformation with W (cf. figure 6). Furthermore, the results show that no plasticity is observable at this scale. While friction and blockage phenomena related to cracking may partially explain the residual deformations, they are not sufficient to fully account for the observed significant levels. Another mechanism (amplifier) operates simultaneously. It could involve a stress relaxation phenomenon during crack formation, preventing their complete closure during unloading and explaining a significant portion of the residual deformations. The existence of internal stresses in the bone tissue is explanable with the bone remodeling mechanism, as demonstrated in the literature [START_REF] Tanaka | Bone remodeling considering residual stress: Preliminary experimental observation and theoretical model development[END_REF][START_REF] Tadano | Residual stress in bone structure and tissue of rabbit's tibiofibula[END_REF][START_REF] Hadjidakis | Bone Remodeling[END_REF]. This internal stress field is also highly heterogeneous, reflecting the nature of the material in which it developed. The release of internal stresses also helps explain the amplification of friction and interlocking phenomena influencing the shape of the cycles. It also explains why the reloading path of a cycle does not pass through the unloading point that initiated it (due to modifications in the cycle's stress field history during reloading).

Conclusion

A three-point bending mechanical test on a section of notched human bone is employed to investigate the propagation of a macrocrack in this type of tissue. The test is adapted to induce transverse crack propagation. The simplest guiding solution chosen involves creating a groove on the external lateral surface of the bone. The preparation of the specimen and its positioning on the machine received special attention to ensure a robust and repeatable experimental protocol. Unloading/reloading cycles show a decrease in the structural stiffness of the bone, a significant residual opening of the notch, and significant dissipative phenomena during the cycles. These observations are explained by the combined action of crack processes in a heterogeneous medium initially subjected to self-balanced internal stresses, a consequence of the bone remodeling mechanism. When a crack is created, it releases these stresses, locally disrupting the stress field (heterogeneous), preventing complete closure, and generating additional friction and amplified residual deformations. All the obtained results, in the form of relatively tight bundles of curves, show that the transverse guiding solution for the macrocrack, while not perfect, remains highly satisfactory.

It is also noteworthy that these tests will be subsequently used for the determination, through inverse analysis, of fracture mechanical properties in the transverse direction.

Figure 1 :

 1 Figure 1: Three-point bending test with indirect control by notch opening. 1) Loading head, 2) Fixed support, 3) Sliding support, 4) Notch and groove (zoom on right figure) and 5) Inductive sensor. From [17].

Figure 2 :

 2 Figure 2: Crack propagation curves -Load vs NOD.

Figure 3 :

 3 Figure 3: Crack propagation paths on each specimen. L and M correspond to the lateral and medial sides of the bone, respectively. The images of specimen 5320 are sourced from [3].

Figure 4 :

 4 Figure 4: Decrease in the stiffness coefficient (W) as a function of the imposed cycle in NOD. The crosses represent the values at the loading peak for each bone. The gray zone corresponds to the overall envelope of similar curves from [3] for non-notched bones.

Figure 5 :

 5 Figure 5: Evolution of the residual NOD as a function of the imposed cycle in NOD. The crosses represent the values at the loading peak for each bone. The gray zone corresponds to the overall envelope of similar curves from [3] for non-notched bones.

Figure 6 :

 6 Figure 6: Evolution of the residual NOD as a function of the stiffness coefficient (W). The crosses represent the values at the loading peak for each bone. The gray zone corresponds to the overall envelope of similar curves from [3] for non-notched bones.

Figure 7 :

 7 Figure 7: Cycle width as a function of the the imposed cycle in NOD. The crosses represent the values at the loading peak for each bone. The gray zone corresponds to the overall envelope of similar curves from [3] for non-notched bones.

Table 1 :

 1

	Subject's references: Age (years), Sex (F for female, M for male), Laterality (femur of origin,
	left (G) or right (D)
	Subject Age (years) Sex Laterality
	150-17D	83	F	Right
	61-21G	82	M	Left
	90-21D	70	M	Right
	43-20G	73	M	Left
	80-21D	86	M	Right

Table 2 :

 2 Maximum forces reached for each specimen (NOD = notch opening displacement measured at the KAMAN KD 2300 inductive sensor.).

	Reference	Max load [N]	NOD [mm]	Initial stiffness [N/mm]
	150-17D	2591.2	0.40	10700
	61-21G	2393.8	0.32	13127
	90-21D	3848.7	0.30	17300
	43-20G	2696.1	0.43	11070
	80-21D	3400.6	0.37	15600

In compression.

With lithium grease.


Activism, strategies, and social structures The paradoxical future temporalities of neo-peasant community projects. For an anthropology of incoherence

MANCEPT 2023 Workshop: Activism, strategies, and social structures

The paradoxical future temporalities of neo-peasant community projects.

For an anthropology of incoherence.

Abstract : Studying people's relationships to the future and how these shape emotional states (individual or collective) is useful for understanding what motivates social practices (Appadurai, 2013;[START_REF] Persoon | The study of the suture in anthropology in relation to the sustainability debate[END_REF][START_REF] Pels | Modern Times: Seven Steps toward an Anthropology of the Future[END_REF]Bryant and Knight, 2019). In this paper, I propose to study how the collapse theories feed the imagination of some protagonists of the "back to the land" phenomenon. Based on long-term fieldwork among a dozen neo-farming collectives in the Massif Central (France), I will mobilise the paradigm of multiple temporalities and attempt to qualify the effects of this catastrophic and dystopian projection on the daily lives of its members.

These neo-peasant collectives are inspired by libertarian anarchism and settle in the French countryside since the end of Mai 68 to develop agricultural projects based on the mutualisation of property and tools of production. They set up practices of food self-sufficiency (market gardening, animal husbandry, processing of products) and deploy emancipatory practices linked to self-construction, mechanics, collective anti-authoritarian organisation, and are part of networks of initiatives that wish to be subversive of capitalism and the State [START_REF] Pruvost | L'alternative écologique. Vivre et travailler autrement[END_REF][START_REF] Sallustio | A la recherche de l'écologie temporelle[END_REF]. I will argue that the projects aiming at rural withdrawal and food autonomy are part of a paradoxical "presentist" [START_REF] Hartog | Régimes d'historicité[END_REF] temporality that manifests itself in the existence of antinomic "temporal horizons" [START_REF] Koselleck | Le Futur Passé. Contribution à La Sémantique Des Temps Historiques[END_REF], both pessimistic and optimistic with regard to the future and the social struggle. Their refusal of great, coherent and linear narratives about social transformation and strategic universal struggle allow me to feed the reflections on human action and the relationship to the social and environmental crisis. Indeed, studying how people relate to the future and how it shapes emotional states (individual or collective) is a way to grasp the configuration of the social world and to improve the understanding of the contemporary dialectic. The "back to the land" movement in France is indeed the manifestation of an abandon of strategic and long-term organised struggle. By favourishing the "here and now" perspective for social transformation, they are confronted with the instability of their projects and choose to "stay with the trouble" [START_REF] Haraway | Making Kin in the Chthulucene[END_REF].

Based on this fieldwork, I will propose a broader epistemological discussion related to how anthropology has historically grasp incoherences and contradictions and, with a critique of the bias of homogenisation and ontologisation of the representation of time in anthropology, I will stand for the paradigm of the multiplicity of temporalities.