,
,
, Contact Dynamics-based Method
, Comparison between the three methods
, Determination of the stress distribution in assemblies of photoelastic particles, Experimental Mechanics, vol.22, issue.9, pp.336-341, 1982.
, Experimental micromechanics : grain-scale observation of sand deformation, Géotechnique Letters, vol.2, issue.3, pp.107-112, 2012.
, Granular element method (GEM): Linking interparticle forces with macroscopic loading, Granular Matter, vol.14, issue.1, pp.51-61, 2012.
, Multiscale modeling and characterization of granular matter: From grain kinematics to continuum mechanics, Journal of the Mechanics and Physics of Solids, vol.59, issue.2, pp.237-250, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00555381
, Force distributions in three-dimensional granular assemblies : Effects of packing order and interparticle friction, Physical Review E, vol.63, issue.4, pp.1-8, 2001.
, Experimental micromechanical analysis of a 2D granular material: Relation between structure evolution and loading path, Mechanics of Cohesive-Frictional Materials, vol.2, pp.121-163, 1997.
, Applications of digital-imagecorrelation techniques to experimental mechanics, Experimental Mechanics, vol.25, issue.3, pp.232-244, 1985.
, Dynamics of drag and force distributions for projectile impact in a granular medium, Physical Review Letters, vol.92, issue.19, pp.1-4, 2004.
, TRACKER: A particle image tracking (PIT) technique dedicated to nonsmooth motions involved in granular packings, AIP Conference Proceedings, vol.1542, pp.461-464, 2013.
, Experimental Validation of a Nonextensive Scaling Law in Confined Granular Media, Physical Review Letters, vol.115, issue.23, pp.1-5, 2015.
, Construction of granular assemblies under static loading, Discrete-element Modeling of Granular Materials, chapter 6, pp.171-201, 2011.
, Model for Force Fluctuations in Bead Packs, Physical Review E, vol.53, issue.5, pp.4673-4685, 1996.
, A discrete numerical model for granular assemblies, Géotechnique, vol.29, pp.47-65, 1979.
, Rheophysics of dense granular materials: Discrete simulation of plane shear flows, Nonlinear, and Soft Matter Physics, vol.72, issue.2, pp.1-17, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01990685
, Photoelastic force measurements in granular materials, Review of Scientific Instruments, vol.88, issue.5, p.51808, 2017.
, Contribution à l'étude mécanique et géométrique des milieux pulvérulents, Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering, 1957.
, Shaft friction changes for cyclically loaded displacement piles: an X-ray investigation, Géotechnique Letters, vol.8, issue.1, pp.1-7, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01995997
, Can intergranular force transmission be identified in sand? First results of spatiallyresolved neutron and X-ray diffraction, Granular Matter, vol.13, issue.3, pp.251-254, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01571002
, Three dimensional fabric evolution of sheared sand, Granular Matter, vol.14, issue.4, pp.469-482, 2012.
, Quantifying Interparticle Forces and Heterogeneity in 3D Granular Materials, Physical Review Letters, vol.117, issue.9, pp.1-5, 2016.
, Dynamic InterParticle Force Inference in Granular Materials: Method and Application, Experimental Mechanics, vol.56, issue.2, pp.217-229, 2016.
, Unilaterality and granular friction in the dynamics of rigid body collections, Proceedings of the Contacy Mechanics International Symposium. Presses Polytechniques Universitaires Romandes, 1992.
, 1?2?: A new shear apparatus to study the behavior of granular materials, Geotechnical Testing Journal, vol.15, p.129, 1992.
, Evaluation of energy contributions using inter-particle forces in granular materials under impact loading, Granular Matter, vol.19, issue.2, pp.1-20, 2017.
, Evolution of deformation and breakage in sand studied using X-ray tomography, Géotechnique, vol.68, issue.2, pp.107-117, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02083355
, All you need is shape: Predicting shear banding in sand with LS-DEM, Journal of the Mechanics and Physics of Solids, vol.111, pp.375-392, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01665568
, Study and generation of optimal speckle patterns for DIC, Proceedings of the annual conference and exposition on experimental and applied mechanics, pp.1643-1652, 2007.
, Force fluctuations in bead packs, Science, vol.269, p.513, 1995.
, Towards Measuring Intergranular Force Transmission Using Confocal Microscopy and Digital Volume Correlation, Advancement of Optical Methods in Experimental Mechanics, vol.3, 2018.
, Contact force measurements and stressinduced anisotropy in granular materials, Nature, vol.435, issue.7045, pp.1079-1082, 2005.
, A novel experimental device for investigating the multiscale behavior of granular materials under shear, Granular Matter, vol.19, issue.4, pp.1-12, 2017.
, Indeterminacy and the onset of motion in a simple granular packing, Physical Review E, vol.72, issue.2, pp.1-12, 2005.
, Measurement of indeterminacy in packings of perfectly rigid disks, Physical Review E-Statistical, Nonlinear, and Soft Matter Physics, vol.70, issue.6, pp.1-12, 2004.
, Evolution problem associated with a moving convex set in a hilbert space, Journal of Differential Equations, vol.13, p.347374, 1977.
URL : https://hal.archives-ouvertes.fr/hal-01660021
, Liasons unilatérales sans frottement et chocs inélastiques. Comptes Rendus de l'Académie des Sciences, vol.296, p.14731476, 1983.
, Bounded variation in time, Topics in Nonsmooth Mechanics, p.174, 1988.
URL : https://hal.archives-ouvertes.fr/hal-01363799
, Unilateral contact and dry friction in finite freedom dynamics. In International Centre for Mechanical Sciences, Courses and Lectures, vol.302, 1988.
URL : https://hal.archives-ouvertes.fr/hal-01713847
, Some numerical methods in multibody dynamics: Application to granular materials, European Journal of Mechanics-A/Solids, vol.13, issue.4, pp.93-114, 1994.
, Numerical investigation of shear zones in granular materials, Friction Arching Contact Dynamics, p.233247, 1997.
URL : https://hal.archives-ouvertes.fr/hal-01825188
, An introduction to unilateral dynamics, Novel approaches in civil engineering, pp.1-46, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01824568
, Stress transmission through three-dimensional ordered granular arrays, Physical Review E, vol.66, pp.1-9, 2002.
, Force distribution in a granular medium, Physical Review E, vol.57, issue.3, pp.3164-3169, 1998.
, Stresses in granular materials, Granular Matter, vol.13, issue.4, pp.395-415, 2011.
, Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review, Measurement Science and Technology, issue.6, p.20, 2009.
, Nonsmoothness, indeterminacy, and friction in two-dimensional arrays of rigid particles, Physical review E, vol.54, issue.1, pp.861-873, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00759667
, Force Distributions in Dense Two-Dimensional Granular Systems, Physical Review Letters, vol.77, issue.2, pp.274-277, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00759668
, Contact dynamics as a nonsmooth discrete element method, Mechanics of Materials, vol.41, issue.6, pp.715-728, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00689866
, Modeling Granular Materials: CenturyLong Research across Scales, J. Eng. Mech, vol.143, issue.4, p.4017002, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01699485
, Turbulentlike fluctuations in quasistatic flow of granular media, Physical Review Letters, vol.89, issue.6, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00122057
, Contact forces in a granular packing, Chaos, vol.9, issue.3, pp.544-550, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01407368
, An Attempt in Assessing Contact Forces From a Kinematic Field, AIP Conference Proceedings, vol.1542, p.429, 2013.
, An experimental assessment of displacement fluctuations in a 2D granular material subjected to shear, Géotechnique Letters, vol.2, pp.113-118, 2012.
, Analytical study of induced anisotropy in idealized granular materials, Géotechnique, vol.39, issue.4, pp.601-614, 1989.
, Geometric origin of mechanical properties of granular materials, Physical Review E, vol.61, issue.6, pp.6802-6836, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00126196
, Dimensional Analysis and Control Parameters, Discrete-element Modeling of Granular Materials, chapter 8, pp.83-116, 2011.
, Quasistatic methods, Discrete-element Modeling of Granular Materials, chapter 3, pp.83-116, 2011.
, Mapping forces in a 3D elastic assembly of grains, Journal of the Mechanics and Physics of Solids, vol.60, issue.1, pp.55-66, 2012.
, Une analogie mécanique pour les terres sans cohésion, Comptes Rendus de l'Academie des Sciences, vol.243, issue.1, pp.125-126, 1956.
, Une analogie mécanique pour l'étude de la stabilité des ouvrages en terre à deux dimensions, Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering, 1957.
, Experimental investigation of mode I fracture for brittle tube-shaped particles, EPJ Web of Conferences. Powders and grains, vol.07015, pp.4-7, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02007564
, Old Earth Pressure Theories and New Test Results. Engineering News-Record, vol.85, pp.632-637, 1920.
, On the modelling of confined buckling of force chains, Journal of the Mechanics and Physics of Solids, vol.57, p.706727, 2009.
, Buckling force chains in dense granular assemblies: physical and numerical experiments, Geomechanics and Geoengineering, vol.4, p.316, 2009.
, Frictional indeterminancy of forces in hard-disk packings, International Journal of Modern Physics B, vol.17, issue.29, pp.5623-5630, 2003.
, Force indeterminacy in the Jammed state of hard disks, Physical Review Letters, vol.94, issue.17, pp.1-4, 2005.
, Bidimensional strain measurement using digital images, Proceedings of the Institution of Mechanical Engineers, vol.213, pp.811-817, 1999.
, Recherches concernant les contraintes intergranulaires dans les milieux pulvérulents, 1966.
, On the metrology of interparticle contacts in sand from x-ray tomography images, Measurement Science and Technology, issue.12, p.28, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02083361
, 15 1.2 Typical stress paths highlighted with photoelasticity, 1998.
, Contact forces inferred with GEM superimposed on difference of principal stresses ? 1 ? ? 2 for a simple shear test, p.19, 2017.
, Contact forces obtained in a 3D, frictional, p.19, 2016.
, , p.27
, Typical CD-DEM contact laws adopted for the, p.31
, Single contact parameters
, Solution of the local Signorini-Coulomb problem
, Solution of the local Signorini-Coulomb problem
, Maps of normal contact forces in an isotropically-loaded packing of about 100 particles at different stages of the Gauss-Seidel iterative procedure, p.47
, Maps of normal contact forces in an isotropically-loaded packing of about 100 particles at different stages of the QSM double projection iterative procedure
, 48 2.10 Maps of normal contact forces estimated with the CDM and QSM on an isotropically-loaded system of ? 1800 particles, Probability Distribution of normal forces estimated with the CDM and QSM, for an isotropically loaded assembly of 1850 particles, during the iterations of the two methods
, Sketch of a simple system used to introduce the three numerical methods for force estimation
, Sketch of the contact 1 ? 3, with indication of the range of admissibility of the force f 1?3
, Evolution of the mobilised friction m in the MD simulation for different initial conditions, represented by the perturbation F noise applied at the first time step
, Evolution of the normal and tangential components of the contact force f 1?3 , in the MD simulation, for five different cases, each corresponding to a different initial condition and resulting in a different final solution, p.53
, Results of the force estimation with the CEM, for different solutions (different mobilised friction m) of a system with 1, p.55
, Characterisation of the range of variability of the solutions found with the CDM for the system in Figure 2.11
, for different values of the interparticle friction coefficient µ, in the application of the CDM to the system in Figure 2.11, Percentage of solutions that mobilise the whole friction (m = ±1)
, 60 2.19 Convergence towards admissible solutions obtained with the CDM when starting from three different initial conditions, Evolution of the normal and tangential components of the contact force f 1?3 , in the CDM application, p.61
, Characterisation of the convergence for a set of 1000 solutions obtained with the CDM for different initial conditions
, Velocity of convergence for a set of 1000 solutions obtained with the CDM for different initial conditions
, Percentage of solutions that mobilise the whole friction, for different values of the interparticle friction coefficient µ, in the application of the QSM to the system in Figure 2.11
, Comparison of the solutions obtained, for the same initial conditions, with the CDM and the QSM
, Characterisation of the range of variability of the solutions found with the QSM for the system in Figure 2.11
, Evolution of the normal and tangential components of the contact force f 1?3 , in the QSM application, from the initial values of normal and tangential contact forces to the final values
, Evolution of the normal and tangential components of the contact force f 1?3 , in the application of the step-wise quasi-static approach, from the initial values of normal and tangential contact forces to the final values, vol.70
, Characterisation of the convergence for a set of 1000 solutions obtained with the QSM for different initial conditions
, Velocity of convergence for a set of 1000 solutions obtained with the CDM for different initial conditions
, Stress-strain curves for the three biaxial vertical MD simulations, p.79
, Evolution of the volumetric deformation for the three DEM simulations, p.79
, QSM-estimated forces (right) from a reference one, plotted with the distance of randomly-assigned initial conditions they start from, Distance of CDM-(left)
, Maps of normal forces for different solutions obtained with the CDM for a single state of one MD simulation (? = 100)
, Evolution of Pearson's r of tangential forces, estimated with the CEM on numerical data (MD simulation with ? = 1000) for different frequencies of data acquisition, when previously accumulated tangential forces are taken into account (left) and when they are neglected (right), p.89
, Evolution of the difference, for Pearson's r of tangential forces estimated with the CEM on numerical data (MD simulation with ? = 100), between two cases: accounting for previously accumulated tangential forces, and neglecting them
, Comparison between the homogenised stresses computed, respectively, from original contact forces and from CEM-estimated forces, with four different frequencies of data acquisition
, Evolution of Pearson's r of normal forces, as estimated with the CEM on numerical data (MD simulation with ? = 100), in two cases: when previously accumulated forces are taken into account and when they are not
, Comparison of maps of normal forces: original forces vs forces estimated via CDM with 7% and 11% error on contacts, due to perturbation on grain positions
, compared with the evolution of Pearson's r between normal (tangential) forces estimated through the CDM and real ones, for an MD simulation of a small system (12 particles, ? = 100), Evolution of one indicator of force variability (?)
, compared with the evolution of Pearson's r between normal (tangential) forces estimated through the CDM and real ones, for an MD simulation of a small system (12 particles, ? = 100), Evolution of one indicator of force variability (?)
, Evolution of the degree of force indeterminacy h with Pearson's r on QSMestimated normal and tangential forces, for the three MD simulations with 1850 particles
, Evolution of the degree of force indeterminacy h, compared with the evolution of Pearson's r between normal (tangential) forces estimated through the CDM and real ones, for an MD simulation with 1850 particles and ? = 100
, 127 3.40 Evolution of Pearson's r of CDM-estimated normal forces for the MDDEM simulation with ? = 100. r is separately computed for the strong and weak force network, Evolution of Pearson's r for normal and tangential forces, between the original set of forces and, respectively, the CDM solution and the QSM one
, Image of an isotropically compressed specimen in the 1?2? device, p.133
, Image of the loading system for the compression test on a pair of grains in contact (left), with plot of the force-displacement response (right), p.134
, Map of the vertical strain ? yy obtained from the software 7D, 1999.
, with a sketch to illustrate the main components (right)
, Working principle of the apparatus with definition of the geometrical constraints
, Evolution with time of the vertical and horizontal strains (? yy and ? xx , respectively), in one of the isotropic compression tests. (b) Stress-strain plot for the third cycle of the test
, Plot of the stress-strain curve and evolution of the volumetric deformation for the biaxial vertical compression test
, Plot of the evolution of the main geometric properties during the biaxial vertical compression test: void ratio e, coordination number z (left) and degree of force indeterminacy h (right)
, Plot of the stress-strain curve (black) and evolution of the volumetric deformation (gray) for the biaxial horizontal compression test, p.143
, Plot of the evolution of the main geometric properties during the biaxial horizontal compression test: void ratio e, coordination number z and degree of force indeterminacy h
, Plot of the stress-strain curve (black) and evolution of the volumetric deformation (gray) for the simple shear test
, Plot of the evolution of the main geometric properties during the simple shear test: void ratio e, coordination number z (a) and degree of force indeterminacy h (b)
, Vertical and horizontal normal stresses in the oedometer compression test, p.145
, Oedometric curve for the loading branch of the first cycle of the oedometer compression test
, Example of a gray level histogram from an image of a 1?2? specimen, p.147
, Zoom on two grains to show the black-and-white dots on their visible face, p.150
, Sketch of two grains in contact, with definition of the convention for the local reference
, Sketch of the applied loading conditions in three different tests, p.153
, Polar histogram of contact orientations for three different tests, p.154
, 155 4.22 Comparison between the 1?2? macroscopic stress components and the Weber stress components computed from contact forces estimated via the CEM for an oedometer compression test
, Comparison between the 1?2? macroscopic stress components and the Weber stress components computed from contact forces estimated via the CEM for an isotropic compression test
, 162 4.25 Comparison between the 1?2? macroscopic stress components and the Weber stress components computed from contact forces estimated via the CEM for biaxial vertical and horizontal compression tests, Distribution of normal stress magnitude acting on planes with different orientations, from contact forces estimated via the CEM
, Map of normal contact forces obtained via the QSM at the end of the first loading cycle of the oedometer compression test
, Evolution of Pearson's r for normal and tangential forces estimated via the QSM in consecutive states of an oedometer compression test, p.167
, 169 4.31 Comparison between the 1?2? macroscopic stress components and the Weber stress components computed from contact forces estimated via the QSM in biaxial vertical (a) and horizontal (b) compression tests, Probability distribution of normalised normal forces, estimated via the QSM at the end of the first loading cycle of an oedometer compression test
, Map of normal contact forces obtained via Contact Dynamics at the end of the first loading cycle of the oedometer compression test, p.173
, Probability Distribution of normalised normal forces, estimated via the CDM at the end of the first loading cycle of an oedometer compression test, p.174
, 176 4.37 Comparison between the 1?2? macroscopic stress components and the Weber stress components computed from contact forces estimated via the CDM to a biaxial vertical compression test, Evolution of Pearson's r for normal and tangential forces estimated via the CDM in consecutive states of an oedometer compression test
, Evolution of Pearson's r for normal and tangential forces estimated via the CDM in consecutive states of a biaxial vertical compression test, with and without using previously computed forces as initial guess for the next state.177 4.39 Comparison between the 1?2? macroscopic stress components and the Weber stress components computed from contact forces estimated via the CDM to a biaxial horizontal compression test
, Map of normal contact forces obtained with the three methods at the end of the first loading cycle of the oedometer compression test: zoom on a part of the specimen
, Cumulative distribution function of the distance from equilibrium for all particles, at the end of the first loading cycle of the oedometer compression test, in the solutions obtained with the three methods, p.181
, Sketch of the set-up for the measurement of the interparticle friction angle µ