We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.

}, keywords = {CONTACT DYNAMICS METHOD; DISCRETE ELEMENT METHOD; SHEAR BANDS; NUMERICAL-SIMULATION; BED COMMINUTION; FRAGMENTATION; BREAKAGE; ROCK; DEM; MODEL}, issn = {1292-8941}, doi = {10.1140/epje/i2018-11656-1}, url = {http://link.springer.com/10.1140/epje/i2018-11656-1}, author = {Duc-Hanh Nguyen and Emilien Az{\'e}ma and Philippe Sornay and Farhang Radja{\"\i}} } @article {596, title = {Three-dimensional bonded-cell model for grain fragmentation}, journal = {Computational Particle Mechanics}, volume = {4}, year = {2017}, month = {Oct-2017}, pages = {441 - 450}, chapter = { Special Issue: SI }, abstract = {We present a three-dimensional numerical method for the simulation of particle crushing in 3D. This model is capable of producing irregular angular fragments upon particle fragmentation while conserving the total volume. The particle is modeled as a cluster of rigid polyhedral cells generated by a Voronoi tessellation. The cells are bonded along their faces by a cohesive Tresca law with independent tensile and shear strengths and simulated by the contact dynamics method. Using this model, we analyze the mechanical response of a single particle subjected to diametral compression for varying number of cells, their degree of disorder, and intercell tensile and shear strength. In particular, we identify the functional dependence of particle strength on the intercell strengths. We find that two different regimes can be distinguished depending on whether intercell shear strength is below or above its tensile strength. In both regimes, we observe a power-law dependence of particle strength on both intercell strengths but with different exponents. The strong effect of intercell shear strength on the particle strength reflects an interlocking effect between cells. In fact, even at low tensile strength, the particle global strength can still considerably increase with intercell shear strength. We finally show that the Weibull statistics describes well the particle strength variability.

}, keywords = {Bonded-cell model; Fragmentation; Discrete element method; Contact dynamics method; Voronoi cell; Weibull statistics}, issn = {2196-4378}, doi = {10.1007/s40571-016-0129-0}, url = {http://link.springer.com/10.1007/s40571-016-0129-0}, author = {Cantor, D and Emilien Az{\'e}ma and Philippe Sornay and Farhang Radja{\"\i}} } @article {153, title = {Bonded-cell model for particle fracture}, journal = {Physical Review E}, volume = {91}, year = {2015}, month = {Feb-09-2015}, pages = {Article Number: 022203}, abstract = {Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.

}, issn = {1539-3755}, doi = {10.1103/PhysRevE.91.022203}, author = {Duc-Hanh Nguyen and Emilien Az{\'e}ma and Philippe Sornay and Farhang Radja{\"\i}} } @article {129, title = {Effects of shape and size polydispersity on strength properties of granular materials.}, journal = {Phys Rev E Stat Nonlin Soft Matter Phys}, volume = {91}, year = {2015}, month = {Mar-18-2015}, pages = {Article Number: 032203}, abstract = {By means of extensive contact dynamics simulations, we analyze the combined effects of polydispersity both in particle size and in particle shape, defined as the degree of shape irregularity, on the shear strength and microstructure of sheared granular materials composed of pentagonal particles. We find that the shear strength is independent of the size span, but unexpectedly, it declines with increasing shape polydispersity. At the same time, the solid fraction is an increasing function of both the size span and the shape polydispersity. Hence, the densest and loosest packings have the same shear strength. At the scale of the particles and their contacts, we analyze the connectivity of particles, force transmission, and friction mobilization as well as their anisotropies. We show that stronger forces are carried by larger particles and propped by an increasing number of small particles. The independence of shear strength with regard to size span is shown to be a consequence of contact network self-organization, with the falloff of contact anisotropy compensated by increasing force anisotropy.

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}, issn = {1550-2376}, doi = {10.1103/PhysRevE.91.032203}, author = {Duc-Hanh Nguyen and Emilien Az{\'e}ma and Philippe Sornay and Farhang Radja{\"\i}} } @proceedings {343, title = {Evolution of particle size distributions in crushable granular materials}, journal = {3rd International Symposium on Geomechanics from Micro to Macro}, volume = {Geomechanics from Micro to Macro}, year = {2015}, month = {Feb-02-2015}, pages = {275 - 280}, publisher = {CRC Press}, address = {SEP 01-03-2014 Univ Cambridge, Cambridge, ENGLAND}, abstract = {By means of the contact dynamics method together with a particle fracture model, in which the particles are cohesive aggregates of irreducible polygonal fragments, we investigate the evolution of particle size distribution in the process of uniaxial compaction of granular materials. The case of single particle breakup under compressive stress is used to test the method and the influence of discretization (number of irreducible fragments). We show that the breaking threshold of the granular assembly scales with the internal cohesion of the particles but it depends also on the initial size distribution and irregularity of polygonal particle shapes. The evolution of size distribution proceeds by consecutive periods of intense particle crushing, characterized by local shattering instability, and periods of little breaking activity. Starting with either monodisperse or power-law distribution of particle sizes, the latter evolves towards a broad distribution of the fragmented particles with a nearly power-law distribution in the range of intermediate particle sizes. Interestingly, a finite number of large particles survive despite ongoing crushing process due to the more homogeneous distribution of forces in the presence of small fragmented particles filling the pores between larger particles.

}, isbn = {978-1-138-02707-7}, doi = {10.1201/b1739510.1201/b17395-48}, author = {Duc-Hanh Nguyen and Emilien Az{\'e}ma and Farhang Radja{\"\i} and Philippe Sornay}, editor = {Kenichi Soga and Krishna Kumar and Giovanna Biscontin and Kuo, Matthew} } @article {273, title = {Effect of size polydispersity versus particle shape in dense granular media}, journal = {Physical Review E}, volume = {90}, year = {2014}, month = {Jul-21-2014}, pages = {Article Number: 012202}, abstract = {We present a detailed analysis of the morphology of granular systems composed of frictionless pentagonal particles by varying systematically both the size span and particle shape irregularity, which represent two polydispersity parameters of the system. The microstructure is characterized in terms of various statistical descriptors such as global and local packing fractions, radial distribution functions, coordination number, and fraction of floating particles. We find that the packing fraction increases with the two parameters of polydispersity, but the effect of shape polydispersity for all the investigated structural properties is significant only at low size polydispersity where the positional and/or orientational ordering of the particles prevail. We focus in more detail on the class of side/side contacts, which is the interesting feature of our system as compared to a packing of disks. We show that the proportion of such contacts has weak dependence on the polydispersity parameters. The side- side contacts do not percolate but they define clusters of increasing size as a function of size polydispersity and decreasing size as a function of shape polydispersity. The clusters have anisotropic shapes but with a decreasing aspect ratio as polydispersity increases. This feature is argued to be a consequence of strong force chains (forces above the mean), which are mainly captured by side-side contacts. Finally, the force transmission is intrinsically multiscale, with a mean force increasing linearly with particle size.

}, issn = {1539-3755}, doi = {10.1103/PhysRevE.90.012202}, author = {Duc-Hanh Nguyen and {\'e}ma, Emilien and Farhang Radja{\"\i} and Philippe Sornay} } @proceedings {367, title = {A benchmark for particle shape dependence}, journal = {7th International Conference on Micromechanics of Granular Media (Powders and Grains)}, volume = {Book Series: AIP Conference Proceedings POWDERS AND GRAINS 2013}, year = {2013}, month = {Jun-18-2013}, pages = {883-886}, publisher = {AIP}, address = {JUL 08-12 2013 Sydney, AUSTRALIA}, abstract = {Particle shape is a major parameter for the space-filling and strength properties of granular materials. For a systematic investigation of shape effect, a numerical benchmark test was set up within a collaborative group using different numerical methods and particles of various shape characteristics such as elongation, angularity and nonconvexity. Extensive 2D shear simulations were performed in this framework and the shear strength and packing fraction were compared for different shapes. We show that the results may be analyzed in terms of a low-order shape parameter \η describing the degree of distortion from a perfectly circular shape. In particular, the shear strength is an increasing function of \η with nearly the same trend for all shapes, the differences being of second order compared to \η. We also observe a nontrivial behavior of packing fraction which, for all our simulated shapes, increases with \η from the random close packing fraction for disks, reaches a peak considerably higher than that for disks, and subsequently declines as \η is further increased. Finally, the analysis of contact forces for the same value of \η leads to very similar statistics regardless of our specific particle shapes.

}, doi = {10.1063/1.4812073}, author = {Gael Combe and C{\'e}cile Nouguier-Lehon and Emilien Az{\'e}ma and Krzysztof Szarf and Baptiste Saint-Cyr and Marie Chaze and Farhang Radja{\"\i} and Pascal Villard and Jean-Yves Delenne and Vincent Richefeu and Philippe Sornay and Charles Voivret and CEGEO Group}, editor = {Yu, A and Dong, K and Yang, R} } @article {281, title = {Cohesive granular materials composed of nonconvex particles}, journal = {Physical Review E}, volume = {87}, year = {2013}, month = {May-28-2013}, pages = {Article Number: 052207}, abstract = {The macroscopic cohesion of granular materials made up of sticky particles depends on the particle shapes. We address this issue by performing contact dynamics simulations of 2D packings of nonconvex aggregates. We find that the macroscopic cohesion is strongly dependent on the strain and stress inhomogeneities developing inside the material. The largest cohesion is obtained for nearly homogeneous deformation at the beginning of unconfined axial compression and it evolves linearly with nonconvexity. Interestingly, the aggregates in a sheared packing tend to form more contacts with fewer neighboring aggregates as the degree of nonconvexity increases. We also find that shearing leads either to an isotropic distribution of tensile contacts or to the same privileged direction as that of compressive contacts.

}, issn = {1539-3755}, doi = {10.1103/PhysRevE.87.052207}, author = {Baptiste Saint-Cyr and Farhang Radja{\"\i} and Jean-Yves Delenne and Philippe Sornay} } @article {282, title = {Rheology of three-dimensional packings of aggregates: Microstructure and effects of nonconvexity}, journal = {Physical Review E}, volume = {87}, year = {2013}, month = {May-22-2013}, pages = {Article Number: 052205}, abstract = {We use 3D contact dynamics simulations to analyze the rheological properties of granular materials composed of rigid aggregates. The aggregates are made from four overlapping spheres and described by a nonconvexity parameter depending on the relative positions of the spheres. The macroscopic and microstructural properties of several sheared packings are analyzed as a function of the degree of nonconvexity of the aggregates. We find that the internal angle of friction increases with nonconvexity. In contrast, the packing fraction increases first to a maximum value but declines as nonconvexity further increases. At high level of nonconvexity, the packings are looser but show a higher shear strength. At the microscopic scale, the fabric and force anisotropy, as well as friction mobilization are enhanced by multiple contacts between aggregates and interlocking, revealing thus the mechanical and geometrical origins of shear strength.

}, issn = {1539-3755}, doi = {10.1103/PhysRevE.87.052205}, author = {Emilien Az{\'e}ma and Farhang Radja{\"\i} and Baptiste Saint-Cyr and Jean-Yves Delenne and Philippe Sornay} } @proceedings {350, title = {Effect of Particle Shape non-Convexity on the Rheology of Granular Media : 3D Contact Dynamics Simulations}, journal = {2nd International Conference on Particle-Based Methods - Fundamentals and Applications (Particles)}, volume = {PARTICLE-BASED METHODS II: FUNDAMENTALS AND APPLICATIONS}, year = {2012}, month = {Apr-10-2012}, pages = {427-434}, address = {OCT 26-28 2011 Barcelona, SPAIN}, abstract = {We analyze the effect of particle shape non-convexity on the quasi-static behavior of granular materials by means of contact dynamics simulations. The particles are regular aggregates of four overlapping spheres described by a nonconvexity parameter depending on the relative positions of the particles. Several packings are first submitted to isotropic compression without friction. We find that, as in 2D, the solid fraction of isotropic packings increases with non-convexity up to a maximum value and then declines to be nearly equal to that of a packing composed of only spheres. It is also remarkable that the coordination number increases quickly and saturates so that the packings composed of grains with a high level of nonconvexity are looser but more strongly connected. Then, the quasi-static behavior, structural and force anisotropies are analyzed by subjecting each packing to a triaxial compression. We find that the shear strength increases with non-convexity. We show that this increase results from the presence of multiple contacts between trimers leading to enhanced frictional interlocking.

}, keywords = {force transmission, Granular Materials, non-convexity, particle shape, texture}, url = {https://hal.archives-ouvertes.fr/hal-00686453}, author = {Baptiste Saint-Cyr and Emilien Az{\'e}ma and Jean-Yves Delenne and Farhang Radja{\"\i} and Philippe Sornay}, editor = {Onate, E and Owen, DRJ} } @article {307, title = {Particle shape dependence in 2D granular media}, journal = {EPL (Europhysics Letters)}, volume = {98}, year = {2012}, month = {Apr-20-2012}, pages = {Article Number: 44008}, abstract = {Particle shape is a key to the space-filling and strength properties of granular matter. We consider a shape parameter

By means of contact dynamics simulations, we investigate the shear strength and internal structure of granular materials composed of two-dimensional nonconvex aggregates. We find that the packing fraction first grows as the nonconvexity is increased but declines at higher nonconvexity. This unmonotonic dependence reflects the competing effects of pore size reduction between convex borders of aggregates and gain in porosity at the nonconvex borders that are captured in a simple model fitting nicely the simulation data both in the isotropic and sheared packings. On the other hand, the internal angle of friction increases linearly with nonconvexity and saturates to a value independent of nonconvexity. We show that fabric anisotropy, force anisotropy, and friction mobilization, all enhanced by multiple contacts between aggregates, govern the observed increase of shear strength and its saturation with increasing nonconvexity. The main effect of interlocking is to dislocate frictional dissipation from the locked double and triple contacts between aggregates to the simple contacts between clusters of aggregates. This self-organization of particle motions allows the packing to keep a constant shear strength at high nonconvexity.

}, issn = {1539-3755}, doi = {10.1103/PhysRevE.84.041302}, author = {Baptiste Saint-Cyr and Jean-Yves Delenne and Charles Voivret and Farhang Radja{\"\i} and Philippe Sornay} }