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 {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} }