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Sliding and rolling are two outstanding deformation modes in granular media. The first one induces frictional dissipation whereas the latter one involves deformation with negligible resistance. Using numerical simulations on two-dimensional shear cells, we investigate the effect of the grain rotation on the energy dissipation and the strength of granular materials under quasistatic shear deformation. Rolling and sliding are quantified in terms of the so-called Cosserat rotations. The observed spontaneous formation of vorticity cells and clusters of rotating bearings may provide an explanation for the long standing heat flow paradox of earthquake dynamics.

We investigate the quasi-static mechanical response of soils under cyclic loading using a discrete model of randomly generated convex polygons. This response exhibits a sequence of regimes, each one characterized by a linear accumulation of plastic deformation with the number of cycles. At the grain level, a quasi-periodic ratchet-like behavior is observed at the contacts, which excludes the existence of an elastic regime. The study of this slow dynamics allows to explore the role of friction in the permanent deformation of unbound granular materials supporting railroads and streets.A particularly intriguing phenomenon in driven systems is the so-called ratchet effect. There is already an extensive body of work on this subject, driven by the need to understand biophysical systems such as molecular motors [1] and certain mechanical and electrical rectifiers [2]. The classic ratchet is a mechanical device consisting of a pawl that engages the sloping teeth of a wheel, permitting motion in one direction only. Ratchet-like motion have been proposed as a mechanism to explain the convective motion and size segregation in vibrated granular materials [3]. The understanding of this phenomenon is crucial in the investigation on the permanent deformation in structures subjected to cyclic loading. In soils, this loading can be induced by earthquakes, sea waves, road traffic, etc. [4].The classical theory of elasto-plasticity describes the cyclic loading response by postulating an elastic region in the stress space, which changes during the deformation [5]. This elastic region, however, is not easy to identify because the onset of the plastic deformation is gradual and not sharply defined. A great variety of modifications have been proposed in order to provide a more appropriate description which, however, make the theory too complicated, and require too many material parameters which are difficult to calibrate [6].This research was motivated by experiments of cyclic loading tests on unbound granular material used to support railroads and streets. A slow deformation is observed during the service life of these structures, where the breakage, corrosion and the friction between the grains play an important role [4]. We emphasise some recent experiments performed in Darmstadt [7]. These experiments show that when the samples consist of very wear resistant grains, the long time cyclic loading behavior is given by a linear accumulation of plastic deformation. This surprising result suggests that the grains attain a periodic irreversible motion at the sliding contacts, which could, in principle, be detected using numerical simulations. Here we report on the first micromechanical observation using molecular dynamic simulations. Ratcheting motion was detected in the sliding contacts on a polygonal packing subjected to quasi-static cyclic loading.The polygons representing the particles in this model are generated by using a simple version of Voronoi tessellation: First, we set a random point in each cell of a regular square lattice o...

We study the effect of the anisotropy induced by loading on the elastoplastic response of a two dimensional discrete element model granular material. The anisotropy of the contact network leads to a breakdown of the linear isotropic elasticity. We report on a linear dependence of the Young moduli and Poisson ratios on the fabric coefficients, measuring the anisotropy of the contact network. The resulting nonassociated plastic flow rule and the linear relationship between dilatancy and stress ratio are discussed in terms of several existing models. We propose a paradigm for understanding soil plasticity, based on the correlation between the plastic flow rule and the induced anisotropy on the subnetwork of sliding contacts.

I present a method to simulate complex-shaped interacting bodies, a problem which appears in many areas, including molecular dynamics, material science, virtual reality, geo-and astrophysics. The particle shape is represented by the classical concept of a Minkowski sum, which permits the representation of complex shapes without the need to define the object as a composite of spherical or convex particles. A well-defined conservative and frictional interaction between these bodies is derived. The model (particles + interactions) is much more efficient, accurate and easier to implement than other models. Simulations with conservative interactions comply with the statistical mechanical principles for conservative systems. Simulations with frictional forces show that particle shape strongly affects the jamming phenomena in granular flow.

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Dry granular materials in a split-bottom ring shear cell geometry show wide shear bands under slow, quasistatic, large deformation. This system is studied in the presence of contact adhesion, using the discrete element method (DEM). Several continuum fields like the density, the deformation gradient and the stress tensor are computed locally and are analyzed with the goal to formulate objective constitutive relations for the flow behavior of cohesive powders. From a single simulation only, by applying time-and (local) space-averaging, and focusing on the regions of the system that experienced considerable deformations, the critical-state yield stress (termination locus) can be obtained. It is close to linear, for non-cohesive granular materials, and nonlinear with peculiar pressure dependence, for adhesive powdersdue to the nonlinear dependence of the contact adhesion on the confining forces. The contact model is simplified and possibly will need refinements and additional effects in order to resemble realistic powders. However, the promising method of how to obtain a critical-state yield stress from a single numerical test of one material is generally applicable and waits for calibration and validation.

SUMMARYThe mechanical response of cohesionless granular materials under monotonic loading is studied by performing molecular dynamic simulations. The diversity of shapes of soil grains is modelled by using randomly generated convex polygons as granular particles. Results of the biaxial test obtained for dense and loose media show that samples achieve the same void ratio at large strains independent of their initial density state. This limit state resembles the so-called critical state of soil mechanics, except for some stress fluctuations, which remain for large deformations. These fluctuations are studied at the micro-mechanical level, by following the evolution of the co-ordination number, force chains and the fraction of the sliding contacts of the sample.