Fernando Alonso-Marroquin

Role of anisotropy in the elastoplastic response of a polygonal packing

The effect of the anisotropy on the elastoplastic response of two dimensional packed samples of polygons is investigated here, using molecular dynamics simulation. We show a correlation between fabric coefficients, characterizing the anisotropy of the granular skeleton, and the anisotropy of the elastic response. We also study the anisotropy induced by shearing on the subnetwork of the sliding contacts. This anisotropy provides an explanation to some features of the plastic deformation of granular media.

Effect of rolling on dissipation in fault gouges.

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.

Ratcheting of Granular Materials

We investigate the quasistatic 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 quasiperiodic ratchetlike behavior is observed at the contacts, which excludes the existence of an elastic regime. The study of this slow dynamics allows exploration of the role of friction in the permanent deformation of unbound granular materials subjected to cyclic loading.

Spheropolygons : A new method to simulate conservative and dissipative interactions between 2D complex-shaped rigid bodies

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.

Calculation of the incremental stress-strain relation of a polygonal packing.

The constitutive relation of the quasistatic deformation on two-dimensional packed samples of polygons is calculated using molecular dynamics simulations. The stress values at which the system remains stable are bounded by a failure surface, which shows a power law dependence on the pressure. Below the failure surface, nonlinear elasticity and plastic deformation are obtained, which are evaluated in the framework of the incremental linear theory. The results show that the stiffness tensor can be directly related to the microcontact rearrangements. The plasticity obeys a nonassociated flow rule with a plastic limit surface that does not agree with the failure surface.

Minkowski-Voronoi diagrams as a method to generate random packings of spheropolygons for the simulation of soils

The Minkowski operators (addition and substraction of sets in vectorial spaces) has been extensively used for Computer Graphics and Image Processing to represent complex shapes. Here we propose to apply those mathematical concepts to extend the Molecular Dynamics (MD) Methods for simulations with complex-shaped particles. A new concept of Voronoi-Minkowski diagrams is introduced to generate random packings of complex-shaped particles with tunable particle roundness. By extending the classical concept of Verlet list we achieve numerical efficiencies that do not grow quadratically with the body number of sides. Simulations of dissipative granular materials under shear demonstrate that the method complies with the first law of thermodynamics for energy balance.

Characterization of the material response in granular ratcheting

The existence of a very special ratcheting regime has recently been reported in a granular packing subjected to cyclic loading. In this state, the system accumulates a small permanent deformation after each cycle. The value of this permanent strain accumulation becomes independent of the number of cycles after a short transient regime. We show in this paper that a characterization of the material response in this peculiar state is possible in terms of three simple macroscopic variables. The definition of these variables is such that they can be easily measured both in the experiments and in the simulations. A thorough investigation of the micro- and macromechanical factors affecting these variables has been carried out by means of molecular-dynamics simulations of a polydisperse disk packing, as a simple model system for granular material. Biaxial test boundary conditions with periodically varying load were implemented. The effect on the plastic response of the confining pressure, the deviatoric stress, and the number of cycles has been investigated. The stiffness of the contacts and friction has been shown to play an important role in the overall response of the system. Especially illustrative is the influence of the peculiar hysteretical behavior in the stress-strain space on the accumulation of permanent strain and the energy dissipation.

Bottlenecks in granular flow: when does an obstacle increase the flow rate in an hourglass?

Bottlenecks occur in a wide range of situations from pedestrians, ants, cattle, and traffic flow to the transport of granular materials. We examine granular flow across a bottleneck using simulations of monodisperse disks. Contrary to expectations but consistent with previous work, we find that the flow rate across a bottleneck actually increases if an obstacle is optimally placed before it. Using the hourglass theory and a velocity-density relation, we show that the peak flow rate corresponds to a transition from free flow to congested flow, similar to the phase transition in traffic flow.

The incremental response of soils. An investigation using a discrete-element model

The incremental stress-strain relation of dense packings of polygons is investigated by using molecular-dynamics simulations. The comparison of the simulation results to the continuous theories is performed using explicit expressions for the averaged stress and strain over a representative volume element. The discussion of the incremental response raises two important questions of soil deformation: Is the incrementally nonlinear theory appropriate to describe the soil mechanical response? Does a purely elastic regime exist in the deformation of granular materials? In both cases the answer will be “no”. The question of stability is also discussed in terms of the Hill condition of stability for non-associated materials. It is contended that the incremental response of soils should be revisited from micromechanical considerations. A micromechanical approach assisted by discrete element simulations is briefly outlined.

Stochastic collision and aggregation analysis of kaolinite in water through experiments and the spheropolygon theory

An approach based on spheropolygons (i.e., the Minkowski sum of a polygon with N vertices and a disk with spheroradius r) is presented to describe the shape of kaolinite aggregates in water and to investigate interparticle collision dynamics. Spheropolygons generated against images of kaolinite aggregates achieved an error between 0.5% and 20% as compared to at least 32% of equivalent spheres. These spheropolygons were used to investigate the probability of collision (Pr[C]) and aggregation (Pr[A]) under the action of gravitational, viscous, contact (visco-elastic), electrostatic and van der Waals forces. In ortho-axial (i.e., frontal) collision, Pr[A] of equivalent spheres was always 1, however, stochastic analysis of collision among spheropolygons showed that Pr[A] decreased asymptotically with N increasing, and decreased further in peri-axial (i.e., tangential) collision. Trajectory analysis showed that not all collisions occurring within the attraction zone of the double layer resulted in aggregation, neither all those occurring outside it led to relative departure. Rather, the relative motion on surface asperities affected the intensity of contact and attractive forces to an extent to substantially control a collision outcome in either instances. Spheropolygons revealed therefore how external shape can influence particle aggregation, and suggested that this is equally important to contact and double layer forces in determining the probability of particle aggregation.