Molecular dynamics simulations of complex shaped particles using Minkowski operators

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.Comment: Submitted to Phys. Rev.

Ratcheting of granular materials

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.Comment: Changed content Submitted to Physical Review Letter

The anisotropy of granular materials

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.Comment: Submitted to PR

Characterization of the material response in the granular ratcheting

The existence of a very special ratcheting regime has recently been reported in a granular packing subjected to cyclic loading \cite{alonso04}. In this state, the system accumulates a small permanent deformation after each cycle. After a short transient regime, the value of this permanent strain accumulation becomes independent on the number of cycles. We show that a characterization of the material response in this peculiar state is possible in terms of three simple macroscopic variables. They are defined that, they can be easily measured both in the experiments and in the simulations. We have carried out a thorough investigation of the micro- and macro-mechanical factors affecting these variables, by means of Molecular Dynamics simulations of a polydisperse disk packing, as a simple model system for granular material. Biaxial test boundary conditions with a periodically cycling 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. Specially elucidating is the influence of the particular hysteretical behavior in the stress-strain space on the accumulation of permanent strain and the energy dissipation.Comment: 13 pages, 20 figures. Submitted to PR

IV Foro Internacional de Ganadería Sustentable: conectividad ecosistémica y articulación territorial hacia la Agenda 2030

En este espacio plural de análisis y reflexiones, buscamos articular conceptos y posibilidades para los territorios de montaña del centro de México, dando importancia a medios de vida vinculados a la ganadería y su interacción ecosistémica, fundamentado en innovaciones, casos de éxito e iniciativas emblemáticas nacionales e internacionales. La socialización de experiencias es uno de los pilares para transitar hacia la sostenibilidad de los sistemas productivos ganaderos: compartir logros e iniciativas, crear sinergias e identificar vulnerabilidades desde distintos enfoques.GIZ, Agencia de Cooperación Aleman

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