Micromechanical study of plasticity of granular materials

Niels P. Kruyt

doi:10.1016/j.crme.2010.09.005

Micromechanical study of plasticity of granular materials
[Étude micromécanique de la plasticité des matériaux granulaires]

Niels P. Kruyt ¹

¹ Department of Mechanical Engineering, University of Twente, NL-7500 AE Enschede, The Netherlands

Comptes Rendus. Mécanique, Volume 338 (2010) no. 10-11, pp. 596-603.

Résumé
Abstract

La déformation plastique des matériaux granulaires est étudiée du point de vue micromécanique, dans lequel l'assemblage des particules et des contacts entre particules est considéré comme une structure mécanique. Ceci est fait de trois façons. Tout d'abord, en analysant le degré de redondance du système obtenu en comparant le nombre de degrés de liberté lié aux forces de contact avec le nombre d'équations d'équilibre ; Deuxièmement, en déterminant le spectre des valeurs propres de la matrice de rigidité de la structure qui est représentée par les particules et leurs contacts ; Troisièmement, en étudiant l'évolution pour une déformation imposée du tenseur de rigidité du milieu continu élastique équivalent au système analysé. Pour une déformation imposée, le degré de redondance évolue rapidement vers un état avec une petite redondance, c'est-à-dire que le système devient quasi isostatique. Le spectre des valeurs propres du système montre les modes singuliers et quasi singuliers au niveau de la résistance au cisaillement maximale et en grandes déformations. Le tenseur de rigidité élastique du milieu continu équivalent devient fortement anisotrope pour une déformation imposée, et fait apparaître la nature non affine de la déformation. L'hypothèse d'un tenseur de rigidité élastique, qui est constant dans des relations constitutives élasto-plastiques des matériaux granulaires, est généralement incorrecte. Globalement, le comportement macroscopique plastique est lié d'une part aux frottements aux contacts et d'autre part à l'évolution du réseau de contacts que l'on peut assimiler à un mécanisme d'endommagement.

Plastic deformation of granular materials is investigated from the micromechanical viewpoint, in which the assembly of particles and interparticle contacts is considered as a mechanical structure. This is done in three ways. Firstly, by investigating the degree of redundancy of the system by comparing the number of force degrees of freedom at contacts with the number of governing equilibrium equations; Secondly, by determining the spectrum of eigenvalues of the stiffness matrix for the structure that is represented by the particles and their contacts; Thirdly, by investigating the evolution with imposed strain of the continuum elastic stiffness tensor of the system. It is found that, with increasing imposed strain, the degree of redundancy rapidly evolves towards a state with small redundancy, i.e. the system becomes nearly statically determinate. The spectrum of the system shows many singular and near-singular modes at peak shear strength and at large strain. The continuum elastic stiffness tensor becomes strongly anisotropic with increasing imposed strain and shows strong non-affinity of deformation. The assumption of a constant and isotropic elastic stiffness tensor in elasto-plastic continuum constitutive relations for granular materials is generally incorrect. Overall, the plastic continuum behaviour of granular materials originates from the plastic frictional behaviour at contacts and from damage in the form of changes in the contact network.

Publié le : 2010-10-01

DOI : 10.1016/j.crme.2010.09.005

Keywords: Granular media, Plasticity, Micromechanics
Mot clés : Milieux granulaires, Plasticité, Micromécanique

Affiliations des auteurs :

Niels P. Kruyt ¹

¹ Department of Mechanical Engineering, University of Twente, NL-7500 AE Enschede, The Netherlands

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Niels P. Kruyt. Micromechanical study of plasticity of granular materials. Comptes Rendus. Mécanique, Volume 338 (2010) no. 10-11, pp. 596-603. doi : 10.1016/j.crme.2010.09.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.09.005/

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Cité par Sources :

^☆ This study is an extended version of that reported by N.P. Kruyt, L. Rothenburg, Plasticity of granular materials: a structural-mechanics view, in: M. Nakagawa, S. Luding (Eds.), Powders and Grains 2009, in: AIP Conference Proceedings, vol. 1145, 2009, pp. 1073–1076.

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