Plasticity of Granular Materials:a Structural-mechanics View

摘要

Plasticity of granular materials during quasi-static deformation is investigated, using a two-dimensional Discrete Element Method simulation of biaxial deformation. From the detailed, discrete information obtained from this simulation, macroscopic continuum plasticity is viewed from the structural-mechanics viewpoint in three different ways. Firstly, by counting the number of governing force and moment equilibrium equations in comparison to the number of force degrees of freedom at contacts, i.e. by investigating the degree of redundancy of the system. Secondly, by investigating the spectrum of eigenvalues of the discrete 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. For the degree of redundancy we find that, with increasing imposed strain, the system evolves towards a state without redundancy, i.e. the system becomes statically determinate. For the spectrum of eigenvalues of the discrete stiffness matrix, we observe that at peak strength and at large strain the spectrum contains many singular and near-singular modes. For the continuum elastic stiffness tensor we observe that: (1) it becomes strongly anisotropic with increasing imposed strain, (2) it shows strong non-affinity of deformation and (3) it becomes nearly singular with increasing imposed strain.