A variational discrete element method for the computation of Cosserat elasticity

TL;DR

This paper introduces a variational discrete element method tailored for Cosserat elastic materials, incorporating rotational degrees of freedom and achieving accurate, robust static and dynamic simulations without microscopic parameters.

Contribution

It adapts a variational discrete element approach to Cosserat elasticity, adding rotational dofs and a polynomial reconstruction for constant strains and stresses.

Findings

Method is robust for static and dynamic simulations

Requires only macroscopic parameters, no microscopic data

Effective in 2D and 3D computations

Abstract

The variational discrete element method developed in [28] for dynamic elasto-plastic computations is adapted to compute the deformation of elastic Cosserat materials. In addition to cellwise displacement degrees of freedom (dofs), cellwise rotational dofs are added. A reconstruction is devised to obtain P 1 non-conforming polynomials in each cell and thus constant strains and stresses in each cell. The method requires only the usual macroscopic parameters of a Cosserat material and no microscopic parameter. Numerical examples show the robustness of the method for both static and dynamic computations in two and three dimensions.