Homogeneous Analysis of Periodic Assemblies of Elastoplastic Disks in Contact

The objective of this article is to capture the macroscopic behavior of an assembly of elastic and inelastic disks in contact by means of a numerical homogenized constitutive relation. An important feature of this work is that the evolving yield surfaces at the macroscopic level are defined through a quasi-static frictional contact analysis of the microstructure composed of deformable elastic and inelastic disks by means of a parametric quadratic programming principle and its corresponding algorithm in numerical analysis. The flow rule and the hardening parameters needed for an elastic–plastic analysis at macroscopic level are directly obtained from the numerically constructed yield surfaces in a self-consistent manner. The generality of the algorithm for the homogeneous analysis is pointed out and, in principle, can be applied to any kind of nonlinear behavior affecting the representative volume element. Numerical examples are given to demonstrate the efficiency of the algorithm presented in this article.