Heterogeneous Mohr-Coulomb plastic material

摘要

We consider a heterogeneous medium which lo- cally obeys a Mohr-Colulomb rigid-plastic behavior. We are interested in the macroscopic yield criterion based on an admissible stress formulation. We propose a two-dimen- sional analysis based on Airy potential formulation, using a first order perturbation. We first derive an upper bound for the meacroscopic yield, and then construct explicitly an admissible stress field which reaches this bound. We finally show that within this framework, the macroscopic friction angle tends to the average of the local friction an- gle. Corrections to this value decay with the system size as [log(L)/L~1/2, for all (narrow) distributions of local fric- tion angle.