Heterogeneous Mohr-Coulomb plastic material

We consider a heterogeneous medium which locally obeys a Mohr-Coulomb rigid-plastic behavior. We are interested in the macroscopic yield criterion based on an admissible stress formulation. We propose a two-dimensional analysis based on Airy potential formulation, using a first order perturbation. We first derive an upper bound for the macroscopic 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 angle. Corrections to this value decay with the system size as log(L)/L]^1/2, for all (narrow) distributions of local friction angle. Received: 26 June 1999