Approximate criteria for ductile porous materials having a Green type matrix: Application to double porous media

In the framework of limit analysis theory, we derive closed-form expressions of approximate criteria for ductile porous materials whose plastically compressible matrix obeys to an elliptic criterion. The general methodology is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. We first consider a porous medium with a Green type matrix and establish the corresponding macroscopic yield function. Then, the obtained results are used in order to investigate double porous materials whose solid phase at the microscale (the smallest scale) obeys a von Mises criterion. The results are assessed by comparing them with numerical data, and with recently published results.