A yield criterion for isotropic porous media for the meso-scale range

A macroscopic yield criteria for isotropic porous materials with spherical voids as the represent unit cell modeled by elliptic-equation yield function was derived by considering the matrix as compressible rigid-perfectly plastic. From the yield function, plastic dissipation work of the material was derived for plastic normality flow, and plastic limit analysis on micro-deformation mechanism of the medium was established. The relationship between macroscopic stress or strain rate and meso-structural parameters was deduced by upper-bound theorem. In addition, the macroscopic yield criteria of containing macro equivalent stress versus macro mean stress was established by theoretical derivation, and it could be reduced to a macroscopic yield criteria or Mises criteria at some special cases. Numerical results show that the yield criteria is dependent not only the macro-stresses but also meso-structural parameters, and reasonable agreement between the calculated and the experimental model are obtained.