An approximate strength criterion of porous materials with a pressure sensitive and tension-compression asymmetry matrix

An approximate analytical criterion is established in the present study to describe the macroscopic strength behavior of porous materials with a pressure sensitive and tension-compression asymmetry solid matrix. The solid matrix is assumed to obey a Mises-Schleicher type criterion at the local scale. By using the stress variational homogenization method (SVH) with a strictly statically admissible stress field, an analytical criterion is first obtained. This criterion can retrieve the exact solution for the hydrostatic loading and provide a good prediction of the strength for the pure deviatoric loading (Σeq/σo). However, for small values of stress triaxiality in compressive domain, the analytical criterion underestimates the strength. Based on the accurate value of Σeq/σo obtained by the SVH method and taking into account some special conditions and requirements, an approximate improved strength criterion is derived. For a wide validation of the proposed criterion, new numerical results are presented based on the finite element simulations. The improved criterion is then verified through comparisons with both the upper and lower bounds given in Pastor, Kondo, and Pastor (2013) and the finite element results for a large range of porosity and tension-compression asymmetry ratio of the matrix. It is found that this new criterion improves existing ones. Finally, the criterion is applied to describe the plastic yield stresses of porous chalk and plaster.