An explicit formulation of the macroscopic strength criterion for porous media with pressure and Lode angle dependent matrix under axisymmetric loading

This paper aims to propose an explicit formulation of the macroscopic strength criterion for porous media with spherical voids. The matrix is assumed rigid and perfectly plastic with yield surface described by the three-parameter strength criterion, which is Lode angle and pressure dependent and capable of accounting for distinct values of the uniaxial tensile strength, uniaxial compressive strength (UCS) and equal biaxial compressive strength (eBCS). An exact upper bound of the macroscopic strength is derived for porous media subjected to purely hydrostatic loading. Besides, an estimate of the macroscopic strength profile of porous media under axisymmetric loading is obtained in parametric form. Moreover, a heuristic strength criterion in explicit form is further developed by examining limit cases of the parametric strength criterion. The developed strength criteria are assessed by finite-element based numerical solutions. Compared with the parametric strength criterion which involves cumbersome functions, the heuristic one is convenient for practical applications. For specific values of the matrix's strength surface, the proposed heuristic strength criterion can recover the well-known Gurson criterion. The present work also addresses the effect of the ratio of matrix's eBCS to UCS on the macroscopic strength of porous media. For matrix with distinct values of eBCS and UCS, neglecting the difference between eBCS and UCS would result in an underestimation of the macroscopic strength, especially when the pressure is large.