Plastic response of porous solids with pressure sensitive matrix

Abstract

A practical straightforward procedure is suggested for constructing the yield surface of solids containing voids embedded in a pressure sensitive matrix. Derivation centers on expanding yield function in powers of porosity ratio f, with zero order term describing the void free matrix. The coefficients of that expansion are determined, in terms of stress invariants, from simple stress patterns (like spherical and cylindrical representative volume elements) at full yield, assuming perfectly plastic response. In this paper we concentrate on two families of matrices described by the Drucker–Prager and Schleicher pressure sensitivity. Limiting the power expansion up to second order terms we determine uniquely the two unknown expansion coefficients from spherical RVE under remote hydrostatic tension and compression. This approach does not employ kinematic fields, averaging methods or energy theorems, yet results are remarkably similar though not identical to available yield conditions. Key findings are supported by asymptotic expansions, at different levels of accuracy, for low hydrostatic pressure and low pressure sensitivity of matrix material.