A macroscopic constitutive law for porous solids with pressure-sensitive matrices and its implications to plastic flow localization

Abstract

A macroscopic yield criterion for porous solids with pressure-sensitive matrices modeled by Coulomb's yield criterion is obtained by generalizing Gurson's yield criterion with consideration of the hydrostatic yield stress for a spherical thick-walled shell and by fitting the finite element results of a voided cube. From the macroscopic yield criterion, a plastic potential function for porous solids is derived for either plastic normality or non-normality flow for pressure-sensitive matrices. In addition, the elastic relation, an evolution rule for the plastic behavior of the matrices, the consistency equation and the void volume evolution equation are presented to complete a set of constitutive relations for porous solids with rate-dependent pressure-sensitive matrices. Based on the constitutive relations, plastic flow localization is analysed for porous solids with various pressure-sensitive dilatant matrices with power-law strain hardening or with intrinsic strain softening under plane strain tension, axisymmetric tension and plane stress biaxial loading. Our numerical results indicate that the non-normality of the pressure-sensitive matrices promotes localization under plane strain tension. Under axisymmetric tension the critical strain at localization decreases significantly as the pressure sensitivity of the matrices increases. Under plane stress biaxial loading conditions, the pressure sensitivity of the matrices with normality retards localization significantly. However, the pressure sensitivity of the matrices with non-normality retards localization slightly for positive strain ratios and promotes localization slightly for negative strain ratios. Under all three deformation modes, the strain softening coupled with a moderate amount of void volume inhomogeneity is shown to have a dominant role in plastic flow localization.