A MACROSCOPIC CONSTITUTIVE LAW FOR POROUS SOLIDS WITH PRESSURE-SENSITIVE MATRICES AND ITS IMPLICATIONS TO PLASTIC-FLOW LOCALIZATION

A macroscopic yield criterion for porous solids with pressure-sensitiv e matrices modeled by Coulomb's yield criterion is obtained by general izing Gurson's yield criterion with consideration of the hydrostatic y ield stress for a spherical thick-walled shell and by fitting the fini te element results of a voided cube. From the macroscopic yield criter ion, a plastic potential function for porous solids is derived for eit her plastic normality or non-normality flow for pressure-sensitive mat rices. In addition, the elastic relation, an evolution rule for the pl astic behavior of the matrices, the consistency equation and the void volume evolution equation are presented to complete a set of constitut ive relations for porous solids with rate-dependent pressure-sensitive matrices. Based on the constitutive relations, plastic flow localizat ion is analysed for porous solids with various pressure-sensitive dila tant 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-no rmality 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 loca lization significantly. However, the pressure sensitivity of the matri ces with non-normality retards localization slightly for positive stra in ratios and promotes localization slightly for negative strain ratio s. Under all three deformation modes, the strain softening coupled wit h a moderate amount of void volume inhomogeneity is shown to have a do minant role in plastic flow localization.