On the structure of poroplastic constitutive relations

The paper discusses from first principles all aspects relevant to the plasticity of porous materials. Emphasis is laid on unhomogeneous yielding, defined as the process of yielding and plastic flow under gradient-free macroscopically nonuniform deformation. The nonuniformity is represented by strain localization in one or more bands of finite thickness. A universal feature of all intrinsic yield criteria is their dependence upon the normal and shear tractions resolved on the band. When specialized to isotropy, a Mohr-Coulomb criterion and a Rankine-Tresca criterion emerge as two extremes. The latter is an ideal that typifies the yield behavior of porous materials under arbitrary loadings. The general theory stands for a finite number of bands or yield systems. Its overall structure bears some features of crystal plasticity, but with dependence upon the resolved normal stress. The evolution of microstructural parameters can be given in general terms, being solely based on the kinematic constraints of unhomogeneous yielding and matrix incompressibility. Throughout the paper, the competition with homogeneous yielding, heretofore taken for granted, is analyzed with or without strain and strain-rate hardening effects. We close by discussing the thermodynamic consistency of this new class of constitutive relations and a link to strain-gradient theories.

Automated summary

This paper discusses the plasticity of porous materials from a fundamental standpoint. It focuses on the concept of unhomogeneous yielding, which involves the yielding and plastic flow under gradient-free macroscopically nonuniform deformation. The nonuniformity is represented by strain localization in one or more bands of finite thickness. The paper presents a general theory for the finite number of bands or yield systems, with a dependence on the resolved normal stress.