Strain localization in frictional materials exhibiting displacement jumps Original Research Article

This paper presents a mathematical model for analyzing strain localization in frictional solids exhibiting displacement jumps. Precise conditions for the appearance of slip lines, including their initiation and evolution, are outlined for a rate-independent, strain-softening Drucker–Prager model, and explicit analytical expressions are used to describe the orientation of the slip line. A stress–displacement relation obtained through the consistency condition is also formulated to describe the quasi-static response in the post-localization regime. The mathematical model, which is cast within the framework of finite element analysis employing the assumed enhanced strain method, circumvents mesh-dependence issues often associated with rate-independent plasticity models. It is shown that the enhancement equation is nothing else but the consistency condition imposed on the band. Numerical examples involving plane strain compression are described to demonstrate objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions.