Critical state plasticity. Part VI: Meso-scale finite element simulation of strain localization in discrete granular materials

Abstract

Development of more accurate mathematical models of discrete granular material behavior requires a fundamental understanding of deformation and strain localization phenomena. This paper utilizes a meso-scale finite element modeling approach to obtain an accurate and thorough capture of deformation and strain localization processes in discrete granular materials such as sands. We employ critical state theory and implement an elastoplastic constitutive model for granular materials, a variant of a model called “Nor-Sand”, allowing for non-associative plastic flow and formulating it in the finite deformation regime. Unlike the previous versions of critical state plasticity models presented in a series of “Cam-Clay” papers, the present model contains an additional state parameter ψ that allows for a deviation or detachment of the yield surface from the critical state line. Depending on the sign of this state parameter, the model can reproduce plastic compaction as well as plastic dilation in either loose or dense granular materials. Through numerical examples we demonstrate how a structured spatial density variation affects the predicted strain localization patterns in dense sand specimens.