Modified Stress Tensors for Anisotropic Behavior of Granular Materials

Abstract

Effects of fabric anisotropy on the mechanical behavior of granular materials have become well known. Without the introduction of variables describing fabric anisotropy into the constitutive formulation, some important deformation features of granular materials can not be formulated in a reasonable way. Although the principle of material objectivity and the thermo-dynamical restrictions in the continuum mechanics give the framework to a class of reasonable constitutive equations associated with anisotropic features, the framework is still too wide to obtain a practical constitutive equation. This fact indicates the necessity of conventional methods within the fundamental restrictions. Modified stress tensors being a consecquence of the linear transformation depending on fabric anisotropy from the stress tensor are poposed and discussed, with a particular emphasis on the elasto-plastic behavior of anisotropic granular materials. It is shown that : (a) classical hardening models (isotropic, kinematic, and combined) are obtained as special cases of the present method ; (b) the shape change of yield surfaces during plastic deformation is a natural consequence if relevant terms are included in the transformation rule. Anisotropic deformation and strength behaviors of granular materials are formulated based on the modified Drucker-Prager yield condition and the non-associated flow model for two dimensional problems in order to demonstrate the effectiveness of the proposed method.