On shear band localization phenomena of liquid-saturated granular elastoplastic porous solid materials accounting for fluid viscosity and micropolar solid rotations

Abstract

Elastoplastic deformations of cohesive-frictional liquid-saturated granular solid materials can be described by use of a macroscopic continuum mechanical approach within the well-founded framework of the theory of porous media (TPM). In the present contribution, the TPM formulation of the skeleton material is extended by micropolar degrees of freedom in the sense of the Cosserat brothers. Proceeding from two basic assumptions, material incompressibility of both constituents (skeleton material and pore liquid) and geometrically linear solid deformations, the non-symmetric effective skeleton stress and the couple stress tensor are determined by linear elasticity laws. In the framework of the ideal plasticity concept, the plastic yield limit is governed by a smooth and closed single-surface yield function together with non-associated flow rules for both the plastic strain rate and the plastic rate of curvature tensor. Fluid viscosity is taken into account by the drag force. The inclusion of micropolar degrees of freedom, in contrast to the usual continuum mechanical approach to the TPM, allows, on the one hand, for the determination of the local average grain rotations and, on the other hand, additionally yields a regularization effect on the solution of the strongly coupled system of governing equations when shear banding occurs. However, in the framework of the original TPM formulation of fluid-saturated porous materials, the inclusion of the fluid viscosity alone also yields a certain regularization on shear band computations. The numerical examples are solved by use of finite element discretization techniques, where, in particular, the computation of shear band localization phenomena is carried out by the example of the well-known base failure problem of geotechnical engineering.