Localization analysis of granular materials in Cosserat elastoplasticity: Formulation and finite element implementation

There are two different approaches to solving solid mechanics problems: a continuum considered in terms of a contiguous and homogenous solid or a continuum that has a distinct microstructure, for which geomaterials is representative. Classical continuum mechanics considers the interaction of microstructural units of the material through stresses and displacements of material points. Therefore, conventional continuum mechanics approaches do not incorporate any intrinsic material length scale in stress, strain or modulus expressions. The mechanical response of solid changes drastically as the deformation evolves from a diffuse state to a highly localized deformation state. The mechanical behavior of the localized shear zone may not be completely characterized by classical continuum theories because they incorporate no 'material length scales' and consequently reflect no size effects. In order to explain the influences of microstructures on the behavior of materials, higher order effects such as moments that reflect the grain geometry and kinematics (eg. Rotations of soil grain) must be incorporated, which in turn lead to a basic asymmetry in shear stress and micropolar (or Cosserat) effects. A Cosserat continuum incorporates the characteristic length that relates the couple stresses and micro-curvatures at the constitutive level. The internal length scale and rotation gradients lead to regularization effects that enable the size of the shear zone to be predicted and whose physical features to be realistically simulated.; The aim of this research is to review classical and Cosserat continuum theories for a more realistic study of the load-displacement behavior and localization analysis of granular materials. Analytical and finite element solutions of localization analysis have been carried out for both classical and Cosserat continua. The aim of this study is also to explore if Cosserat theory is feasible for analyzing geotechnical problems. The equations of the Cosserat elasto-plasticity, which include effects of couple stress, micro-rotation and length scale have been formulated for small deformation theory. The formulations of Cosserat elastoplasticity have been implemented in a nonlinear commercial finite element code using the user defined element utility. The mesh dependency effect in finite element solution is reduced. Analytical and finite element results demonstrate that localization can occur either in the hardening or softening regime in classical continua. However, softening is needed to trigger localization in Cosserat continua. Orientation of the localization zone and critical hardening parameters depend on the Cosserat shear modulus and the intrinsic length scale. The numerical results demonstrate that localization in granular materials can realistically be determined with a Cosserat elastoplastic constitutive law. However, special attention must be given to Cosserat material parameters.