Static analysis of 2D micropolar model for describing granular media by considering relative rotations

The micropolar continuum theory has attracted enormous attention for studying many mechanical problems specially when the microstructure effects (size scale) could not be ignored like granular materials. This enriched continuum model refers to the Cosserat-type theories which take into account independently the rotational degrees of freedom (DOF) in addition to the translational ones. This theory provides the essential features for studying the granular media by taking into account the additional DOF. In this study we investigate an efficient formulation of nonlinear micropolar continuum model based on a new contribution of the relative micro rotations. Thus, a novel relative rotation tensor is used as a measure of deformation in addition to the classical strain tensor and the wryness tensor. Accordingly, an orthogonal microrotation matrix is considered with four degrees of freedom which admits four opportune constraints. The consequences of the proposed micropolar model are then discussed with the aid of numerical examples. To this aim, several numerical applications of 2D plate specimens subjected to in-plane loads are considered by performing a finite element code based on a variational formulation. Some new key features of the novel model, in comparison with the classical one, are illustrated by the sensitive numerical analysis.