3D finite element modeling of shear band localization via the micro-polar Cosserat continuum theory

In this paper, a micro-polar continuum model is presented based on the Cosserat theory for 3D modeling of localization phenomena. Since the classical continuum model suffers from the pathological mesh-dependence in strain localization problem, the governing equations are regularized by adding the rotational degrees-of-freedom to conventional degrees-of-freedom. The fundamental relations in three-dimensional Cosserat continuum are presented and the internal length parameters are introduced in the elasto-plastic constitutive matrix to control the shear bandwidth. The mesh independency of Cosserat model in strain-softening problem is verified and the effect of internal parameters is investigated. The efficiency of proposed computational algorithm is demonstrated by 3D numerical simulations of the vertical cut, slope problem and a tensile specimen. A comparison is performed between the classical and Cosserat theories and the effect of internal length parameter is demonstrated.