An enriched-FEM model for simulation of localization phenomenon in Cosserat continuum theory

The standard finite element models, i.e. the finite element methods that use the classical continuum models, suffer from the excessive mesh dependence when a strain-softening model is used. It cannot converge to a meaningful solution and the governing differential equation loses the ellipticity. This paper presents an enriched finite element algorithm for simulation of localization phenomenon using a higher order continuum model based on the Cosserat continuum theory. The governing equations are regularized by adding the rotational degrees-of-freedom to the conventional degrees-of-freedom and including the internal length parameter in the model. The extended finite element method (X-FEM) is employed, in which the discontinuity interfaces are represented independent of element boundaries and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the domain of elements. Finally, several numerical examples are analyzed to demonstrate the efficiency of the mixed XFEM – Cosserat continuum model in shear band localization.