Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1563245 | Computational Materials Science | 2008 | 17 Pages |
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.