Computational aspects of the Cosserat finite element analysis of localization phenomena

The computational aspects of the finite element solution procedure based on the Cosserat theory are studied for some elastic-plastic problems, in which the localization occurs. For this purpose, the equations of the Cosserat elasto-plasticity, which include effects of couple stress, micro-rotation and length scale, are presented. The Cosserat finite element formulation is derived and an algorithm for the solution procedure is proposed. For the elastic-plastic problems considered here, the mesh-independency of the Cosserat-based results is quantified and effects of the internal length and Cosserat material parameter a are investigated on the results. Also, the influence of the internal length on the convergence rate of the solution procedure is studied. A comparison of the results based on the Cosserat theory and those based on the couple stress and classical theories is presented. In addition, the results of the Cosserat theory are compared with the experimental data available in the literature. It is shown that in spite of an additional degree of freedom for each node in the Cosserat theory, the computational effort for the solution procedure in this theory is less than the classical theory. Also, convergence rate is affected more significantly by decrease of the internal length in finer discretizations.