Analysis of Cosserat materials with Voronoi cell finite element method and parametric variational principle

The elastic–plastic analysis of heterogeneous Cosserat materials is carried out with the Voronoi cell finite element method (VCFEM) under small deformation. The parametric complementary energy principle of the Cosserat theory is developed. By using the parametric variational principle, the quadratic programming model and finite element formulation for the VCFEM are established. Compared with the conventional finite element method (FEM), the newly developed method requires no tedious iterative procedures, and has no convergence problems. Based on the developed method, the influence of microscopic heterogeneities on the overall mechanical responses of heterogeneous materials is studied. Numerical examples are given to demonstrate the validity and efficiency of the method developed.