Parametric variational principle based elastic-plastic analysis of heterogeneous materials with Voronoi cell finite element method

The Voronoi cell finite element method (VCFEM) was adopted to replace the classical displacement based finite element method in numerical simulation of the equivalent mechanical property of heterogeneous materials. The parametric variational principle and quadratic programming method were coupled with the VCFEM for the analysis of the two-dimensional heterogeneous problem. Finite element formulations were derived and a standard quadratic programming model was deduced from the problem. The influence of the microscopic inclusion on the overall mechanical response of heterogeneous materials was studied. The mechanical properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Some numerical examples were presented and compared with ANSYS, and the results demonstrate the validity and effectiveness of the method developed.