Parametric variational principle based elastic–plastic analysis of materials with polygonal and Voronoi cell finite element methods

Parametric variational principle based polygonal finite element method (PFEM) and Voronoi cell finite element method (VCFEM) are developed for the numerical simulations of the elastic–plastic mechanical behavior of heterogeneous materials under small deformation. The shape functions for the polygonal element are given and the parametric potential energy principle of the elastic–plastic system is verified. Based on the parametric complementary energy principle, the formulations of VCFEM and the corresponding parametric quadratic programming model are deduced for the elastic–plastic analysis of materials. Numerical examples are computed to demonstrate the validity and efficiency of the methods developed.