Parametric variational principle based elasticplastic 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 elasticplastic 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 elasticplastic 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 elasticplastic analysis of materials. Numerical examples are computed to demonstrate the validity and efficiency of the methods developed.
parametric variational principle voronoi cell finite element method polygonal finite element method quadratic programming method