Two new Voronoi cell finite element models for fracture simulation in porous material under inner pressure

Abstract

Two new elements based on Voronoi cell finite element (VCFEM) model are developed for fracture simulation of material containing massive holes under inner pressure. One is the element with crack initiating from edge of the inner hole. The other one is the element with crack initiating from the edge of cell which generates when cracks extend from adjacent cells. In addition, analytical solution of stress components near crack tip is added to stress function applying to complementary energy functional. When the number of the holes is over a hundred thousand, the ordinary finite element needs about hundreds of millions of meshes which are solved impossibly. However, there is the characteristic of keeping the number of grids with hole number in new Voronoi cell which makes large scale simulation possible. Also grids number in VCFEM remains constant while the number in ordinary element increases greatly with cracks. The results for a large number of numerical experiments which are to calculate stress intensity factor (SIF) have demonstrated that the present models have high precision and capture stress intensity accurately.