Thermo-mechanical analysis of elastic cracks in heterogeneous materials by FEM and VCFEM

The present paper presents a numerical method for the evaluation of the stress intensity factor in two dimensional heterogeneous materials under mechanical and thermal loads. The proposed method uses both FEM (Finite Element Method) and VCFEM (Voronoi Cell Finite Element Method), and has been developed using the Mathematica™ environment. The numerical models are obtained by combining the traditional finite elements, used to model the crack tip, and the Voronoi Cells, based on an hybrid formulation of the element, in order to represent the second phase. The use of this method in investigating the crack interaction in heterogeneous materials allows a simple mesh generation and a low computational cost, compared with traditional finite element method. In the present paper the proposed model has been verified by evaluating the stress intensity factors in an homogeneous material and by comparing them with those reported in literature; then the stress intensity factors for a heterogeneous material with periodic distribution of the second phase has been evaluated by introducing a variance in temperature.