Contribution to the modelling and homogenization of 3D structures in the presence of flaws by XFEM

•Development of a software tool for modelling 3D structures containing flaws.•Displacement field and the homogenization effective parameters by XFEM/Level-set.•Flattening progressively voids (cylinder, sphere) to simulate a crack situation. The aim of this study is the development of software code based on the eXtended Finite Element Method (XFEM) to model the behavior of three-dimensional structures containing heterogeneity (inclusions, voids and cracks). The shape of flaws are presented using combinations of spatial level functions called Level-Set. Firstly, the obtained results for several validate tests are compared to those evaluated analytically and those obtained by using the free software “Caste3M2018” based on the Finite Element Method (FEM), where good correlations are observed. This shows the efficiency and the robustness of the proposed programmed approach. In homogenization context, several cases of Representative Volume Elementary (RVE) are then studied, to get the evolution of the bulk compressibility modulus according to the void flattening ratio and according to its size when the flaws became cracks.