Image-based computational homogenization and localization: comparison between X-FEM/levelset and voxel-based approaches

In material science, images are increasingly used as input data for computational models. In most of the published papers, voxel-based finite element models are employed using a mesh that is automatically built by converting each voxel into a finite element. We have recently proposed (Legrain et al., Int J Numer Methods Eng 86(7): 915-934, 2011) another computational approach for incorporating images in models, based on the extended finite element method (X-FEM) and levelsets. Its main advantages are that the mesh does not need to conform to the geometry and that a smooth representation of physical surfaces is obtained. The aim of this paper is to compare the two approaches in the framework of computational homogenization in elasticity, starting from material microstructural images. Attention will be paid to geometrical approximations, macroscopic properties and local quantities (e.g. stress oscillations, local error etc.). It is shown that the X-FEM/levelset approach is more efficient than voxel-based FEM.