Advanced geometry representations and tools for microstructural and multiscale modeling

The macroscopic behavior of complex heterogeneous materials is governed by the interactions between their constituents at the microstructural scale. This has fostered a large number of contributions on multiscale modeling of materials, with the aim of combining the behaviors of their constituents with their geometrical organization. However, many contributions focused on the investigation of advanced physics while using simplified geometries to represent the spatial organization of the phases. Conversely, the recent development of experimental imaging techniques has allowed the use of real geometries in full microstructural simulations. This exploitation of experimental images however convolutes the effects of all morphological features, and does not allow unraveling the dominant geometrical effects. Recent developments allow bridging this gap by using advanced geometry representation tools. This chapter presents an integrated set of tools to address complex geometries based on distance fields and level sets. This integrated approach allows (i) generating microstructural geometries in a controlled fashion for a wide range of microstructural morphologies starting from a population of inclusions and (ii) discretizing the obtained geometries using high quality conformal tetrahedral finite element meshes. Based on a presentation of explicit and implicit descriptions of geometries, the use of distance fields to improve the efficiency of packing algorithms is presented. The recombination of such distance fields to generate representative volume elements (RVEs) for various microstructural morphologies is next detailed. Inclusion-based materials and coated and cemented materials are considered. Distance field-based morphing of inclusions is also used to obtain generalized spatial tessellations. Further generalizations useful for other types of materials such as foams and composites are briefly discussed. The attention is next shifted toward the automated discretization of such geometries for simulations. The exploitation of the implicit description of the heterogeneous geometries for conformal discretization is illustrated. A mesh optimization approach is exploited, based on a targeted element size map that is directly derived from the distance fields describing the geometry. The procedure is outlined in details for the case of 2D RVEs, with a discussion on the specific aspects related to its extension for 3D problems.