Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

A survey of recent contributions on three-dimensional grain-scale mechanical modelling of polycrystalline materials is given in this work. The analysis of material microstructures requires the generation of reliable micro-morphologies and affordable computational meshes as well as the description of the mechanical behavior of the elementary constituents and their interactions. The polycrystalline microstructure is characterized by the topology, morphology and crystallographic orientations of the individual grains and by the grain interfaces and microstructural defects, within the bulk grains and at the inter-granular interfaces. Their analysis has been until recently restricted to twodimensional cases, due to high computational requirements. In the last decade, however, the wider affordability of increased computational capability has promoted the development of fully three-dimensional models. In this work, different aspects involved in the grain-scale analysis of polycrystalline materials are considered. Different techniques for generating artificial micro-structures, ranging from highly idealized to experimentally based high-fidelity representations, are briefly reviewed. Structured and unstructured meshes are discussed. The main strategies for constitutive modelling of individual bulk grains and inter-granular interfaces are introduced. Some attention has also been devoted to three-dimensional multiscale approaches and some established and emerging applications have been discussed.