A method of step-by-step packing and its application in generating 3D microstructures of polycrystalline and composite materials

Micromechanical simulations with an explicit account of the material microstructure provide valuable information on the microscale stress and strain distributions under loading. The construction of 3D microstructure models reproducing realistic microstructure morphology is a challenging task of computational mechanics and materials science. In this paper, a semi-analytical method of step-by-step packing to construct 3D microstructure models of polycrystalline and composite materials is presented. The main idea of the method is to pack a pre-meshed volume with 3D microstructure elements in a stepwise fashion in accordance with a set of geometrical-based algorithms specific for each type of the microstructure. The seed distributions and growth laws are the main parameters controlling the microstructural patterns. It is shown in particular examples that using different growth laws and seed distributions as well as their various combinations it is possible to construct 3D microstructure models with a wide variety of geometrical features. Some aspects of the numerical implementation not addressed before are given in detail.