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In this paper, the transient computational homogenization scheme is extended to allow for nonlinear elastodynamic phenomena. The framework is used to analyze wave propagation in a locally resonant metamaterial containing hyperelastic rubber-coated inclusions. The ability to properly simulate realistic nonlinearities in elasto-acoustic metamaterials constitutes a step forward in metamaterial design as, so far, the literature has focused only on academic nonlinear material models and simple lattice structures. The accuracy and efficiency of the framework are assessed by comparing the results with direct numerical simulations for transient dynamic analysis. It is found that the band gap features are adequately captured. The ability of the framework to perform accurate nonlinear transient dynamic analyses of finite-size structures is also demonstrated, along with the significant computational time savings achieved.

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At the microstructural scale, Voronoi tessellations are commonly used to represent a polycrystalline morphology. However, due to spherical growth of nuclei, an anisotropic tessellation with spatially varying elongated grain directions, which is present in many applications, cannot be obtained. In this work, a novel 3D anisotropic Voronoi algorithm is presented, together with its implementation and two application cases. The proposed algorithm takes into account preferred grain growth directions, aspect ratios and sizes in the definition of an ellipsoidal growth velocity field defined per grain. For applications in which a predetermined mesh is used, e.g. voxel-mesh based simulations, the grains are extracted in a straight-forward manner. In cases where a fully grain conforming discretization is desired, e.g. finite element simulations, a hexahedral mesh generator is incorporated to arrive at a discretization which can be directly used in microstructural modeling simulations. Two application cases are studied (a wire + arc additively manufactured and a magnesium alloy microstructure) in which the algorithm’s capability for curved, non-convex, periodic domains is shown. Furthermore, the resulting grain morphology is compared to experimental data in terms of grain size, grain aspect ratio and grain columnar direction distribution. In both cases, the algorithm adequately produces a representative volume element with convincing representativeness of the experimental data. The 3D anisotropic Voronoi algorithm is highly versatile in a wide range of application cases, specifically suitable for the generation of polycrystalline microstructures that include grains with spatially varying elongated directions.