An enhanced three-dimensional (3D) framework for computational homogenization and intergranular cracking of polycrystalline materials is presented. The framework is aimed at reducing the computational cost of polycrystalline micro simulations, with an aim towards effective multiscale modelling. The scheme is based on a recently developed Voronoi cohesive-frictional grain-boundary formulation. A regularization scheme is used to avoid excessive mesh refinements often induced by the presence of small edges and surfaces in mathematically exact 3D Voronoi morphologies. For homogenization purposes, periodic boundary conditions are enforced on non-prismatic periodic micro representative volume elements (μRVEs), eliminating pathological grains generally induced by the procedures used to generate prismatic periodic μRVEs. An original meshing strategy is adopted to retain mesh effectiveness without inducing numerical complexities at grain edges and vertices. The proposed methodology offers remarkable computational savings and high robustness, both highly desirable in a multiscale perspective. The determination of the effective properties of several polycrystalline materials demonstrate the accuracy of the technique. Several microcracking simulations complete the study and confirm the performance of the method

In this work, a discontinuous Galerkin formulation for higher-order plate theories is presented.The starting point of the formulation is the strong form of the governing equations, which are derived in the context of the Generalized Unified Formulation and the Equivalent Single Layer approach from the Principle of Virtual Displacements. To express the problem within the discontinuous Galerkin framework, an auxiliary flux variable is introduced and the governing equations are rewritten as a system of first-order partial differential equations, which are weakly stated over each mesh element. The link among neighbouring mesh elements is then retrieved by introducing suitably defined numerical fluxes, whose explicit expressions define the proposed Interior Penalty discontinuous Galerkin formulation. Furthermore, to account for the presence of generally curved boundaries of the considered plate domain, the discretisation mesh is built by combining a background grid and an implicit representation of the domain. hp-convergence analyses and a comparison with the results obtained using the Finite Element Method are provided to show the accuracy of the proposed formulation as well as the computational savings in terms of overall degrees of freedom.

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In the present paper a fast solver for dual boundary element analysis of 3D anisotropic crack problems\ud is formulated, implemented and tested. The fast solver is based on the use of hierarchical matrices for\ud the representation of the collocation matrix. The admissible low rank blocks are computed by adaptive\ud cross approximation (ACA). The performance of ACA against the accuracy of the adopted computational\ud scheme for the evaluation of the anisotropic kernels is investigated, focusing on the balance between the\ud kernel representation accuracy and the accuracy required for ACA. The system solution is computed by\ud a preconditioned GMRES and the preconditioner is built exploiting the hierarchical arithmetic and taking\ud full advantage of the hierarchical format. The effectiveness of the proposed technique for anisotropic crack\ud problems has been numerically demonstrated, highlighting the accuracy as well as the significant reduction\ud in memory storage and analysis time. In particular, it has been numerically shown that the computational\ud cost grows almost linearly with the number of degrees of freedom, obtaining up to solution speedups of\ud order 10 for systems of order 104. Moreover, the sensitivity of the performance of the numerical scheme\ud to materials with different degrees of anisotropy has been assessed