Automatic polyhedral mesh generation and adaptive analysis of fracture processes in brittle polycrystalline materials

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The proposed project addresses the numerical modeling of both intergranular and transgranular fracture phenomena in brittle polycrystalline material. Such materials, e.g. solar grade silicon, are used in various engineering applications where accurate prediction of failure modes is imperative. A major objective of the project is to devise, implement and benchmark robust and automatic mesh generation and analysis techniques tailored to the specific requirements of fracture modelling in solids that are composed of randomly oriented polygonal or polyhedral regions. Here, challenges arise due to the fact that grain sizes may vary strongly in size, grain boundaries must be retained and fine meshes may be required near grain boundaries and in transgranular fracture zones. To this end, an integrated meshing, refinement and modeling approach will be developed in close cooperation with project partners who are experts in the field of geometrical modeling. In addition to adopting a hierarchical polytree approach to facilitate highly localized refinement we aim to develop an innovative alternative meshing approach that is based on increasing mesh density by shifting nodes while retaining the connectivity. Automated analyses on hierarchical meshes are facilitated by the scaled boundary finite element method (SBFEM), which can be used on arbitrarily faceted star-convex polygonal or polyhedral domains with hanging nodes. Taking into account the geometrical aspects explained above, we also aim to develop an adaptive framework for brittle fracture modeling where both intergranular and transgranular failure modes will be addressed. To this end, we strive to develop a scaled-boundary based multi-phase field approach for purely mechanical fracture in a first step and to extend the latter to multi-physical / thermally-induced fracture in a second step. Since the SBFEM in its original form has been derived for linear elasticity, we therefore aim to further develop the concept of polygonal / polyhedral shape functions based on SBFEM to solve multi-physical fracture problems. The final simulation framework will facilitate multi-physical brittle fracture modeling on complex polycrystalline geometries and will thus contribute to the greater objective of developing polytope element technology for the analysis of nonlinear problems in mechanics.