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

拟议的项目涉及脆性多晶材料中的晶间和穿晶断裂现象的数值模拟。这类材料，例如太阳能级硅，被用于各种工程应用中，其中必须准确预测故障模式。该项目的一个主要目标是设计、实施和测试健壮的自动网格生成和分析技术，以适应由随机取向的多边形或多面体区域组成的实体中的断裂建模的特定要求。在这里，由于晶粒度变化很大，必须保留晶界，在晶界附近和穿晶断裂区可能需要精细的网状结构，这就产生了挑战。为此，将与几何建模领域的专家项目伙伴密切合作，制定一种综合的网格化、精细化和建模方法。除了采用层次多叉树方法来促进高度局部化的细化之外，我们的目标是开发一种创新的替代网格方法，该方法基于在保持连通性的情况下通过移动节点来增加网格密度。尺度边界有限元方法可用于任意面片的星凸多边形或带有悬挂节点的多面体区域，便于层次化网格的自动分析。考虑到上面解释的几何方面，我们还致力于开发一个适用于脆性断裂模拟的框架，其中将处理沿晶和穿晶破坏模式。为此，我们致力于在第一步中发展一种基于尺度边界的多相场方法，用于纯机械断裂，并在第二步中将后者扩展到多物理/热诱导断裂。由于SBFEM的原始形式是用于线弹性力学的，因此我们的目标是进一步发展基于SBFE的多边形/多面体形状函数的概念，以解决多物理断裂问题。最终的模拟框架将促进复杂多晶几何形状的多物理脆性断裂建模，从而有助于开发用于分析力学中的非线性问题的多晶元素技术这一更大的目标。

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.