基于本征化和有限单元的体素非均匀结构裂纹扩展模拟
Simulation of crack propagation through voxel-based, heterogeneous structures based on eigenerosion and finite cells
摘要：
本文提出了一种有效的模拟韧性裂纹扩展通过异质结构，例如金属微观结构，这是作为体素数据的算法。这些类型的模拟是需要的，例如，小尺度下磨损机制的数值研究，这在工程上仍然是一个具有挑战性的任务。所提出的算法的基本思想是结合有限单元法的优点，允许一个方便的集成异构有限元问题与eigenerosion方法，仍然使网格独立模拟裂纹扩展。主要的组成部分是从有限的子单元切换到有限元裂纹的进展，从而自动自适应地细化裂纹尖端通过管理新出现的节点作为悬挂节点。在微观尺度上，裂纹扩展的技术相关问题大多与亚临界裂纹扩展有关，其中裂纹随着随后的载荷循环快速且逐步地移动。因此，惯性可能变得很重要，这就是为什么通过将侵蚀元件的质量分散到节点来考虑动力学，以避免侵蚀过程导致的质量损失。此外，为了保证计算效率和计算精度，还考虑了有限胞腔剖分的处理方法。数值框架以及体素分解技术进行了详细的分析，在不同的三维数值例子，以显示所提出的方法的性能。
英文摘要：
This paper presents an algorithm for the efficient simulation of ductile crack propagation through heterogeneous structures, as e.g. metallic microstructures, which are given as voxel data. These kinds of simulations are required for e.g., the numerical investigation of wear mechanisms at small length scales, which is still a challenging task in engineering. The basic idea of the proposed algorithm is to combine the advantages of the Finite Cell Method allowing for a convenient integration of heterogeneous finite element problems with the eigenerosion approach to still enable the mesh-independent simulation of crack propagation. The major component is to switch from finite subcells to finite elements wherever the crack progresses, thereby automatically adaptively refining at the crack tip by managing the newly appearing nodes as hanging nodes. Technically relevant problems of crack propagation at the microscale are mostly linked with sub-critical crack growth where the crack moves fast and stepwise with subsequent load cycles. Therefore, inertia may become important which is why dynamics are taken into account by spreading the mass of the eroded elements to the nodes to avoid a loss in mass resulting from the erosion procedure. Furthermore, a certain treatment for the finite cell decomposition is considered in order to ensure efficiency and accuracy. The numerical framework as well as the voxel decomposition techniques are analyzed in detail in different three-dimensional numerical examples to show the performance of the proposed approach.
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