Efficient image-based simulation techniques for 3D phase-field modelling of fracture processes in micro-heterogeneous materials

提出的项目涉及非均质介质中复杂三维断裂现象的数值模拟。这种模拟对于基础设施和技术部件的安全性和耐久性评估具有重要意义，并且在计算材料设计领域具有高度相关性。相场方法将用于断裂，因为它能够模拟复杂的裂纹路径和现象，如裂纹分支和合并。它消除了复杂的重新网格划分程序的需要，也不需要选择裂纹扩展准则。尽管有这些优点，相场方法在三维问题中的应用目前仍受到解决弹性固体中扩散断裂的多场问题所需的过多数值努力的阻碍。相场法的效率受到扩散裂纹公式中涉及的长度尺度参数的限制，这必须通过数值模型中足够精细的网格来解决。在本项目中，我们的目标是通过基于缩放边界有限元法（SBFEM）开发相场方程的半解析解来克服这一限制。SBFEM简化了多面体单元的构建，因此可以在八叉树网格上使用，从而允许在破裂带中快速转换单元尺寸。为了充分利用这一优势，该项目的第二个目标是开发一种自适应八叉树网格细化策略。在这里，我们将使用一个误差指示器，它直接来自缩放边界有限元解。现有的自动八叉树网格生成和分析技术将通过加入过渡元素来优化裂缝相场建模。提出的正则裂纹拓扑变分问题的尺度边界有限元解将为位移-相场耦合方程的交错和整体解方案的发展提供基础。最终的模拟框架将促进三维微非均质样品的虚拟测试，从而有助于更好地理解复合材料的损伤和断裂过程。

The proposed project addresses the numerical modelling of complex three-dimensional fracture phenomena in heterogeneous media. Such simulations are of importance with respect to safety and durability assessment of infrastructure and technical components and highly relevant in the field of computational material design. A phase-field approach to fracture will be used due to its capability to model complex crack paths and phenomena such as crack branching and coalescence. It eliminates the need for sophisticated re-meshing procedures and does not require the choice of crack propagation criteria. Despite these advantages, the application of the phase-field approach to three-dimensional problems is currently precluded by the excessive numerical effort needed to solve the multi-field problem of diffusive fracture in elastic solids. The efficiency of a phase-field approach is limited by the length-scale parameter involved in the diffusive crack formulation, which must be resolved by a sufficiently fine mesh in a numerical model. In this project, we aim to overcome this limitation by developing a semi-analytical solution of the phase-field equation based on the scaled boundary finite element method (SBFEM). The SBFEM facilitates the formulation of polyhedral elements and can thus be used on octree meshes, which allow for a rapid element size transition in fracture zones. To fully exploit this advantage, the second objective of this project is to develop an adaptive octree mesh refinement strategy. Here, we will use an error indicator, which follows directly from the scaled boundary finite element solution. An existing automatic octree mesh generation and analysis technique will be optimised for phase-field modelling of fracture by incorporating transition elements. The proposed scaled boundary finite element solution of the variational problem of regularised crack topology will provide the basis for the development of staggered and monolithic solution schemes for the coupled displacement-phase-field equations. The final simulation framework will facilitate virtual testing of three-dimensional micro-heterogeneous samples and thus contribute to gaining a better understanding of damage and fracture processes in composite materials.