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

拟议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。 相场方法断裂将被用于由于其能力，以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化程序的需要，并且不需要选择裂纹扩展标准。尽管有这些优点，相场方法的三维问题的应用目前被排除在解决弹性固体中的扩散断裂的多场问题所需的过多的数值工作。相场方法的效率是有限的扩散裂纹配方中所涉及的长度尺度参数，这必须解决一个足够细的网格在一个数值模型。在这个项目中，我们的目标是克服这个限制，开发一个半解析解的相场方程的比例边界有限元法（SBFEM）的基础上。SBFEM有利于制定多面体元素，因此可以用于八叉树网格，允许在断裂带的快速元素大小的过渡。为了充分利用这一优势，本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标，它直接从比例边界有限元解。现有的自动八叉树网格生成和分析技术将优化相场建模的裂缝，通过纳入过渡元素。正则化裂纹拓扑变分问题的比例边界有限元解将为耦合位移-相场方程的交错和整体解方案的发展提供基础。最终的模拟框架将有助于三维微观非均匀样品的虚拟测试，从而有助于更好地了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.