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

• Applicant: Professorin Dr.-Ing. Carolin Birk
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 444616865

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.

• DFG Programme: Research Grants
• Co-Investigator: Dr. Hauke Gravenkamp