Numerical methods and multi-scale modeling for phase-field fracture - With applications in linear elastic and poro-elastic media

Abstract: This thesis presents novel numerical methods and a multi-scale modelling framework tailored for advancing the phase-field fracture model with applications in linear elastic and poro-elastic media. In the realm of the numerical methods, the focus lies on devising computationally efficient and robust monolithic solution techniques. These techniques aim to solve non-convex fracture problems, while ensuring the irreversibility of fracture in a variationally consistent way. The multi-scale modelling framework seeks to incorporate microstructural heterogeneities (such as material constituents, voids, and defects) and fractures to derive engineering-scale mechanical responses. Within the range of monolithic solution techniques proposed in this thesis, the fracture energy-based arc-length method and the Hessian scaling method stand out for their demonstrated computational efficiency and robustness on benchmark mechanical problems. Furthermore, to ensure the irreversibility of fracture in a variational context, a micromorphic variant of the phase-field fracture model is presented. The micromorphic variant not only allows a point-wise treatment of the fracture irreversibility constraint, but also demonstrates compatibility with the aforementioned arc-length method. Based on the computational efficiency and robustness proven by the arc-length method, this thesis presents a time-step computing variant of the method for hydraulic fracturing problems. Furthermore, in the context of multiphysics fracture problems, a novel energy functional is proposed for soil desiccation cracking. The energy functional incorporates the part of the water pressure propagating into the solid skeleton in the fracture driving energy. Numerical experiments that utilize the integration point Hessian scaling method showcase the model’s ability to capture experimentally observed phenomenon. Finally, a hierarchical multi-scale phase-field fracture framework is developed using the variationally consistent homogenization technique. The framework allows the selective upscaling of micro-structural information to the engineering scale. The numerical multi-scale ‘finite element squared’ (FE2 ) experiment conducted in this thesis successfully demonstrates the solvability of the engineering and fine-scale governing equations in a nested sequence. The culmination of the novel numerical methods and the multi-scale framework represents a significant step towards robust, computationally efficient, and accurate modelling of fractures in engineering materials and structures