Extension of the spatially adaptive phase-field model to various forms of fracture

The phase field approach has proved to be efficient and has received ample attention amongst the available techniques to model fracture. However, high computational cost still imposes substantial difficulties in the phase-field simulation of fractures. This contribution is based on a recently proposed variational approach for spatial adaptivity in a phase-field model of fracture. The main idea is to consider the regularisation length $ϵ$ as a space-dependent variable in the argument of the energy functional. We extend this now by implementing a strain energy split to ensure that only the tensile energy drives the crack propagation. The displacement, phase field, and optimal regularisation length are then determined locally by minimisation of the modified energy functional. Subsequently, the computed optimal regularisation length is used to refine the mesh size locally. The resultant solution procedure is implemented in the finite element library FEniCS. Numerical investigations on selected examples of different fracture modes demonstrate that the spatially adaptive phase field model has a comparable convergence rate, but a subjacent energy convergence curve resulting in significant computational savings. Moreover, it also computes the peak force more accurately illustrating its potential for usage in practical applications.