A spatially adaptive phase-field model of fracture

Phase-field models of fracture introduce smeared cracks width commensurate with a regularisation length parameter $\epsilon$ and obeying minimum energy principle. Mesh adaptivity naturally suggests itself as means supplying spatial resolution were needed while simultaneously keeping the computational size model small possible. Here, variational-based is proposed for phase-field fracture. The conventional generalised by allowing variation in functional. optimal then follows minimisation same manner displacement phase fields. extended utilised basis an adaptive mesh refinement strategy, whereby required to resolve locally. resulting solution procedure implemented framework finite element library FEniCS. Selected numerical tests suggest that spatially exhibits convergence rate model, albeit vastly superior constant, which results considerable savings.