Three-dimensional phase-field modeling of mode I + II/III failure in solids

One major merit of phase-field models for fracture is that cracks nucleation, propagation, branching, merging, coalescence and even fragmentation, etc., can be accounted for seamlessly within a standalone regularized variational framework. This fascinating feature overcomes the cumbersomeness in the characterization of non-smooth crack surfaces and the tracking of complex crack paths. However, the numerical algorithms frequently adopted in solving the coupled governing equations are not robust or efficient enough, together with the high computational cost in resolving the fracture process zone, largely hindering application of these models to general 3D problems. In this work, several 3D benchmark problems involving mode I, I+II or I+III failure in brittle and quasi-brittle solids is addressed based on our recent theoretical and numerical progresses on the unified phase-field theory for damage and fracture (Wu, 2017). Complex 3D fracture problems with over 2 million elements and more than 6 million degrees of freedom (dofs) can be tackled using normal computation facilities within acceptable computational time. Moreover, we are able to not only reproduce qualitatively evolution of the complex fracture pattern, but also compare quantitatively the global responses against experimental results. With the need neither to characterize the non-smooth crack surface nor to track the twisting crack path, the 3D computer implementation is almost the same as the 2D counterpart, paving the way to the phase-field modeling of large scale engineering problems.