An extended hydrostatic–deviatoric strain energy density decomposition for phase-field fracture theories

Abstract

The interest in using phase-field theories to numerically analyze fracture has sky-rocketed in the last years. However, in phase-field fracture models are splits, or decompositions, of the strain energy density vital to avoid interpenetration of crack surfaces and to select physically trustworthy crack paths. The most popular decomposition strategies use either a spectral decomposition or a hydrostatic–deviatoric decomposition. Both decompositions have significant disadvantages; the most important is that none of them can handle mixed-mode load scenarios in compression. To circumvent these problems, a generalized decomposition method is derived that unifies some features of the hydrostatic–deviatoric and spectral decompositions, enhanced with a classical Mohr–Coulomb failure criterion. The derived decomposition scheme has the potential to judge whether or not a compressive deformation field will assist in the crack driving process in brittle materials. The enhanced decomposition is scrutinized in numerical models and revealing biaxially loaded crack experiments in global compression. Simulations using the decomposition scheme capture the experiments in a remarkable way: complex crack patterns are reproduced, as well as critical loads. The enhanced decomposition strategy hence provides mechanistic insight into fracture processes in brittle materials subject to mixed-mode loads.