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Due to its computational robustness and versatility, the phase field fracturemodel has become the preferred tool for predicting a wide range of crackingphenomena. However, in its conventional form, its intrinsic tension-compressionsymmetry in damage evolution prevents its application to the modelling ofcompressive failures in brittle and quasi-brittle solids, such as concrete orrock materials. In this work, we present a general methodology for decomposingthe phase field fracture driving force, the strain energy density, so as toreproduce asymmetrical tension-compression fracture behaviour. The generalisedapproach presented is particularised to the case of linear elastic solids andthe Drucker-Prager failure criterion. The ability of the presented model tocapture the compressive failure of brittle materials is showcased bynumerically implementing the resulting strain energy split formulation andaddressing four case studies of particular interest. Firstly, insight is gainedinto the capabilities of the model in predicting friction and dilatancy effectsunder shear loading. Secondly, virtual direct shear tests are conducted toassess fracture predictions under different pressure levels. Thirdly, aconcrete cylinder is subjected to uniaxial and triaxial compression toinvestigate the influence of confinement. Finally, the localised failure of asoil slope is predicted and the results are compared with other formulationsfor the strain energy decomposition proposed in the literature. The resultsprovide a good qualitative agreement with experimental observations anddemonstrate the capabilities of phase field fracture methods to predict cracknucleation and growth under multi-axial loading in materials exhibitingasymmetric tension-compression fracture behaviour.

A general framework for decomposing the phase field fracture driving force, particularised to a Drucker-Prager failure surface