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"561", "lastPage" : "584", "firstPageOrInternalIdForSort" : "561", "pageLength" : 24, "publishedYear" : 2018, "abstractText" : "Under a pure tensile loading, cracks in brittle, isotropic, and homogeneous materials often propagate such that pure mode I kinematics are maintained at the crack tip. However, experiments performed on geo-materials, such as sedimentary rock, shale, mudstone, concrete and gypsum, often lead to the conclusion that the mode I and mode II critical fracture energies/surface energy release rates are distinctive. This distinction has great influence on the formation and propagation of wing cracks and secondary cracks from pre-existing flaws under a combination of shear and tensile or shear and compressive loadings. To capture the mixed-mode fracture propagation, a mixed-mode I/II fracture model that employs multiple critical energy release rates based on Shen and Stephansson, IJRMMS, 1993 is reformulated in a regularized phase field fracture framework. We obtain the mixed-mode driving force of the damage phase field by balancing the microforce. Meanwhile, the crack propagation direction and the corresponding kinematics modes are determined via a local fracture dissipation maximization problem. Several numerical examples that demonstrate mode II and mixed-mode crack propagation in brittle materials are presented. Possible extensions of the model capturing degradation related to shear/compressive damage, as commonly observed in sub-surface applications and triaxial compression tests, are also discussed. (C) 2018 Elsevier B.V. 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