A multiphase-field approach for elasto-plastic and anisotropic brittle crack propagation in geological systems consisting of different regions of brittle and ductile materials is presented and employed to computationally study crack propagation. Plastic deformation in elasto-plastic materials such as frictional, granular or porous materials is modelled with the pressure-sensitive Drucker-Prager plasticity model. This plasticity model is combined with a multiphase-field model fulfilling the mechanical jump conditions in diffuse solid-solid interfaces. The validity of the plasticity model with phase-inherent stress and strain fields is shown, in comparison with sharp interface finite element solutions. The proposed model is capable of simulating crack formation in heterogeneous multiphase systems comprising both purely elastic and inelastic phases. We investigate the influence of different material parameters on the crack propagation with tensile tests in single- and two-phase materials. To show the applicability of the model, crack propagation in a multiphase domain with brittle and elasto-plastic components is performed.

提出了一种在由脆性和延性材料的不同区域组成的地质系统中弹塑性和各向异性脆性裂纹扩展的多相场方法，并将其用于计算研究裂纹扩展。使用压力敏感的Drucker-Prager可塑性模型对弹塑性材料（例如摩擦，颗粒或多孔材料）中的塑性变形进行建模。该可塑性模型与满足弥散固体-固体界面中机械跳跃条件的多相场模型相结合。与尖锐的界面有限元解决方案相比，显示了具有相位固有应力和应变场的塑性模型的有效性。所提出的模型能够模拟包含纯弹性和非弹性相的非均质多相系统中的裂纹形成。我们通过单相和两相材料的拉伸试验研究了不同材料参数对裂纹扩展的影响。为了显示该模型的适用性，在具有脆性和弹塑性成分的多相域中进行了裂纹扩展。