This paper focuses on the modelling of mixed‐mode fracture using the conventional smoothed particle hydrodynamics (SPH) method and a mixed‐mode cohesive fracture law embedded in the particles. The combination of conventional SPH and a mixed‐mode cohesive model allows capturing fracture and separation under various loading conditions efficiently. The key advantage of this framework is its capability to represent complex fracture geometries by a set of cracked SPH particles, each of which can possess its own mixed‐mode cohesive fracture with arbitrary orientations. Therefore, this can naturally capture complex fracture patterns without any predefined fracture topologies. Because a characteristic length scale related to the size of the fracture process zone is incorporated in the constitutive formulation, the proposed approach is independent from the spatial discretisation of the computational domain (or mesh independent). Furthermore, the anisotropic fracture responses of materials can be naturally captured thanks to the orientation of the fracture process zone embedded at the particle level. The performance of the proposed approach demonstrates its potentials in modelling mixed‐mode fracture of rocks and similar quasi‐brittle materials.

中文翻译：

---

使用带有嵌入式断裂过程带的SPH颗粒模拟混合模式断裂

本文着重于使用常规平滑粒子流体动力学（SPH）方法以及嵌入粒子中的混合模式内聚断裂定律对混合模式裂缝进行建模。常规SPH和混合模式内聚模型的组合可有效捕获各种载荷条件下的裂缝和分离。该框架的主要优点是它能够通过一组破裂的SPH颗粒来表示复杂的裂缝几何形状，每个破裂的SPH颗粒都可以拥有自己的任意方向的混合模态内聚裂缝。因此，这可以自然地捕获复杂的裂缝模式而无需任何预定义的裂缝拓扑。由于与断裂过程区大小有关的特征长度尺度被纳入本构公式中，所提出的方法与计算域的空间离散化无关（或与网格无关）。此外，由于嵌入在颗粒级的压裂过程区的方向，可以自然地捕获材料的各向异性压裂响应。所提出方法的性能证明了其在模拟岩石和类似准脆性材料的混合模式断裂中的潜力。