Dynamic brittle fracture is a numerically challenging problem that involves crack nucleation, formation, propagation, and material fragmentation. In this work, we use two forms of Smoothed Particle Hydrodynamics (SPH), namely Eulerian SPH (ESPH) and Total Lagrangian SPH (TLSPH) augmented with the pseudo-spring or virtual-link analogy for seamless modelling of crack formation, subsequent propagation, and material fragmentation. Being particle-based in nature, SPH is naturally capable of capturing finite deformation in materials, and the pseudo-spring or virtual-link analogies provide modelling of multiple discrete cracks without any additional condition, such as visibility criteria. We simulate the crack branching and propagation in a brittle polymeric material subjected to biaxial tensile loading with a pre-existing central notch. The numerical results using ESPH and TLSPH agree with the previously published experimental and numerical results. We have also simulated the dynamic fragmentation of a cylinder and compared the results. This work shows the capability of both ESPH and TLSPH frameworks to model dynamic brittle fracture especially crack branching and curving. It is also observed that the ESPH and TLSPH frameworks present similar results for minor material deformation problems. However, the ESPH framework shows better stability and capability for finite material deformation problems.

动态脆性断裂是一个具有挑战性的数值问题，涉及裂纹的成核、形成、扩展和材料破碎。在这项工作中，我们使用两种形式的平滑粒子流体动力学 (SPH)，即欧拉 SPH (ESPH) 和总拉格朗日 SPH (TLSPH)，并通过伪弹簧或虚拟链接类比进行增强，以对裂纹形成、后续扩展、和物质碎片化。SPH 本质上是基于粒子的，因此自然能够捕获材料中的有限变形，并且伪弹簧或虚拟链接类比无需任何附加条件（例如可见性标准）即可对多个离散裂纹进行建模。我们模拟脆性聚合物材料中的裂纹分支和扩展，该材料受到预先存在的中心凹口的双轴拉伸载荷。使用 ESPH 和 TLSPH 的数值结果与之前发表的实验和数值结果一致。我们还模拟了圆柱体的动态破碎并比较了结果。这项工作展示了 ESPH 和 TLSPH 框架模拟动态脆性断裂尤其是裂纹分支和弯曲的能力。还观察到 ESPH 和 TLSPH 框架对于较小的材料变形问题呈现相似的结果。然而，ESPH 框架对于有限材料变形问题表现出更好的稳定性和能力。这项工作展示了 ESPH 和 TLSPH 框架模拟动态脆性断裂尤其是裂纹分支和弯曲的能力。还观察到 ESPH 和 TLSPH 框架对于较小的材料变形问题呈现相似的结果。然而，ESPH 框架对于有限材料变形问题表现出更好的稳定性和能力。这项工作展示了 ESPH 和 TLSPH 框架模拟动态脆性断裂尤其是裂纹分支和弯曲的能力。还观察到 ESPH 和 TLSPH 框架对于较小的材料变形问题呈现相似的结果。然而，ESPH 框架对于有限材料变形问题表现出更好的稳定性和能力。