Dynamic crack propagation problems, including intersonic rupture, are simulated with two Hamiltonian based formulations of particle discretization scheme (PDS) FEM: the traditional displacement momentum form and the strain momentum form, for which consistent momentum conserving and symplectic integration schemes are derived. Numerical results are verified, and validated by comparing with photoelastic observations of a dynamic mode-I crack captured with a 1 Mfps camera. Both methods are successful in accurately reproducing the crack patterns observed in classical 2D and 3D dynamic rupture scenarios, as well as the near crack tip stress field during the propagation. The two methods are found to be numerically indifferentiable, although the displacement based method offers a significantly better computational performance. As a demonstrative application, we simulate the super-shear rupture in earthquakes, modeling the contact at the fault surface by a linear slip weakening friction law. The Burridge–Andrews mechanism naturally appears in the simulations, making the crack front jump from the sub-Rayleigh regime to the intersonic regime and propagate while producing shear Mach cones.

中文翻译：

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应用PDS-FEM模拟动态裂纹扩展和超剪切断裂

动态裂纹扩展问题，包括声波破裂，用粒子离散化方案 (PDS) 有限元法的两种基于哈密顿量的公式进行模拟：传统的位移动量形式和应变动量形式，为此导出了一致的动量守恒和辛积分方案。通过与使用 1 Mfps 相机捕获的动态模式 I 裂纹的光弹性观察进行比较，验证了数值结果。这两种方法都成功地准确再现了在经典 2D 和 3D 动态破裂场景中观察到的裂纹模式，以及传播过程中的近裂纹尖端应力场。尽管基于位移的方法提供了明显更好的计算性能，但发现这两种方法在数值上是不可微的。作为示范应用，我们模拟地震中的超剪切破裂，通过线性滑动减弱摩擦定律对断层表面的接触进行建模。Burridge-Andrews 机制自然地出现在模拟中，使裂纹前沿从亚瑞利状态跳跃到声速状态并在产生剪切马赫锥的同时传播。