Application of PDS-FEM to the Simulation of Dynamic Crack
Application of PDS-FEM to the Simulation of Dynamic Crack
复制标题
PDS-FEM在动态裂纹模拟中的应用
DOI：
10.1007/s00466-020-01819-z
复制
发表时间：
2020
影响因子：
4.1
通讯作者：
T. Okinaka and M.Hori
中科院分区：
文献类型：
--
作者：
L.Quaranta;L.Maddegedara;T. Okinaka and M.Hori
采用两种基于Hamilton的质点离散格式（PDS）有限元法：传统的位移-动量格式和应变-动量格式，对动态裂纹扩展问题（包括跨音速断裂）进行了数值模拟，推导了两种格式的动量守恒格式和辛积分格式。数值计算结果进行了验证，并通过与光弹性观测的动态模式I裂纹捕获与1 Mfps的相机进行比较验证。这两种方法都成功地准确再现了在经典的2D和3D动态断裂的情况下观察到的裂纹图案，以及在传播过程中的裂纹尖端应力场附近。这两种方法被发现是数值不可微的，虽然基于位移的方法提供了一个显着更好的计算性能。作为示范性应用，我们模拟了地震中的超剪切破裂，通过线性滑动弱化摩擦定律来模拟断层面的接触。Burridge-Andrews机制自然地出现在模拟中，使得裂纹前缘从亚瑞利区域跳到跨音速区域，并在产生剪切马赫锥的同时扩展。
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.