Comparison study of MPM and SPH in modeling hypervelocity impact problems
Comparison study of MPM and SPH in modeling hypervelocity impact problems
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DOI：
10.1016/j.ijimpeng.2008.07.001
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发表时间：
2009-02
影响因子：
5.1
通讯作者：
S. Ma;Xiong Zhang;X. Qiu
中科院分区：
文献类型：
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作者：
S. Ma;Xiong Zhang;X. Qiu
由于超高速碰撞过程中的高度非线性和大变形，其数值模拟是一个具有挑战性的课题。无网格粒子方法，如光滑粒子流体动力学（SPH）和物质点方法（MPM），是模拟超高速碰撞问题的一种很有前途的方法。本文将物质点法应用于超高速碰撞问题的数值模拟，并编制了三维MPM程序MPM 3D。采用了Johnson-Cook材料模型和Mie-Grüneisen状态方程。比较了MPM和SPH的基本公式，并利用MPM 3D和LS-DYNA SPH模块对MPM和SPH的性能进行了数值比较。研究表明，物质点法是一种有效的、有前途的超高速碰撞数值模拟方法。MPM具有许多突出的特点。MPM的公式简单，与传统的有限元法（FEM）相似。在MPM中，空间导数是基于规则的计算网格计算的，因此不需要在大多数无网格方法中强制执行的耗时的邻域搜索。该方法仅利用三维问题中8个网格节点的信息，有效地计算了场变量及其空间导数的近似值，且形函数严格满足常数和线性一致性。边界条件在MPM中的应用与在有限元中的应用一样简单，接触算法可以有效地实现，其代价与体数成线性关系。由于所有时间步长都可以使用相同的规则计算网格，因此MPM模拟的时间步长保持不变。
Due to the high nonlinearities and extreme large deformation, the hypervelocity impact simulation is a challenging task for numerical methods. Meshfree particle methods, such as the smoothed particle hydrodynamics (SPH) and material point method (MPM), are promising for the simulation of hypervelocity impact problems. In this paper, the material point method is applied to the simulation of hypervelocity impact problems, and a three-dimensional MPM computer code, MPM3D, is developed. The Johnson–Cook material model and Mie–Grüneisen equation of state are implemented. Furthermore, the basic formulations of MPM are compared with SPH, and their performances are compared numerically by using MPM3D and LS-DYNA SPH module. This study shows that the material point method is an efficient and promising method for simulating the hypervelocity impact problems. MPM possesses many prominent features. The formulation of MPM is simple and similar to the traditional finite element method (FEM). Spatial derivatives are calculated based on a regular computational grid in MPM, so that the time consuming neighbor searching, which is compulsory in most meshfree methods, is not required. The approximation of field variables and their spatial derivatives is efficiently evaluated using the information of only 8 grid nodes in three-dimensional problem, and the shape functions exactly satisfy the constant and linear consistency. The boundary conditions can be applied in MPM as easily as in FEM, and contact algorithm can be efficiently implemented whose cost is linear in the number of bodies. Because the same regular computational grid can be used in all time steps, the time step size keeps constant in MPM simulation.