中文摘要：

简要介绍了物质点法（material point method）的离散原理，通过引入Johnson-Cook材料模型和Mie-Gruneisen状态方程。将其用于超高速碰撞问题的分析中，并编制了相应三维物质点法程序MPM3D。该方法避免了拉格朗日格式因网格畸变产生的数值困难，也克服了欧拉格式材料界面跟踪问题以及因非线性对流扩散项而引起的数值困难。利用该程序对Taylor杆高速碰撞问题和空间碎片防护超高速碰撞问题进行了数值模拟，所得数值结果与实验结果基本吻合，验证了程序的正确性，说明了物质点法在分析超高速碰撞问题时相对于有限元法的优势。

英文摘要：

The discrete principle of the material point method （MPM） was briefly introduced, and a three-dimensional MPM code （MPM3D） was developed with the Johnson-Cook material model and Mie-Gruneisen equation of state to analyze the hypervelocity impact problems. The MPM avoids difficulty resulted from mesh distortion as in the Lagrangian method, and overtakes interface tracking and nonlinear convection term as in Eulerian scheme. The Taylor impact and orbital debris shielding problems are simulated by the MPM3D, and the calculated results are in agreement with the experimental results. The MPM is more efficient than the FEM in the analysis of hypervelocity impact problems.