基于OTM方法的超高速碰撞问题数值模拟

最优输运无网格方法（optimal transportation meshfree method，OTM）相比传统的SPH方法，可以有效克服现有显式分析中能量不守恒问题，完全避免SPH方法中存在的拉力不稳定性，并可规避零能模式的出现.本文采用OTM方法对铝制球形弹丸超高速撞击铝合金靶板问题开展了数值模拟研究.为描述铝在高温高压和高应变率条件下的动态力学响应，采用Johnson-Cook材料模型和Mie-Grüneisen状态方程对超高速撞击单层靶板进行数值模拟，得到的弹坑直径、碎片云长度与宽度以及内核碎片云的形态和分布与实验吻合较好.此外，对超高速撞击双层靶板问题也进行了数值模拟，模拟得到的碎片云形貌参数符合实验结果，二次碎片云的模拟长度与实验结果仅相差2.6%.数值模拟结果表明OTM方法非常适合于模拟超高速碰撞问题. 

Numerical Simulation of Hypervelocity Impact Based on the Optimal Transportation Meshfree Method

Compared with the SPH method, the optimal transportation meshfree method (OTM) can effectively overcome the non-conservation of energy, and completely avoid the tensile instability and the zero energy mode. Numerical simulations of hypervelocity impact of aluminum alloy plates by aluminum spherical projectile were presented using the OTM method. The Johnson-Cook constitutive model and the Mie-Grüneisen state equation were employed to describe the dynamic response of aluminum subjected to high strain rates, high pressures and high temperatures. In the simulation of the impact on single plate, the OTM''s numerical results of crater diameters, the width and the length of debris cloud and the core debris cloud''s shape and distribution were in good agreement with the experimental results. Furthermore, the hypervelocity impact on double plates was also simulated by the OTM method, and the results indicated that the morphology characteristics of debris cloud fitted the experimental results well, and the error of secondary debris cloud''s length between numerical and experimental results was only 2.6%. All the numerical results prove that the OTM method is more suitable for the simulation of hypervelocity impact.