【作者】 黄鹏；

【导师】 张雄；

【作者基本信息】 清华大学 ， 力学， 2010， 博士

【摘要】 冲击动力学问题在军事和航天航空科技上有广泛而重要的应用,数值模拟是解决该类问题的有效方法。冲击动力学问题涉及多种物理现象,诸如非线性波传播、摩擦和磨损、大变形、高应变率、动态损伤与断裂。与拉格朗日和欧拉网格类方法相比较,无网格法在处理冲击和侵彻问题时更具有优势。物质点法属于质点类无网格法,采用质点离散物体,易于描述材料的破碎。物质点法采用规则背景网格计算动量方程,因此不受网格畸变的限制。目前,物质点法已经在爆炸问题和裂纹扩展问题中取得了成功应用。本文主要针对冲击和侵彻问题,研究适合于金属和岩土冲击动力学问题的物质点法。尽管物质点法在超高速撞击问题中得到了应用,但小规模模拟无法获得高精度计算结果。针对这一问题,本文基于共享内存OpenMP技术开展物质点法并行化研究。为了解决并行化中的数据竞争问题,提出了物质点法的两种OpenMP并行算法:数组扩展法和背景网格区域分解法;为了得到高精度的超高速撞击碎片云结果,开展了1300万质点数的大规模物质点法并行计算。标准物质点法中的粘着接触条件导致了较大的侵彻阻力,为了克服这个缺陷,本文将接触物质点算法用于侵彻计算。在关于冲击问题的接触算法中,提出了一种新的接触界面法向量算法,给出了接触算法的完整数学描述和数值实现,并采用多个算例验证了接触算法的正确性。侵彻数值计算表明标准物质点算法得到的剩余弹速远低于实验值,而接触物质点算法得到的剩余弹速和实验值吻合。针对刚柔接触问题,提出了一种刚柔接触物质点算法,通过算例验证了该算法的正确性。进而,采用刚柔接触物质点算法模拟了Taylor杆撞击刚性墙的过程,以及水珠冲击台阶的过程。物质点法不受网格畸变限制,尤其适合岩土类软材料的数值模拟。文中开展了物质点法在岩土冲击动力学问题中的应用,采用Drucker-Prager模型和物质点法模拟了岩土边坡的失效过程;采用刚柔接触物质点算法模拟了堆积物的坍塌流动过程,计算结果和实验一致;最后模拟了半球壳对岩土的侵彻过程。更多还原

【Abstract】 The impact dynamics problems have broad and significant applications in the military and aerospace technologies. Numerical simulation is an important study approach for this kind of problems. Some physical phenomena, such as nonlinear wave propagation, friction and abrasion, large deformation, high strain rate, dynamic damage and fracture arise from the problems of impact dynamics. Compared with the Lagrangian and Eulerian mesh methods, meshfree methods have some advantages to solve the problems involving impact and penetration. Material point method (MPM) is a meshfree particle method. In MPM, each body is discretized by a set of particles, so that the material fragments can be efficiently simulated. MPM uses a predefined regular background grid to solve the momentum equations, so that the grid distortion and entanglement are completely avoided. MPM has been successfully applied to explosion problems and crack growth problems. In this study, the MPM simulations of the impact and penetration problems are carried out, especially for metal and soil material.Although MPM has been applied to hypervelocity problems, the small-scale MPM simulation is unable to obtain high-resolution results. The parallel MPM is developed using the shared memory OpenMP in this study. Two OpenMP parallel methods, the array expansion method and the domain decomposition method of background grid, are proposed to avoid data races in parallelizing MPM. The parallel MPM is applied to a large-scale simulation with 13 million particles for obtaining the high-resolution results of debris cloud in hypervelocity impact.The inherent non-slip contact constraint in the standard MPM creates a great penetration resistance. To overcome this deficiency, a contact MPM algorithm is presented and applied to the problems involving impact and penetration. A new method is proposed for the calculation of the normal vector of contact surface in the impact and penetration simulation. The mathematic description and numerical implementation of the contact algorithm are presented. The contact MPM algorithm is verified by some numerical examples. In the penetration simulations, the projectile’s residual velocities obtained by the standard MPM are significantly lower than the experimental data. Whereas, the projectile’s residual velocities obtained by the proposed contact MPM have agreements with the experimental results.A rigid-deformable contact MPM algorithm is proposed to simulate the contact between the rigid and deformable bodies. Some numerical examples are given to verify this rigid-deformable contact MPM algorithm. Using this contact algorithm, the Taylor bar impact on a rigid wall is simulated, and the water ball impact on a stair is also simulated.Because of avoiding mesh distortion, MPM can efficiently simulate the mechanical behavior of soft material, such as soil. In this paper, MPM is applied to the soil impact dynamics problems. The slope failure is simulated using MPM and Drucker-Prager material model. The collapse of granular layer under gravity is simulated by the rigid-deformable contact MPM algorithm. The computed final configurations of granular layer are in good agreement with the experimental results. Finally, the penetration process of a hemispherical shell into soil is simulated by MPM.更多还原