金属及岩土冲击动力学问题的物质点法研究
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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。
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.
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。
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.
引文
[1]钱伟长.穿甲力学.北京:国防工业出版社.1984.
[2] Meyers M A. Dynamic Behavior of Materials. John Wiley & Sons, 1994.
[3] Young C W. Penetration equations. Technical Report SAND97-22426, Sandia National Laboratories, 1997.
[4] Young C W. Simplified Analytical Model of Penetration with Lateral Loading-User's Guide. Technical Report SAND98-0978, Sandia National Laboratories, 1998.
[5] Forrestal M J, Brar N S, Luk V K. Penetration of strain-hardening targets with rigid spherical-nose rods. ASME Journal of Applied Mechanics, 1991, 58(1):7-10.
[6] Forrestal M J, Luk V K. Penetration into soil targets, International Journal of Impact Engineering. 1992, 12:427-444.
[7] Forrestal M J, Tzou D Y, Askari E, Longcope D B. Penetration into ductile metal targets with rigid spherical-nose rods. International Journal of Impact Engineering, 1995, 16:699-710.
[8] Forrestal M J, Tzou D Y. A spherical cavity-expansion penetration model for concrete targets. International Journal of Solids and Structures, 1997, 34: 4127-4146.
[9] Hertel E S Jr. A survey of numerical methods for shock physics applications. Technical Report SAND97-1015c, Sandia National Laboratories, 1997.
[10] Kusnezov D F. Advanced simulation & computing: the next ten years. Technical Report SAND2004-3740P, Sandia National Laboratories, 2004.
[11] Benioff M R, Lazowska E D. Computational science: ensuring America's competitiveness. President’s Information Technology Advisory Committee, 2005.
[12] Johnson W E, Anderson C E. History and application of hydrocodes in hypervelocity impact. International Journal of Impact Engineering, 1987, 5:423-439.
[13] Benson D J. Computational methods in Lagrangian and Eulerian hydrocodes. Computer Methods in Applied Mechanics Engineering, 1992, 99: 235-394.
[14]恽寿榕,涂侯杰,梁德寿,等.爆炸力学计算方法.北京:北京理工大学出版社, 1995.
[15] Belytschko T, Liu W K, Moran B. Nonlinear Finite Elements for Continua and Structures. John Wiley & Sons, 2000.
[16] Belytschko T, Neal M O. Contact-impact by the pinball algorithm with penalty and Lagrangian methods. International Journal for Numerical Methods in Engineering, 1991, 31:547-572.
[17] Hallquist J O, Goodreau G L, Benson D J. Sliding interfaces with contact-impact in largescale Lagrangian computations. Computer Methods in Applied Mechanics Engineering, 1985, 51:107–137.
[18] Belytschko T, Neal M O, Contact-impact by the pinball algorithm with penalty, projection, and Lagrangian methods. Computational Techniques for Contact, Impact, Penetration and Perforation of Solids, New York, 1989, 103:97-140.
[19] Hallquist J O. LS-DYNA Theoretical Manual. Livermore Software Technology Corporation. 1998.
[20] Taylor L M, Flanagan D P. PRONTO 3D a three-dimensional transient solid dynamics program. Technical Report SAND87-1912, Sandia National Laboratories, 1989.
[21] Scheffler D R, Zukas J A. Practical aspects of numerical simulation of dynamic events:material interfaces. International Journal of Impact Engineering , 2000, 24:821-842.
[22] Bessette G C, Becker E B, Taylor L M,et al. Modeling of impact problems using an h-adaptive, explicit Lagrangian finite element method in three dimensions. Computer Methods in Applied Mechanics Engineering, 2003, 192:1649-1679.
[23] Camacho G T, Ortiz M. Adaptive Lagrangian modeling of ballistic penetration of metallic targets. Computer Methods in Applied Mechanics Engineering, 1997, 142:269-301.
[24] Camacho G T, Ortiz M. Computational modeling of impact damage in brittle materials, International Journal of Solids and Structures. 1996, 33:2899-2938.
[25] Littlefield D L.The use of r-adaptivity in explicit Lagrangian finite element codes, Proceedings of the 15th US Army Symposium on Solid Mechanics, 1999:305-320.
[26] Martineau R L, Prime M B, Duffey T. Penetration of HSLA-100 steel with tungsten carbide spheres at striking velocities between 0.8 and 2.5 km/s. International Journal of Impact Engineering, 2004, 30:505-520.
[27] Resnyansky A D. DYNA-modelling of the high-velocity impact problems with a split-element algorithm. International Journal of Impact Engineering, 2002, 27:709-727.
[28] B?rvik T, Hopperstad O S, Berstad T, Langseth M. Perforation of 12mm thick steel plates by 20mm diameter projectiles with blunt, hemispherical and conical noses, part II: numerical simulations. International Journal of Impact Engineering, 2002, 27:37-64.
[29] Attaway S W, Brown M J, Heinstein M W, et al. PRONTO3D User’s Instructions: A Transient Dynamic Code for Nonlinear Structural Analysis. Technical Report SAND98-1361, Sandia National Laboratory, 1998.
[30] Brown K, Attaway S, Plimpton S, Hendrickson B. Parallel strategies for crash and impact simulations. Computer Methods in Applied Mechanics and Engineering, 2000, 184: 375-390.
[31] Attaway S W, Hendrickson B A, Plimpton S J, et al. A parallel contact detection algorithm for transient solid dynamics simulations using PRONTO3D. Computational Mechanics,1998, 22: 143-159.
[32] Warren T L, Tabbara M R. Spherical Cavity-Expansion Forcing Function in PRONTO3D for Application to Penetration Problems. SAND97-1174, Sandia National Laboratories, 1997.
[33] Warren T L, Fossum A F, Frew D J. Penetration into low-strength (23 MPa) concrete: target characterization and simulations. International Journal of Impact Engineering, 2004, 30(5):477-503.
[34] Warren T L, Poormon K L. Penetration of 6061-T6511 aluminum targets by ogive-nosed VAR 4340 steel projectiles at oblique angles: experiments and simulations. International Journal of Impact Engineering, 2001, 25:993-1022.
[35] Vorobiev Y O, Liu B T, Lomov I N, et al. Simulation of penetration into porous geologic media. International Journal of Impact Engineering, 2007, 34: 721-731.
[36] ABAQUS Inc. Getting Started with ABAQUS Version 6.6, ABAQUS Inc, 2006.
[37] Iqbal M A, Chakrabarti A, Beniwal S, et al. 3D numerical simulations of sharp nosed projectile impact on ductile targets. International Journal of Impact Engineering, 2010, 37:185-195.
[38] Gupta N K, Iqbal M A , Sekhon G S. Experimental and numerical studies on the behavior of thin aluminumplates subjected to impact by blunt and hemispherical nosed projectiles. International Journal of Impact Engineering, 2006, 32:1921-1944.
[39] Gupta N K, Iqbal M A, Sekhon G S. Effect of projectile nose shape, impact velocity and target thickness on deformation behavior of aluminum plates. International Journal of Solids and Structures, 2007, 44:3411-3439.
[40] MSC Inc. MSC.Dytran User’s Manual. MSC.Software Corporation, 1999.
[41] Wingate C A, Stellingwerf R F, Davidson R F, et al. Models of High Velocity Impact Phenomena. International Journal of Impact Engineering, 1993, 14:819-830.
[42] Wilkins M L. Computer Simulation of Dynamic Phenomena. Spinger, 1999.
[43] Birnbaum N K, Tancreto J, Hager K. Calculation of Blast Loading in the High Performance Magazine with AUTODYN-3D. Proceedings of the Twenty-Sixth DOD Explosives Safety Seminar, 1994.
[44] Century Dynamics Inc. AUTODYN-3D Users Manual. Century Dynamics Inc. 1994.
[45] Tham C Y. Numerical and Empirical Approach in Predicting the Penetration of a Concrete Target by an Ogive-Nosed Projectile. Finite Elements in Analysis and Design, 2006, 42:1258-1268.
[46]王肖钧,胡秀章,刘胜求.四边形单元中的沙漏控制.计算物理, 1991, 8(3): 312-318.
[47]胡秀章,王肖钧,李永池.一种弹塑性弹丸侵彻靶板的滑移面处理.结构与介质相互作用理论与应用,南京:河海大学出版社, 1993.
[48]李永池,袁福平,胡秀章等.卵形头部弹丸对混凝土靶板侵彻的二维数值模拟.弹道学报, 2002, 14(1):14-19.
[49]王峰.有限元方法及其在高速碰撞中的应用[博士学位论文].合肥:中国科学技术大学, 2007.
[50]宋顺成.轴对称冲击有限元一致质量矩阵迭代解.力学学报, 1998, 30(3):285-291.
[51]宋顺成,谭多望,蔡鸿年.穿破甲有限元的几何非线性及物理参数的确定.爆炸与冲击, 2002, 22(2):137-143.
[52]宋顺成,谭多望.高速冲击非线性有限元计算.西南交通大学学报, 2001, 36:565-571.
[53]马天宝,王静,宁建国.一种VOF与PIC耦合多物质界面处理算法及其在侵彻问题中的应用.中国科学(G辑), 2009, 39(9): 1185-1194.
[54] Couch R, Albright E, Alexander N. The JOY computer code. Technical Report UCID-19688, Lawrence Livermore National Laboratories, 1983.
[55] McGlaun J M, Thompson S L, Elrick M G. CTH: A three-dimensional shock wave physics code. International Journal of Impact Engineering, 1990, 10:351-360.
[56] Noh W F, Woodward P. SLIC (Simple Line Interface Calculation). Lecture Notes in Physics, 1976, 59:330-340.
[57] Youngs D L. Time-Dependent Multi-Material Flow with Large Fluid Distortion. Numerical Methods for Fluid Dynamics. New York: Academic Press, 1982.
[58] Fahrenthold E P, Yew C H. Hydrocode simulation of hypervelocity impact fragmentation. International Journal of Impact Engineering, 1995, 17: 303-310.
[59] Silling S A. CTH reference manual: boundary layer algorithm for sliding interfaces in two dimensions. Technical Report SAND93-2487, Sandia National Laboratories, 1994.
[60] Scheffler D R. Modeling non-eroding perforation of an oblique aluminum target using the Eulerian CTH hydrocode. International Journal of Impact Engineering, 2005, 32:461-472.
[61]刘军,何长江,梁仙红.三维弹塑性流体力学自适应欧拉方法研究.高压物理报, 2008, 22(01):72-78.
[62]何长江,于志鲁,冯其京.高速碰撞的三维欧拉数值模拟方法.爆炸与冲击, 1999, 19(3): 216-221.
[63]马天宝,宁建国.三维爆炸与冲击问题仿真软件研究.计算力学学报, 2009,26(4):600-603.
[64]吴开腾.爆炸与冲击问题的三维数值模拟及算法研究[博士学位论文].北京:北京理工大学, 2002.
[65]马天宝,郝莉,宁建国. Euler多物质流体动力学数值方法中的界面处理算法.计算物理, 2008, 25(2):133-138.
[66]陈龙伟,孙远翔,宁建国.动能弹对混凝土靶板侵彻三维数值模拟.北京理工大学学报, 2003, 23(5):536-539.
[67]王景焘,张德良,刘凯欣.基于CE/SE方法的二维Euler型多物质流体弹塑性问题计算.计算物理, 2007, 24(4):395-401.
[68] Wang J, Liu K, Zhang D. An improved CE/SE scheme for multi-material elastic-plastic flows and its applications. Computers & Fluids, 2009, 38(3):544-551.
[69]张雄,陆明万,王建军.任意拉格朗日-欧拉描述法研究进展.计算力学学报, 1997, 14(1): 91-102.
[70] Benson D J. An efficient, accurate and simple ALE method for nonlinear finite element programs. Computer Methods in Applied Mechanics and Engineering, 1989, 72:305-350.
[71] Liu W K, Belytschko T, Chang H. An arbitrary Lagrangian-Eulerian finite element method for path-dependant materials. Computer Methods in Applied Mechanics and Engineering, 1986:227-245.
[72] Sheng D,Wriggers P, Sloan S W. Improved numerical algorithms for friction contact in pile penetration analysis. Computers and Geotechnics, 2006, 33:341-354.
[73] Sheng D, Nazem M, Carter J P. Some computational aspects for solving deep penetration problems in geomechanics. Computational Mechanics, 2009, 44:549-561.
[74] Liyanapathirana D S. Arbitrary Lagrangian Eulerian based finite element analysis of cone penetration in soft clay. Computers and Geotechnics, 2009, 36: 851-860.
[75] Walker J, Yu H S. Adaptive finite element analysis of cone penetration in clay. Acta Geotechnica, 2006, 1:43-57.
[76] Alme M L, Rhoades C E. A Computational Study of Projectile Melt in Impact With Typical Whipple Shields. International Journal of Impact Engineering, 1995, 17:1-12.
[77]张雄,刘岩.无网格法.北京:清华大学出版社, 2004.
[78] Liu G R, Yan L. A study on numerical integration in element-free Galerkin method. Fourth International Asia-Pacific Conference on Computational Mechanics, Singapore, 1999.
[79]张雄,刘岩,马上.无网格法的理论及应用,力学进展, 2009,39(1):1-36.
[80]顾元通,丁桦.无网格法及其最新进展,力学进展, 2005, 35(3):323-337.
[81] Belytschko T, Krongauz Y, Organ D, et al. Mesh-less methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4): 3-47.
[82] Li S, Liu W K. Meshfree and particle methods and their applications. Applied Mechanics Reviws, 2002,55(1): 1-34.
[83] Monaghan J J. An introduction to SPH. Computer Physics Communications, 1988, 48: 89-96.
[84] Swegle J W, Hicks D L, Attaway W S. Smoothed particled hydrodynamics stabilityanalisys. Journal of Computational Physics, 1995, 116:123-134.
[85] Liu W K, Chen Y, Aziz U. Generalized multiple scale reproducing kernel particle methods. Computer Methods in Applied Mechanics and Engineering, 1996, 139:91-157.
[86] Liu W K, Chen Y, Chang C T. Advances in multiple scale kernel particle methods. Computational Mechanics, 1996, 18:73-111.
[87] Nayroles P, Touzot G, Villon P. Generalizing the finite element methods: diffuse approximation and diffuse elements. Computational Mechanics, 1992, 10:307-318.
[88] Belyschko T, Touzot G, Gu L. Element free galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37:229-256.
[89] Atluri S N, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, 1998, 22:117-127.
[90] Atluri S N, Zhu T. The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Computational Mechanics, 2000, 25:169-179.
[91] Libersky L, Petschek A G, Carney T C, et al. High strain largrangian hydrodynamics a three-dimensional SPH code for dynamics material response. Journal of Computational Physics, 1993, 109:67-75.
[92] Stellingwerf R F, Wingate C A. Impact modeling with smooth particle hydrodynamics. International Journal of Impact Engineering, 1993, 14: 707-718.
[93] Benz W, Asphaug E. Simulations of brittle solids using smooth particle hydrodynamics. Computer Physics Communications, 1995, 87(1-2): 253-265.
[94] Campbell J, Vignjevic R, Libersky L. A contact algorithm for smoothed particle hydrodynamics. Computer Methods in Applied Mechanics and Engineering, 2000, 184(1): 49-65.
[95] Vignjevic R, De Vuyst T, Campbell J C. A frictionless contact algorithm for meshless methods. CMES-Computer Modeling in Engineering & Sciences, 2006,13(1): 35-48.
[96] Johnson G R, Stryk R A, Beissel S R. SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4):347-373.
[97] Johnson G R, Beissel S R. Normalized smoothing functions for SPH impact computations. International Journal for Numerical Methods in Engineering, 1996, 39(16): 2725-2741.
[98] Johnson G R, Beissel S R, Stryk R A. A generalized particle algorithm for high velocity impact computations. Computational Mechanics, 2000, 25(2-3):245-256.
[99] Johnson G R, Stryk R A, Beissel S R, et al. An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation. International Journal of Impact Engineering, 2002, 27(10): 997-1013.
[100] Johnson G R, Stryk R A. Conversion of 3D distorted elements into meshless particles during dynamic deformation. International Journal of Impact Engineering, 2003, 28(9):947-966.
[101] Han Z D, Liu H T, Rajendran A M, et al. The applications of meshless local Petrov-Galerkin (MLPG) approaches in high-speed impact, penetration and perforation problems. CMES-Computer Modeling in Engineering & Sciences, 2006, 14(2): 119-128.
[102] Fahrenthold E P, Horban B A. An improved hybrid particle-element method for hypervelocity impact simulation. International Journal of Impact Engineering, 2001, 26(1-10): 169-178.
[103] Park Y K, Fahrenthold E P. A kernel free particle-finite element method for hypervelocity impact simulation. International Journal for Numerical Methods in Engineering, 2005, 63(5): 737-759.
[104] Quinn M J. Parallel Programming in c with MPI and OpenMP. New York: McGraw-Hill Companies, 2004.
[105] Grama A, Gupta A, Karypis G. Introduction to Parallel Computing(2nd edition). Benjamin-cummings Publishing Company, 2003.
[106] Har J, Fulton R E. A parallel finite element procedure for contact-impact problems. Engineering with Computers, 2003, 19: 67-84.
[107] Guo Y, Jin X, Ding J. Parallel numerical simulation with domain decomposition for seismic response analysis of shield tunnel. Advances in Engineering Software, 2006, 37: 450-456.
[108]王裴,洪涛.三维光滑粒子流体动力学并行计算程序.计算物理, 2006, 23(4):431-435.
[109] Danielson K T, Uras R A, Adley M D, et al. Large-scale application of some modern CSM methodologies by parallel computation. Advances in Engineering Software, 2000, 31:501-509.
[110] PantaléO. Parallelization of an object-oriented FEM dynamics code: influence of the strategies on the Speedup. Advances Engineering Software, 2005, 36: 361-373.
[111] Couturier R, Chipot C. Parallel molecular dynamics using OPENMP on a shared memory machine. Computer Physics Communications, 2000, 124:49-59.
[112] Ayguadea E, Gonzaleza M, Martorella X, et al. Employing nested OpenMP for the parallelization of multi-zone computational fluid dynamics applications. Journal of Parallel and Distributed Computing, 2006, 66:686-697.
[113] Thacker R J, Couchman H M P. A parallel adaptive P3M code with hierarchical particle reordering. Computer Physics Communication, 2006, 174: 540-554.
[114] Harlow F H. The particle-in-cell computing method for fluid dynamics. Methods in Computational Physics, 1963, 3: 319-343.
[115] Brackbill J U, Ruppel H M. FLIP: a method for adaptively zoned, particle-in-cell calculations in two dimensions. Journal of Computational Physics, 1986, 65:314-343.
[116] Brackbill J U, Kothe D B, Ruppel H M. FLIP: a low-dissipation, particle-in-cell method for fluid flow. Computer Physics Communications, 1988, 48:25-38.
[117] Sulsky D, Chen Z, Schreyer H L. A Particle Method for History-Dependent Materials. Computer Methods in Applied Mechanics and Engineering, 1994, 118(1-2):179-196.
[118] Sulsky D, Zhou S J, Schreyer H L. Application of a Particle-in-Cell Method to Solid Mechanics. Computer Physics Communications, 1995, 87(1-2):236-252.
[119] Sulsky D, Schreyer H L. Axisymmetric form of the material point method with applications to upsetting and Taylor impact problems. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4):409-429.
[120] Sulsky D, Kaul A. Implicit dynamics in the material-point method. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12-14):1137-1170.
[121] Cummins S J, Brackbill J U. An implicit particle-in-cell method for granular materials. Journal of Computational Physics, 2002, 180(2):506-548.
[122] Guilkey J E, Weiss J A. An implicit time integration strategy for use with the material point method. MIT Conference on Computational Fluid and Solid Mechanics, 2001.
[123] Guilkey J E, Weiss J A. Implicit time integration for the material point method: Quantitative and algorithmic comparisons with the finite element method. International Journal for Numerical Methods in Engineering, 2003, 57(9):1323-1338.
[124] Tan H L, Nairn J A. Hierarchical, adaptive, material point method for dynamic energy release rate calculations. Computer Methods in Applied Mechanics and Engineering, 2002, 191(19-20):2095-2109.
[125] Love E, Sulsky D L. An energy-consistent material-point method for dynamic finite deformation plasticity. International Journal for Numerical Methods in Engineering, 2006, 65(10):1608-1638.
[126] Love E, Sulsky D L. An unconditionally stable, energy-momentum consistent implementation of the material-point method. Computer Methods in Applied Mechanics and Engineering, 2006, 195(33-36):3903-3925.
[127] Bardenhagen S G, Kober E M. The generalized interpolation material point method. CMES- Computer Modeling in Engineering & Sciences, 2004, 5(6):477-495.
[128] Steffen M, Wallstedt P C, Guilkey J E, et al. Examination and Analysis of Implementation Choices within the Material Point Method (MPM). CMES-Computer Modeling in Engineering & Sciences, 2008, 31(2):107-127.
[129] Ma S, Zhang X, Lian Y, Zhou X. Simulation of high explosive explosion using adaptive material point method. CMES-Computer Modeling In Engineering & Sciences, 2009, 39:101-123.
[130] York A R II, Sulsky D, Schreyer H L. The material point method for simulation of thinmembranes. International Journal for Numerical Methods in Engineering, 1999, 44: 1429-1456.
[131] Hu W, Chen Z. A multi-mesh MPM for simulating the meshing process of spur gears. Computers and Structures, 2003, 81:1991-2002.
[132] Bardenhagen S G, Brackbill J U, Sulsky D. The material point method for granular materials. Computer Methods in Applied Mechanics Engineering, 2000, 187:529-541.
[133] Bardenhagen S G, Guilkey J E, Roessig K M, et al. An improved contact algorithm for the material point method and application to stress propagation in granular material. CMES-Computer Modeling in Engineering and Sciences, 2001, 2(4): 509-522.
[134] Parker S G. A component-based architecture for parallel multi-physics PDE simulation. Future Generation Computer Systems, 2006 ,22:204-216.
[135] Parker S G, Guilkey J, Harman T. A component-based parallel infrastructure for the simulation of fluid-structure interaction. Engineering with Computers, 2006, 22: 277-292.
[136] Ma J, Lu H, Komanduri R. Structured mesh refinement in generalized interpolation material point (GIMP) method for simulation of dynamic problems. CMES: Computer Modeling in Engineering and Sciences, 2006, 12(3):213-227.
[137] Zhang X, Sze K Y, Ma S. An explicit material point finite element method for hyper-velocity impact. International Journal for Numerical Methods in Engineering, 2006, 66:689-706.
[138] Guilkey J E, Harman T B, Banerjee B. An Eulerian-Lagrangian approach for simulating explosions of energetic devices. Computers & Structures, 2007, 85(11-14):660-674.
[139] Ma S, Zhang X, Qiu X M. Comparison study of MPM and SPH in modeling hypervelocity impact problems. International Journal of Impact Engineering, 2009, 36:272-282.
[140] Lee W H, Painter J W. Material void-opening computation using particle method. International Journal of Impact Engineering, 1999, 22:1-22.
[141] Hu W Q, Chen Z. Model-based simulation of the synergistic effects of blast and fragmentation on a concrete wall using the MPM. International Journal of Impact Engineering, 2006, 32(12):2066-2096.
[142]王宇新.多相介质爆炸冲击响应物质点法分析[博士学位论文].大连:大连理工大学, 2006.
[143] Nairn J A. Material point method calculations with explicit cracks. CMES-Computer Modeling in Engineering & Sciences, 2003, 4(6):649-663.
[144] Guo Y, Nairn J A. Calculation of J-integral and stress intensity factors using The Material Point Method. CMES-Computer Modeling in Engineering & Sciences, 2004, 6(3):295-308.
[145] Nairn J A. On the calculation of energy release rates for cracked laminates with residual stresses. International Journal of Fracture, 2006, 139(2):267-293.
[146] Wang B, Karuppiah V, Lu H, et al. Two-dimensional mixed mode crack simulation using the material point method. Mechanics of Advanced Materials and Structures, 2005, 12(6):471-484.
[147] Daphalapurkar N P, Lu H, Coker D, et al. Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method. International Journal of Fracture, 2007, 143(1):79-102.
[148] Chen Z, Hu W, Shen L, et al. An evaluation of the MPM for simulating dynamic failure with damage diffusion. Engineering Fracture Mechanics, 2002, 69(17):1873-1890.
[149] Chen Z, Feng R, Xin X, et al. A computational model for impact failure with shear-induced dilatancy. International Journal for Numerical Methods in Engineering, 2003, 56(14):1979-1997.
[150] Shen L M, Chen Z. A multi-scale simulation of tungsten film delamination from silicon substrate. International Journal of Solids and Structures, 2005, 42(18-19):5036-5056.
[151] Shen L M, Chen Z. A silent boundary scheme with the material point method for dynamic analyses. CMES-Computer Modeling in Engineering & Sciences, 2005, 7(3):305-320.
[152] Schreyer H L, Sulsky D L, Zhou S J. Modeling delamination as a strong discontinuity with the material point method. Computer Methods in Applied Mechanics and Engineering, 2002, 191(23-24):2483-2507.
[153] Sulsky D, Schreyer L. MPM simulation of dynamic material failure with a decohesion constitutive model. European Journal of Mechanics A/Solids, 2004, 23(3):423-445.
[154] Bardenhagen S G, Brydon A D, Guilkey J E. Insight into the physics of foam densification via numerical simulation. Journal of the Mechanics and Physics of Solids, 2005, 53(3):597-617.
[155] Brydon A D, Bardenhagen S G, Miller E A, et al. Simulation of the densification of real open-celled foam microstructures. Journal of the Mechanics and Physics of Solids, 2005, 53(12):2638-2660.
[156] Wieckowski Z, Youn S K, Yeon J H. A particle-in-cell solution to the silo discharging problem. International Journal for Numerical Methods in Engineering, 1999, 45(9):1203-1225.
[157] Wieckowski Z. The material point method in large strain engineering problems. Computer Methods in Applied Mechanics and Engineering, 2004, 193(39-41):4417-4438.
[158] Bardenhagen S G, Brackbill J U, Sulsky D. Numerical study of stress distribution in sheared granular material in two dimensions. Physical Review E, 2000, 62(3):3882–3890.
[159] Coetzee C J, Basson A H, Vermeer P A. Discrete and continuum modelling of excavator bucket filling. Journal of Terramechanics, 2007, 44(2):177–186.
[160] Sulsky D, Schreyer H, Peterson K, et al. Using the material-point method to model sea icedynamics. Journal of Geophysical Research-Oceans, 2007, 112(C2):C02S90.
[161] Zhang H W, Wang K P, Chen Z. Material point method for dynamic analysis of saturated porous media under external contact/impact of solid bodies. Computer Methods in Applied Mechanics and Engineering, 2009, 198(17-20):1456–1472.
[162] Guilkey J E, Hoying J B, Weiss J A. Computational modeling of multicellular constructs with the material point method. Journal of Biomechanics, 2006, 39(11):2074–2086.
[163] Zhang D Z, Zou Q, VanderHeyden W B, Ma X. Material point method applied to multiphase flows. Journal of Computational Physics, 2008, 227: 3159-3173.
[164] Bardenhagen S G. Energy conservation error in the material point method for solid mechanics. Journal of Computational Physics, 2002, 180(1):383-403.
[165] Anderson C E Jr. An overview of the theory of hydrocodes. International Journal of Impact Engineering, 1987, 5:33–59.
[166]经福谦等.实验物态方程导引.北京:科学出版社, 1986.
[167]王仁,黄文彬,黄祝平.塑性力学引论.北京:北京大学出版社, 1992.
[168] Liu M B, Liu G R, Lam K Y. Investigation into water mitigations using a meshless particle method. Shock Waves, 2002, 12(3):181–195.
[169] De Vuyst T, Vignjevic R, Campbell J C. Coupling between meshless and finite element methods. International Journal of Impact Engineering, 2005, 31: 1054-1064.
[170] Wingate C A, Dilts G A, Mandell D A, et al. Progress in smooth particle hydrodynamics. Technical Report LA-UR-98-300, Los Alamos National Laboratories, 1998.
[171] Voyiadjis G Z, Palazotto A N, Gao X L. Modeling of metallic materials at high strain rates with continuum damage mechanics. Applied Mechanics Review, 2002, 55(5):481-493.
[172] Candel A E, Dehler M M, Troyer M. A massively parallel particle-in-cell code for the simulation of field-emitter based electron sources. Nuclear Instruments and Methods in Physics Research A, 2006, 558:154-158.
[173] Chandra R, Dagum L, Kohr D, et al. Parallel Programming in OpenMP. Morgan Kaufmann Publishers, 2001.
[174] Chapman B, Jost G, VanderPas R. Using OpenMP : portable shared memory parallel programming. The MIT Press, 2007.
[175] Johnson G R, Holmquist T J. Evaluation of cylinder-impact test data for constitutive model constants. Journal of Applied Physics, 1988, 64:3901-3910.
[176] Mehra V, Chaturvedi S. High velocity impact of metal sphere on thin metallic plates: a comparative smooth particle hydrodynamics study. Journal of Computational Physics, 2006, 212:318-337.
[177] Beissel S R, Gerlach C A, Johnson G R. Hypervelocity impact computations with finiteelements and meshfree particles. International Journal of Impact Engineering, 2006, 33:80-90.
[178] Anderson C E JR, Trucano T G, Mullin S A. Debris cloud dynamics. International Journal of Impact Engineering, 1990, 9: 89-113.
[179] Wang F J, Wang L P, Cheng J G, et al. Contact force algorithm in explicit transient analysis using finite-element method. Finite Elements in Analysis and Design, 2007, 43:580-587.
[180] Chapman D J, Radford D D, Reynolds M, et al. Shock induced void nucleation during Taylor impact. International Journal of Fracture, 2005, 134:41-57.
[181] Seoa S W, Min O K, Lee J H. Application of an improved contact algorithm for penetration analysis in SPH. International Journal of Impact Engineering, 2008, 35: 578-588.
[182] Piekutowski A J, Forrestal M J, Poormon K L, et al. Perforation of aluminium plates with ogive-nose steel rods at normal and oblique impacts. International Journal of Impact Engineering, 1996, 18:877- 887.
[183] Liu G R, Liu M B. Smoothed Particle Hydrodynamics: a meshfree particle method. World Scientific, 2003.
[184] Bui H H, Lagrangian Mesh-free Particle Method(SPH) for Large Deformation and Post-failure of Geomaterial using Elasto-plastic Constitutive Models [Ph. D. thesis], Japan: Ritsumeikan University, 2006.
[185] Coetzee C J, Vermeer P A, Basson A H. The modelling of anchors using the material point method. International Journal for Numerical and Analytical Methods in Geomechanics, 2005, 29:879-895.
[186] Tanaka H, Momozu M, Oida A, et al. Simulation of soil deformation and resistance at bar penetration by the Distinct Element Method. Journal of Terramechanics, 2000, 37:41-56.
[187] Itasca Consulting Group Inc. FLAC-Fast Lagrangian Analysis of Continua User’s Manual (Version 5.0). Minneapolis: Itasca Consulting Group Inc, 2005.
[188] Chen W F, Mizuno E. Nonlinear analysis in soil mechanics. Amsterdam: Elsevier Science Publishers, 1990.
[189]张雄,王天舒.计算动力学.北京:清华大学出版社, 2007.
[190] Fasanella E L, Jones Y, Knight N F Jr, et al.Low velocity earth-penetration test and analysis. Technical Report: AIAA-2001-1388, American Institute of Aeronautics and Astronautics, 2001.
[191]郑颖人,沈珠江,龚晓南.广义塑性力学—岩土塑性力学原理.北京:中国建筑工业出版社, 2002.
[192]张雄.冲击爆炸三维物质点法数值仿真软件MPM3D:中国, 2009SRBJ4761. (计算机软件著作权登记号)
[193] Andersen S, Andersen L. Modelling of landslides with the material-point method.Computational Geosciences, 2010, 14:137-147.
[194]马上.冲击爆炸问题的物质点无网格法研究[博士论文].北京:清华大学, 2009.
[2] Meyers M A. Dynamic Behavior of Materials. John Wiley & Sons, 1994.
[3] Young C W. Penetration equations. Technical Report SAND97-22426, Sandia National Laboratories, 1997.
[4] Young C W. Simplified Analytical Model of Penetration with Lateral Loading-User's Guide. Technical Report SAND98-0978, Sandia National Laboratories, 1998.
[5] Forrestal M J, Brar N S, Luk V K. Penetration of strain-hardening targets with rigid spherical-nose rods. ASME Journal of Applied Mechanics, 1991, 58(1):7-10.
[6] Forrestal M J, Luk V K. Penetration into soil targets, International Journal of Impact Engineering. 1992, 12:427-444.
[7] Forrestal M J, Tzou D Y, Askari E, Longcope D B. Penetration into ductile metal targets with rigid spherical-nose rods. International Journal of Impact Engineering, 1995, 16:699-710.
[8] Forrestal M J, Tzou D Y. A spherical cavity-expansion penetration model for concrete targets. International Journal of Solids and Structures, 1997, 34: 4127-4146.
[9] Hertel E S Jr. A survey of numerical methods for shock physics applications. Technical Report SAND97-1015c, Sandia National Laboratories, 1997.
[10] Kusnezov D F. Advanced simulation & computing: the next ten years. Technical Report SAND2004-3740P, Sandia National Laboratories, 2004.
[11] Benioff M R, Lazowska E D. Computational science: ensuring America's competitiveness. President’s Information Technology Advisory Committee, 2005.
[12] Johnson W E, Anderson C E. History and application of hydrocodes in hypervelocity impact. International Journal of Impact Engineering, 1987, 5:423-439.
[13] Benson D J. Computational methods in Lagrangian and Eulerian hydrocodes. Computer Methods in Applied Mechanics Engineering, 1992, 99: 235-394.
[14]恽寿榕,涂侯杰,梁德寿,等.爆炸力学计算方法.北京:北京理工大学出版社, 1995.
[15] Belytschko T, Liu W K, Moran B. Nonlinear Finite Elements for Continua and Structures. John Wiley & Sons, 2000.
[16] Belytschko T, Neal M O. Contact-impact by the pinball algorithm with penalty and Lagrangian methods. International Journal for Numerical Methods in Engineering, 1991, 31:547-572.
[17] Hallquist J O, Goodreau G L, Benson D J. Sliding interfaces with contact-impact in largescale Lagrangian computations. Computer Methods in Applied Mechanics Engineering, 1985, 51:107–137.
[18] Belytschko T, Neal M O, Contact-impact by the pinball algorithm with penalty, projection, and Lagrangian methods. Computational Techniques for Contact, Impact, Penetration and Perforation of Solids, New York, 1989, 103:97-140.
[19] Hallquist J O. LS-DYNA Theoretical Manual. Livermore Software Technology Corporation. 1998.
[20] Taylor L M, Flanagan D P. PRONTO 3D a three-dimensional transient solid dynamics program. Technical Report SAND87-1912, Sandia National Laboratories, 1989.
[21] Scheffler D R, Zukas J A. Practical aspects of numerical simulation of dynamic events:material interfaces. International Journal of Impact Engineering , 2000, 24:821-842.
[22] Bessette G C, Becker E B, Taylor L M,et al. Modeling of impact problems using an h-adaptive, explicit Lagrangian finite element method in three dimensions. Computer Methods in Applied Mechanics Engineering, 2003, 192:1649-1679.
[23] Camacho G T, Ortiz M. Adaptive Lagrangian modeling of ballistic penetration of metallic targets. Computer Methods in Applied Mechanics Engineering, 1997, 142:269-301.
[24] Camacho G T, Ortiz M. Computational modeling of impact damage in brittle materials, International Journal of Solids and Structures. 1996, 33:2899-2938.
[25] Littlefield D L.The use of r-adaptivity in explicit Lagrangian finite element codes, Proceedings of the 15th US Army Symposium on Solid Mechanics, 1999:305-320.
[26] Martineau R L, Prime M B, Duffey T. Penetration of HSLA-100 steel with tungsten carbide spheres at striking velocities between 0.8 and 2.5 km/s. International Journal of Impact Engineering, 2004, 30:505-520.
[27] Resnyansky A D. DYNA-modelling of the high-velocity impact problems with a split-element algorithm. International Journal of Impact Engineering, 2002, 27:709-727.
[28] B?rvik T, Hopperstad O S, Berstad T, Langseth M. Perforation of 12mm thick steel plates by 20mm diameter projectiles with blunt, hemispherical and conical noses, part II: numerical simulations. International Journal of Impact Engineering, 2002, 27:37-64.
[29] Attaway S W, Brown M J, Heinstein M W, et al. PRONTO3D User’s Instructions: A Transient Dynamic Code for Nonlinear Structural Analysis. Technical Report SAND98-1361, Sandia National Laboratory, 1998.
[30] Brown K, Attaway S, Plimpton S, Hendrickson B. Parallel strategies for crash and impact simulations. Computer Methods in Applied Mechanics and Engineering, 2000, 184: 375-390.
[31] Attaway S W, Hendrickson B A, Plimpton S J, et al. A parallel contact detection algorithm for transient solid dynamics simulations using PRONTO3D. Computational Mechanics,1998, 22: 143-159.
[32] Warren T L, Tabbara M R. Spherical Cavity-Expansion Forcing Function in PRONTO3D for Application to Penetration Problems. SAND97-1174, Sandia National Laboratories, 1997.
[33] Warren T L, Fossum A F, Frew D J. Penetration into low-strength (23 MPa) concrete: target characterization and simulations. International Journal of Impact Engineering, 2004, 30(5):477-503.
[34] Warren T L, Poormon K L. Penetration of 6061-T6511 aluminum targets by ogive-nosed VAR 4340 steel projectiles at oblique angles: experiments and simulations. International Journal of Impact Engineering, 2001, 25:993-1022.
[35] Vorobiev Y O, Liu B T, Lomov I N, et al. Simulation of penetration into porous geologic media. International Journal of Impact Engineering, 2007, 34: 721-731.
[36] ABAQUS Inc. Getting Started with ABAQUS Version 6.6, ABAQUS Inc, 2006.
[37] Iqbal M A, Chakrabarti A, Beniwal S, et al. 3D numerical simulations of sharp nosed projectile impact on ductile targets. International Journal of Impact Engineering, 2010, 37:185-195.
[38] Gupta N K, Iqbal M A , Sekhon G S. Experimental and numerical studies on the behavior of thin aluminumplates subjected to impact by blunt and hemispherical nosed projectiles. International Journal of Impact Engineering, 2006, 32:1921-1944.
[39] Gupta N K, Iqbal M A, Sekhon G S. Effect of projectile nose shape, impact velocity and target thickness on deformation behavior of aluminum plates. International Journal of Solids and Structures, 2007, 44:3411-3439.
[40] MSC Inc. MSC.Dytran User’s Manual. MSC.Software Corporation, 1999.
[41] Wingate C A, Stellingwerf R F, Davidson R F, et al. Models of High Velocity Impact Phenomena. International Journal of Impact Engineering, 1993, 14:819-830.
[42] Wilkins M L. Computer Simulation of Dynamic Phenomena. Spinger, 1999.
[43] Birnbaum N K, Tancreto J, Hager K. Calculation of Blast Loading in the High Performance Magazine with AUTODYN-3D. Proceedings of the Twenty-Sixth DOD Explosives Safety Seminar, 1994.
[44] Century Dynamics Inc. AUTODYN-3D Users Manual. Century Dynamics Inc. 1994.
[45] Tham C Y. Numerical and Empirical Approach in Predicting the Penetration of a Concrete Target by an Ogive-Nosed Projectile. Finite Elements in Analysis and Design, 2006, 42:1258-1268.
[46]王肖钧,胡秀章,刘胜求.四边形单元中的沙漏控制.计算物理, 1991, 8(3): 312-318.
[47]胡秀章,王肖钧,李永池.一种弹塑性弹丸侵彻靶板的滑移面处理.结构与介质相互作用理论与应用,南京:河海大学出版社, 1993.
[48]李永池,袁福平,胡秀章等.卵形头部弹丸对混凝土靶板侵彻的二维数值模拟.弹道学报, 2002, 14(1):14-19.
[49]王峰.有限元方法及其在高速碰撞中的应用[博士学位论文].合肥:中国科学技术大学, 2007.
[50]宋顺成.轴对称冲击有限元一致质量矩阵迭代解.力学学报, 1998, 30(3):285-291.
[51]宋顺成,谭多望,蔡鸿年.穿破甲有限元的几何非线性及物理参数的确定.爆炸与冲击, 2002, 22(2):137-143.
[52]宋顺成,谭多望.高速冲击非线性有限元计算.西南交通大学学报, 2001, 36:565-571.
[53]马天宝,王静,宁建国.一种VOF与PIC耦合多物质界面处理算法及其在侵彻问题中的应用.中国科学(G辑), 2009, 39(9): 1185-1194.
[54] Couch R, Albright E, Alexander N. The JOY computer code. Technical Report UCID-19688, Lawrence Livermore National Laboratories, 1983.
[55] McGlaun J M, Thompson S L, Elrick M G. CTH: A three-dimensional shock wave physics code. International Journal of Impact Engineering, 1990, 10:351-360.
[56] Noh W F, Woodward P. SLIC (Simple Line Interface Calculation). Lecture Notes in Physics, 1976, 59:330-340.
[57] Youngs D L. Time-Dependent Multi-Material Flow with Large Fluid Distortion. Numerical Methods for Fluid Dynamics. New York: Academic Press, 1982.
[58] Fahrenthold E P, Yew C H. Hydrocode simulation of hypervelocity impact fragmentation. International Journal of Impact Engineering, 1995, 17: 303-310.
[59] Silling S A. CTH reference manual: boundary layer algorithm for sliding interfaces in two dimensions. Technical Report SAND93-2487, Sandia National Laboratories, 1994.
[60] Scheffler D R. Modeling non-eroding perforation of an oblique aluminum target using the Eulerian CTH hydrocode. International Journal of Impact Engineering, 2005, 32:461-472.
[61]刘军,何长江,梁仙红.三维弹塑性流体力学自适应欧拉方法研究.高压物理报, 2008, 22(01):72-78.
[62]何长江,于志鲁,冯其京.高速碰撞的三维欧拉数值模拟方法.爆炸与冲击, 1999, 19(3): 216-221.
[63]马天宝,宁建国.三维爆炸与冲击问题仿真软件研究.计算力学学报, 2009,26(4):600-603.
[64]吴开腾.爆炸与冲击问题的三维数值模拟及算法研究[博士学位论文].北京:北京理工大学, 2002.
[65]马天宝,郝莉,宁建国. Euler多物质流体动力学数值方法中的界面处理算法.计算物理, 2008, 25(2):133-138.
[66]陈龙伟,孙远翔,宁建国.动能弹对混凝土靶板侵彻三维数值模拟.北京理工大学学报, 2003, 23(5):536-539.
[67]王景焘,张德良,刘凯欣.基于CE/SE方法的二维Euler型多物质流体弹塑性问题计算.计算物理, 2007, 24(4):395-401.
[68] Wang J, Liu K, Zhang D. An improved CE/SE scheme for multi-material elastic-plastic flows and its applications. Computers & Fluids, 2009, 38(3):544-551.
[69]张雄,陆明万,王建军.任意拉格朗日-欧拉描述法研究进展.计算力学学报, 1997, 14(1): 91-102.
[70] Benson D J. An efficient, accurate and simple ALE method for nonlinear finite element programs. Computer Methods in Applied Mechanics and Engineering, 1989, 72:305-350.
[71] Liu W K, Belytschko T, Chang H. An arbitrary Lagrangian-Eulerian finite element method for path-dependant materials. Computer Methods in Applied Mechanics and Engineering, 1986:227-245.
[72] Sheng D,Wriggers P, Sloan S W. Improved numerical algorithms for friction contact in pile penetration analysis. Computers and Geotechnics, 2006, 33:341-354.
[73] Sheng D, Nazem M, Carter J P. Some computational aspects for solving deep penetration problems in geomechanics. Computational Mechanics, 2009, 44:549-561.
[74] Liyanapathirana D S. Arbitrary Lagrangian Eulerian based finite element analysis of cone penetration in soft clay. Computers and Geotechnics, 2009, 36: 851-860.
[75] Walker J, Yu H S. Adaptive finite element analysis of cone penetration in clay. Acta Geotechnica, 2006, 1:43-57.
[76] Alme M L, Rhoades C E. A Computational Study of Projectile Melt in Impact With Typical Whipple Shields. International Journal of Impact Engineering, 1995, 17:1-12.
[77]张雄,刘岩.无网格法.北京:清华大学出版社, 2004.
[78] Liu G R, Yan L. A study on numerical integration in element-free Galerkin method. Fourth International Asia-Pacific Conference on Computational Mechanics, Singapore, 1999.
[79]张雄,刘岩,马上.无网格法的理论及应用,力学进展, 2009,39(1):1-36.
[80]顾元通,丁桦.无网格法及其最新进展,力学进展, 2005, 35(3):323-337.
[81] Belytschko T, Krongauz Y, Organ D, et al. Mesh-less methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4): 3-47.
[82] Li S, Liu W K. Meshfree and particle methods and their applications. Applied Mechanics Reviws, 2002,55(1): 1-34.
[83] Monaghan J J. An introduction to SPH. Computer Physics Communications, 1988, 48: 89-96.
[84] Swegle J W, Hicks D L, Attaway W S. Smoothed particled hydrodynamics stabilityanalisys. Journal of Computational Physics, 1995, 116:123-134.
[85] Liu W K, Chen Y, Aziz U. Generalized multiple scale reproducing kernel particle methods. Computer Methods in Applied Mechanics and Engineering, 1996, 139:91-157.
[86] Liu W K, Chen Y, Chang C T. Advances in multiple scale kernel particle methods. Computational Mechanics, 1996, 18:73-111.
[87] Nayroles P, Touzot G, Villon P. Generalizing the finite element methods: diffuse approximation and diffuse elements. Computational Mechanics, 1992, 10:307-318.
[88] Belyschko T, Touzot G, Gu L. Element free galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37:229-256.
[89] Atluri S N, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, 1998, 22:117-127.
[90] Atluri S N, Zhu T. The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Computational Mechanics, 2000, 25:169-179.
[91] Libersky L, Petschek A G, Carney T C, et al. High strain largrangian hydrodynamics a three-dimensional SPH code for dynamics material response. Journal of Computational Physics, 1993, 109:67-75.
[92] Stellingwerf R F, Wingate C A. Impact modeling with smooth particle hydrodynamics. International Journal of Impact Engineering, 1993, 14: 707-718.
[93] Benz W, Asphaug E. Simulations of brittle solids using smooth particle hydrodynamics. Computer Physics Communications, 1995, 87(1-2): 253-265.
[94] Campbell J, Vignjevic R, Libersky L. A contact algorithm for smoothed particle hydrodynamics. Computer Methods in Applied Mechanics and Engineering, 2000, 184(1): 49-65.
[95] Vignjevic R, De Vuyst T, Campbell J C. A frictionless contact algorithm for meshless methods. CMES-Computer Modeling in Engineering & Sciences, 2006,13(1): 35-48.
[96] Johnson G R, Stryk R A, Beissel S R. SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4):347-373.
[97] Johnson G R, Beissel S R. Normalized smoothing functions for SPH impact computations. International Journal for Numerical Methods in Engineering, 1996, 39(16): 2725-2741.
[98] Johnson G R, Beissel S R, Stryk R A. A generalized particle algorithm for high velocity impact computations. Computational Mechanics, 2000, 25(2-3):245-256.
[99] Johnson G R, Stryk R A, Beissel S R, et al. An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation. International Journal of Impact Engineering, 2002, 27(10): 997-1013.
[100] Johnson G R, Stryk R A. Conversion of 3D distorted elements into meshless particles during dynamic deformation. International Journal of Impact Engineering, 2003, 28(9):947-966.
[101] Han Z D, Liu H T, Rajendran A M, et al. The applications of meshless local Petrov-Galerkin (MLPG) approaches in high-speed impact, penetration and perforation problems. CMES-Computer Modeling in Engineering & Sciences, 2006, 14(2): 119-128.
[102] Fahrenthold E P, Horban B A. An improved hybrid particle-element method for hypervelocity impact simulation. International Journal of Impact Engineering, 2001, 26(1-10): 169-178.
[103] Park Y K, Fahrenthold E P. A kernel free particle-finite element method for hypervelocity impact simulation. International Journal for Numerical Methods in Engineering, 2005, 63(5): 737-759.
[104] Quinn M J. Parallel Programming in c with MPI and OpenMP. New York: McGraw-Hill Companies, 2004.
[105] Grama A, Gupta A, Karypis G. Introduction to Parallel Computing(2nd edition). Benjamin-cummings Publishing Company, 2003.
[106] Har J, Fulton R E. A parallel finite element procedure for contact-impact problems. Engineering with Computers, 2003, 19: 67-84.
[107] Guo Y, Jin X, Ding J. Parallel numerical simulation with domain decomposition for seismic response analysis of shield tunnel. Advances in Engineering Software, 2006, 37: 450-456.
[108]王裴,洪涛.三维光滑粒子流体动力学并行计算程序.计算物理, 2006, 23(4):431-435.
[109] Danielson K T, Uras R A, Adley M D, et al. Large-scale application of some modern CSM methodologies by parallel computation. Advances in Engineering Software, 2000, 31:501-509.
[110] PantaléO. Parallelization of an object-oriented FEM dynamics code: influence of the strategies on the Speedup. Advances Engineering Software, 2005, 36: 361-373.
[111] Couturier R, Chipot C. Parallel molecular dynamics using OPENMP on a shared memory machine. Computer Physics Communications, 2000, 124:49-59.
[112] Ayguadea E, Gonzaleza M, Martorella X, et al. Employing nested OpenMP for the parallelization of multi-zone computational fluid dynamics applications. Journal of Parallel and Distributed Computing, 2006, 66:686-697.
[113] Thacker R J, Couchman H M P. A parallel adaptive P3M code with hierarchical particle reordering. Computer Physics Communication, 2006, 174: 540-554.
[114] Harlow F H. The particle-in-cell computing method for fluid dynamics. Methods in Computational Physics, 1963, 3: 319-343.
[115] Brackbill J U, Ruppel H M. FLIP: a method for adaptively zoned, particle-in-cell calculations in two dimensions. Journal of Computational Physics, 1986, 65:314-343.
[116] Brackbill J U, Kothe D B, Ruppel H M. FLIP: a low-dissipation, particle-in-cell method for fluid flow. Computer Physics Communications, 1988, 48:25-38.
[117] Sulsky D, Chen Z, Schreyer H L. A Particle Method for History-Dependent Materials. Computer Methods in Applied Mechanics and Engineering, 1994, 118(1-2):179-196.
[118] Sulsky D, Zhou S J, Schreyer H L. Application of a Particle-in-Cell Method to Solid Mechanics. Computer Physics Communications, 1995, 87(1-2):236-252.
[119] Sulsky D, Schreyer H L. Axisymmetric form of the material point method with applications to upsetting and Taylor impact problems. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4):409-429.
[120] Sulsky D, Kaul A. Implicit dynamics in the material-point method. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12-14):1137-1170.
[121] Cummins S J, Brackbill J U. An implicit particle-in-cell method for granular materials. Journal of Computational Physics, 2002, 180(2):506-548.
[122] Guilkey J E, Weiss J A. An implicit time integration strategy for use with the material point method. MIT Conference on Computational Fluid and Solid Mechanics, 2001.
[123] Guilkey J E, Weiss J A. Implicit time integration for the material point method: Quantitative and algorithmic comparisons with the finite element method. International Journal for Numerical Methods in Engineering, 2003, 57(9):1323-1338.
[124] Tan H L, Nairn J A. Hierarchical, adaptive, material point method for dynamic energy release rate calculations. Computer Methods in Applied Mechanics and Engineering, 2002, 191(19-20):2095-2109.
[125] Love E, Sulsky D L. An energy-consistent material-point method for dynamic finite deformation plasticity. International Journal for Numerical Methods in Engineering, 2006, 65(10):1608-1638.
[126] Love E, Sulsky D L. An unconditionally stable, energy-momentum consistent implementation of the material-point method. Computer Methods in Applied Mechanics and Engineering, 2006, 195(33-36):3903-3925.
[127] Bardenhagen S G, Kober E M. The generalized interpolation material point method. CMES- Computer Modeling in Engineering & Sciences, 2004, 5(6):477-495.
[128] Steffen M, Wallstedt P C, Guilkey J E, et al. Examination and Analysis of Implementation Choices within the Material Point Method (MPM). CMES-Computer Modeling in Engineering & Sciences, 2008, 31(2):107-127.
[129] Ma S, Zhang X, Lian Y, Zhou X. Simulation of high explosive explosion using adaptive material point method. CMES-Computer Modeling In Engineering & Sciences, 2009, 39:101-123.
[130] York A R II, Sulsky D, Schreyer H L. The material point method for simulation of thinmembranes. International Journal for Numerical Methods in Engineering, 1999, 44: 1429-1456.
[131] Hu W, Chen Z. A multi-mesh MPM for simulating the meshing process of spur gears. Computers and Structures, 2003, 81:1991-2002.
[132] Bardenhagen S G, Brackbill J U, Sulsky D. The material point method for granular materials. Computer Methods in Applied Mechanics Engineering, 2000, 187:529-541.
[133] Bardenhagen S G, Guilkey J E, Roessig K M, et al. An improved contact algorithm for the material point method and application to stress propagation in granular material. CMES-Computer Modeling in Engineering and Sciences, 2001, 2(4): 509-522.
[134] Parker S G. A component-based architecture for parallel multi-physics PDE simulation. Future Generation Computer Systems, 2006 ,22:204-216.
[135] Parker S G, Guilkey J, Harman T. A component-based parallel infrastructure for the simulation of fluid-structure interaction. Engineering with Computers, 2006, 22: 277-292.
[136] Ma J, Lu H, Komanduri R. Structured mesh refinement in generalized interpolation material point (GIMP) method for simulation of dynamic problems. CMES: Computer Modeling in Engineering and Sciences, 2006, 12(3):213-227.
[137] Zhang X, Sze K Y, Ma S. An explicit material point finite element method for hyper-velocity impact. International Journal for Numerical Methods in Engineering, 2006, 66:689-706.
[138] Guilkey J E, Harman T B, Banerjee B. An Eulerian-Lagrangian approach for simulating explosions of energetic devices. Computers & Structures, 2007, 85(11-14):660-674.
[139] Ma S, Zhang X, Qiu X M. Comparison study of MPM and SPH in modeling hypervelocity impact problems. International Journal of Impact Engineering, 2009, 36:272-282.
[140] Lee W H, Painter J W. Material void-opening computation using particle method. International Journal of Impact Engineering, 1999, 22:1-22.
[141] Hu W Q, Chen Z. Model-based simulation of the synergistic effects of blast and fragmentation on a concrete wall using the MPM. International Journal of Impact Engineering, 2006, 32(12):2066-2096.
[142]王宇新.多相介质爆炸冲击响应物质点法分析[博士学位论文].大连:大连理工大学, 2006.
[143] Nairn J A. Material point method calculations with explicit cracks. CMES-Computer Modeling in Engineering & Sciences, 2003, 4(6):649-663.
[144] Guo Y, Nairn J A. Calculation of J-integral and stress intensity factors using The Material Point Method. CMES-Computer Modeling in Engineering & Sciences, 2004, 6(3):295-308.
[145] Nairn J A. On the calculation of energy release rates for cracked laminates with residual stresses. International Journal of Fracture, 2006, 139(2):267-293.
[146] Wang B, Karuppiah V, Lu H, et al. Two-dimensional mixed mode crack simulation using the material point method. Mechanics of Advanced Materials and Structures, 2005, 12(6):471-484.
[147] Daphalapurkar N P, Lu H, Coker D, et al. Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method. International Journal of Fracture, 2007, 143(1):79-102.
[148] Chen Z, Hu W, Shen L, et al. An evaluation of the MPM for simulating dynamic failure with damage diffusion. Engineering Fracture Mechanics, 2002, 69(17):1873-1890.
[149] Chen Z, Feng R, Xin X, et al. A computational model for impact failure with shear-induced dilatancy. International Journal for Numerical Methods in Engineering, 2003, 56(14):1979-1997.
[150] Shen L M, Chen Z. A multi-scale simulation of tungsten film delamination from silicon substrate. International Journal of Solids and Structures, 2005, 42(18-19):5036-5056.
[151] Shen L M, Chen Z. A silent boundary scheme with the material point method for dynamic analyses. CMES-Computer Modeling in Engineering & Sciences, 2005, 7(3):305-320.
[152] Schreyer H L, Sulsky D L, Zhou S J. Modeling delamination as a strong discontinuity with the material point method. Computer Methods in Applied Mechanics and Engineering, 2002, 191(23-24):2483-2507.
[153] Sulsky D, Schreyer L. MPM simulation of dynamic material failure with a decohesion constitutive model. European Journal of Mechanics A/Solids, 2004, 23(3):423-445.
[154] Bardenhagen S G, Brydon A D, Guilkey J E. Insight into the physics of foam densification via numerical simulation. Journal of the Mechanics and Physics of Solids, 2005, 53(3):597-617.
[155] Brydon A D, Bardenhagen S G, Miller E A, et al. Simulation of the densification of real open-celled foam microstructures. Journal of the Mechanics and Physics of Solids, 2005, 53(12):2638-2660.
[156] Wieckowski Z, Youn S K, Yeon J H. A particle-in-cell solution to the silo discharging problem. International Journal for Numerical Methods in Engineering, 1999, 45(9):1203-1225.
[157] Wieckowski Z. The material point method in large strain engineering problems. Computer Methods in Applied Mechanics and Engineering, 2004, 193(39-41):4417-4438.
[158] Bardenhagen S G, Brackbill J U, Sulsky D. Numerical study of stress distribution in sheared granular material in two dimensions. Physical Review E, 2000, 62(3):3882–3890.
[159] Coetzee C J, Basson A H, Vermeer P A. Discrete and continuum modelling of excavator bucket filling. Journal of Terramechanics, 2007, 44(2):177–186.
[160] Sulsky D, Schreyer H, Peterson K, et al. Using the material-point method to model sea icedynamics. Journal of Geophysical Research-Oceans, 2007, 112(C2):C02S90.
[161] Zhang H W, Wang K P, Chen Z. Material point method for dynamic analysis of saturated porous media under external contact/impact of solid bodies. Computer Methods in Applied Mechanics and Engineering, 2009, 198(17-20):1456–1472.
[162] Guilkey J E, Hoying J B, Weiss J A. Computational modeling of multicellular constructs with the material point method. Journal of Biomechanics, 2006, 39(11):2074–2086.
[163] Zhang D Z, Zou Q, VanderHeyden W B, Ma X. Material point method applied to multiphase flows. Journal of Computational Physics, 2008, 227: 3159-3173.
[164] Bardenhagen S G. Energy conservation error in the material point method for solid mechanics. Journal of Computational Physics, 2002, 180(1):383-403.
[165] Anderson C E Jr. An overview of the theory of hydrocodes. International Journal of Impact Engineering, 1987, 5:33–59.
[166]经福谦等.实验物态方程导引.北京:科学出版社, 1986.
[167]王仁,黄文彬,黄祝平.塑性力学引论.北京:北京大学出版社, 1992.
[168] Liu M B, Liu G R, Lam K Y. Investigation into water mitigations using a meshless particle method. Shock Waves, 2002, 12(3):181–195.
[169] De Vuyst T, Vignjevic R, Campbell J C. Coupling between meshless and finite element methods. International Journal of Impact Engineering, 2005, 31: 1054-1064.
[170] Wingate C A, Dilts G A, Mandell D A, et al. Progress in smooth particle hydrodynamics. Technical Report LA-UR-98-300, Los Alamos National Laboratories, 1998.
[171] Voyiadjis G Z, Palazotto A N, Gao X L. Modeling of metallic materials at high strain rates with continuum damage mechanics. Applied Mechanics Review, 2002, 55(5):481-493.
[172] Candel A E, Dehler M M, Troyer M. A massively parallel particle-in-cell code for the simulation of field-emitter based electron sources. Nuclear Instruments and Methods in Physics Research A, 2006, 558:154-158.
[173] Chandra R, Dagum L, Kohr D, et al. Parallel Programming in OpenMP. Morgan Kaufmann Publishers, 2001.
[174] Chapman B, Jost G, VanderPas R. Using OpenMP : portable shared memory parallel programming. The MIT Press, 2007.
[175] Johnson G R, Holmquist T J. Evaluation of cylinder-impact test data for constitutive model constants. Journal of Applied Physics, 1988, 64:3901-3910.
[176] Mehra V, Chaturvedi S. High velocity impact of metal sphere on thin metallic plates: a comparative smooth particle hydrodynamics study. Journal of Computational Physics, 2006, 212:318-337.
[177] Beissel S R, Gerlach C A, Johnson G R. Hypervelocity impact computations with finiteelements and meshfree particles. International Journal of Impact Engineering, 2006, 33:80-90.
[178] Anderson C E JR, Trucano T G, Mullin S A. Debris cloud dynamics. International Journal of Impact Engineering, 1990, 9: 89-113.
[179] Wang F J, Wang L P, Cheng J G, et al. Contact force algorithm in explicit transient analysis using finite-element method. Finite Elements in Analysis and Design, 2007, 43:580-587.
[180] Chapman D J, Radford D D, Reynolds M, et al. Shock induced void nucleation during Taylor impact. International Journal of Fracture, 2005, 134:41-57.
[181] Seoa S W, Min O K, Lee J H. Application of an improved contact algorithm for penetration analysis in SPH. International Journal of Impact Engineering, 2008, 35: 578-588.
[182] Piekutowski A J, Forrestal M J, Poormon K L, et al. Perforation of aluminium plates with ogive-nose steel rods at normal and oblique impacts. International Journal of Impact Engineering, 1996, 18:877- 887.
[183] Liu G R, Liu M B. Smoothed Particle Hydrodynamics: a meshfree particle method. World Scientific, 2003.
[184] Bui H H, Lagrangian Mesh-free Particle Method(SPH) for Large Deformation and Post-failure of Geomaterial using Elasto-plastic Constitutive Models [Ph. D. thesis], Japan: Ritsumeikan University, 2006.
[185] Coetzee C J, Vermeer P A, Basson A H. The modelling of anchors using the material point method. International Journal for Numerical and Analytical Methods in Geomechanics, 2005, 29:879-895.
[186] Tanaka H, Momozu M, Oida A, et al. Simulation of soil deformation and resistance at bar penetration by the Distinct Element Method. Journal of Terramechanics, 2000, 37:41-56.
[187] Itasca Consulting Group Inc. FLAC-Fast Lagrangian Analysis of Continua User’s Manual (Version 5.0). Minneapolis: Itasca Consulting Group Inc, 2005.
[188] Chen W F, Mizuno E. Nonlinear analysis in soil mechanics. Amsterdam: Elsevier Science Publishers, 1990.
[189]张雄,王天舒.计算动力学.北京:清华大学出版社, 2007.
[190] Fasanella E L, Jones Y, Knight N F Jr, et al.Low velocity earth-penetration test and analysis. Technical Report: AIAA-2001-1388, American Institute of Aeronautics and Astronautics, 2001.
[191]郑颖人,沈珠江,龚晓南.广义塑性力学—岩土塑性力学原理.北京:中国建筑工业出版社, 2002.
[192]张雄.冲击爆炸三维物质点法数值仿真软件MPM3D:中国, 2009SRBJ4761. (计算机软件著作权登记号)
[193] Andersen S, Andersen L. Modelling of landslides with the material-point method.Computational Geosciences, 2010, 14:137-147.
[194]马上.冲击爆炸问题的物质点无网格法研究[博士论文].北京:清华大学, 2009.