冲击爆炸问题的物质点无网格法研究
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摘要
冲击爆炸问题在国民经济和科学技术中有广泛而重要的应用。数值模拟是进行这类问题研究的重要手段，但冲击爆炸问题涉及多种学科，往往非常复杂，对数值方法提出了很大的挑战。无网格法在处理大变形问题以及涉及材料破坏的问题具有优势，为冲击爆炸问题的数值模拟提供了有效工具。一些质点类无网格法，如光滑质点动力学方法（SPH）已经取得了相当丰富的成果，得到了工程界的认可。本文针对超高速碰撞和爆炸问题，基于无网格物质点法（MPM），研究适合对冲击爆炸问题进行模拟的数值方法，研制三维物质点法程序，建立有效的数值模拟工具。
针对有限元在求解超高速碰撞问题遇到的网格畸变这一困难，本文借鉴物质点法的思想，提出了物质点有限元法。在物质点有限元法中，仍用有限单元离散物体，在大变形区域布置背景网格，被背景网格覆盖的区域将结点视为物质点，用物质点法进行计算，其他区域仍用有限元法求解，从而解决有限元法在处理大变形问题时网格畸变的问题。通过Taylor杆碰撞的模拟和弹丸超高速碰撞薄板的模拟，说明了此方法在效率上和在描述碎片云的形成过程上都比有限元法具有优势。
针对物质点法存在的数值断裂问题，本文提出了在物质点法中自适应分裂质点的方案，使物质点法可以在质点变形最大的方向上自适应分裂质点，从而避免了数值断裂。将自适应分裂质点物质点法用于激波管、爆轰驱动飞片、聚能射流等问题的模拟和分析，取得了较好的效果。
在理论和算法研究的基础上，研制了用于冲击爆炸问题的三维显式物质点法程序MPM3DPP。从影响点搜索、形函数、稳定性、时间积分、边界条件和接触算法等方面对物质点法和SPH方法进行了比较，通过Taylor杆问题和超高速碰撞问题的模拟了进行比较和分析。
The impact and explosion problems have broad and significant applications in thenational economy and technology. Numerical simulation is an important study ap-proach for this kind of problems. However, the impact and explosion problems covera broad range of disciplines, and are often very complicated. It is a great challengefor numerical methods. Meshfree methods have advantages in dealing with large de-formation and material fracture. They are effective tools for simulation of impact andexplosion problems. Some meshfree particle methods, such as smoothed particle hy-drodynamics (SPH), have many successful applications in this area, and are acceptedby engineers. In this paper, studies are carried out based on the material point method(MPM) with the aim of solving hypervelocity impact and explosion problems. Thenumerical methods for impact and explosion problems are investigated. A three di-mensional material point method code has been developed as an effective numericalsimulation tool.
Finite element method has the difficulty of mesh distortion in solving the hyper-velocity impact problems. An explicit material point finite element method is proposedby using the idea of the material point method. The material domain is discretized byfinite elements. The momentum equations are solved on a predefined computationalgrid (like the material point method) in the large deformation zone, and on the finiteelement mesh (like the traditional finite element method) elsewhere. Mesh distortionproblem is avoided in material point finite element method. The advantages of theproposed method in efficient and depicting debris cloud are illustrated by simulatingTaylor bar impact problem and hypervelocity impact problem.
To solve the numerical fracture problem existing in the material point method , anadaptive particle splitting scheme was proposed. The particle can be split adaptively inthe direction with the largest deformation. The adaptive material point method has beenapplied in the shock tube, explosively driven ?yer, and shaped charge jet formation problems with good performance.
Based on theoretical and algorithmic studies, three dimensional explicit materialpoint method code MPM3DPP is developed. SPH and MPM are compared in neighborsearching, approximation functions, consistency of shape functions, instability, timeintegration, boundary conditions and contact algorithm. The taylor bar impact problemand hypervelocity impact problem are analyzed by the two methods for comparison.
针对有限元在求解超高速碰撞问题遇到的网格畸变这一困难，本文借鉴物质点法的思想，提出了物质点有限元法。在物质点有限元法中，仍用有限单元离散物体，在大变形区域布置背景网格，被背景网格覆盖的区域将结点视为物质点，用物质点法进行计算，其他区域仍用有限元法求解，从而解决有限元法在处理大变形问题时网格畸变的问题。通过Taylor杆碰撞的模拟和弹丸超高速碰撞薄板的模拟，说明了此方法在效率上和在描述碎片云的形成过程上都比有限元法具有优势。
针对物质点法存在的数值断裂问题，本文提出了在物质点法中自适应分裂质点的方案，使物质点法可以在质点变形最大的方向上自适应分裂质点，从而避免了数值断裂。将自适应分裂质点物质点法用于激波管、爆轰驱动飞片、聚能射流等问题的模拟和分析，取得了较好的效果。
在理论和算法研究的基础上，研制了用于冲击爆炸问题的三维显式物质点法程序MPM3DPP。从影响点搜索、形函数、稳定性、时间积分、边界条件和接触算法等方面对物质点法和SPH方法进行了比较，通过Taylor杆问题和超高速碰撞问题的模拟了进行比较和分析。
The impact and explosion problems have broad and significant applications in thenational economy and technology. Numerical simulation is an important study ap-proach for this kind of problems. However, the impact and explosion problems covera broad range of disciplines, and are often very complicated. It is a great challengefor numerical methods. Meshfree methods have advantages in dealing with large de-formation and material fracture. They are effective tools for simulation of impact andexplosion problems. Some meshfree particle methods, such as smoothed particle hy-drodynamics (SPH), have many successful applications in this area, and are acceptedby engineers. In this paper, studies are carried out based on the material point method(MPM) with the aim of solving hypervelocity impact and explosion problems. Thenumerical methods for impact and explosion problems are investigated. A three di-mensional material point method code has been developed as an effective numericalsimulation tool.
Finite element method has the difficulty of mesh distortion in solving the hyper-velocity impact problems. An explicit material point finite element method is proposedby using the idea of the material point method. The material domain is discretized byfinite elements. The momentum equations are solved on a predefined computationalgrid (like the material point method) in the large deformation zone, and on the finiteelement mesh (like the traditional finite element method) elsewhere. Mesh distortionproblem is avoided in material point finite element method. The advantages of theproposed method in efficient and depicting debris cloud are illustrated by simulatingTaylor bar impact problem and hypervelocity impact problem.
To solve the numerical fracture problem existing in the material point method , anadaptive particle splitting scheme was proposed. The particle can be split adaptively inthe direction with the largest deformation. The adaptive material point method has beenapplied in the shock tube, explosively driven ?yer, and shaped charge jet formation problems with good performance.
Based on theoretical and algorithmic studies, three dimensional explicit materialpoint method code MPM3DPP is developed. SPH and MPM are compared in neighborsearching, approximation functions, consistency of shape functions, instability, timeintegration, boundary conditions and contact algorithm. The taylor bar impact problemand hypervelocity impact problem are analyzed by the two methods for comparison.
引文
[1]张庆明,黄风雷.超高速碰撞动力学引论.北京,科学出版社, 2000.
[2]恽寿榕,赵衡阳.爆炸力学.北京:国防工业出版社, 2005.
[3]王礼立.应力波基础.北京:国防工业出版社, 2005.
[4] Quinn M J. Parallel programming in C with MPI and OpenMP.北京:清华大学出版社,2005.
[5] http://www.top500.org/.
[6] Computational Science: Ensuring America’s Competitiveness. Technical report, President’sInformation Technology Advisory Committee, 2005.
[7]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.
[8] Johnson N L. The Legacy and Future of CFD At Los Alamos. Technical Report LA-UR-96-1426, Los Alamos National Laboratory, 1996.
[9] Zukas J A. Introduction to Hydrocodes. Elsevier Science, 2004.
[10]张雄,王天舒.计算动力学.北京:清华大学出版社, 2007.
[11]洪友士.郑哲敏对应用力学和技术科学的贡献.力学进展, 2005, 35(1):1–4.
[12] Anderson J D. Computational Fluid Dynamics, the Basics with Applications.北京:清华大学出版社, 2002.
[13] McGlaun J M, Thompson S L, Elrick M G. CTH: A three-dimensional shock wave physicscode. International Journal of Impact Engineering, 1990, 10:351–360.
[14] Scheffler D R. Modeling non-eroding perforation of an oblique aluminum target using theEulerian CTH hydrocode. International Journal of Impact Engineering, 2005, 32:461–472.
[15] Huerta M, Vigil M G. Design, analyses, and field test of a 0.7 m conical shaped charge.International Journal of Impact Engineering, 2006, 32(8):1201–1213.
[16] Berger M, Oliger J. Adaptive Mesh Refinement For Hyperbolic Partial-Differential Equations.Journal of Computational Physics, 1984, 53(3):484–512.
[17] Berger M, Colella P. Local Adaptive Mesh Refinement for Shock Hydrodynamics. Journalof Computational Physics, 1989, 82(1):64–84.
[18] MacNeice P, Olson K M, Mobarry C, et al. PARAMESH: A parallel adaptive mesh refinementcommunity toolkit. Computer Physics Communications, 2000, 126:330–354.
[19] Luketa-Hanlin A, Attaway S. Massively parallel computations of damage to a thin-walledstructure from blast. Proceedings of ASME International Mechanical Engineering Congressand Exposition, Seattle, WA: Amer Soc Mechanical Engineers, 2007. 887–891.
[20] http://www.sandia.gov/media/NewsRel/NR2001/cth.htm.
[21] Wilkins M L. Computer Simulation of Dynamic Phenomena. Spinger, 1999.
[22] Wingate C A, Stellingwerf R F, RF D, et al. Models of High Velocity Impact Phenomena.International Journal of Impact Engineering, 1993, 14:819–830.
[23] Meyer H W Jr. A Modified Zerilli-Armstrong Constitutive Model Describing the Strengthand Localizing Behavior of Ti-6Al-4V. Technical Report ARL-CR-0578, Army ResearchLaboratory, 2006.
[24] Attaway S W, Brown M J, Heinstein M W, et al. PRONTO3D User’s Instructions: A TransientDynamic Code for Nonlinear Structural Analysis. Sandia National Laboratory, 1998.
[25] Bessette G C, Bixler N E, Hewson J C, et al. Methodology Assessment and Recommendationsfor the Mars Science Laboratory Launch Safety Analysis. Technical ReportSAND2006-4563, Sandia National Laboratories, 2006.
[26] Hallquist J O. LS-DYNA Theoretical Manual. Livermore Software Technology Corporation,1998.
[27] Zukas J A, (eds.). High Velocity Impact Dynamics. John Wiley & Sons, 1990.
[28]宁建国,刘凯欣,何长江,等.,编.第四届全国计算爆炸力学会议论文集, 2008.
[29]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.
[30] Ma T B, Wang C, Ning J G. Multi-material Eulerian Formulations and Hydrocode for theSimulation of Explosions. CMES-Computer Modeling in Engineering & Sciences, 2008,33(2):155–178.
[31]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.高压物理学报,2008, 22(1):72–78.
[32]冯其京,郝鹏程,杭义洪,等.聚能装药的欧拉数值模拟.爆炸与冲击, 2008, 28:138–143.
[33]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.
[34] Wang G, Zhang D L, Liu K X. An improved CE/SE scheme and its application to detonationpropagation. Chinese Physics Letters, 2007, 24(12):3563–3566.
[35] Wang J, Liu K, Zhang D. An improved CE/SE scheme for multi-material elastic-plasticflows and its applications. Computers & Fluids, 2009, 38(3):544–551.
[36]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.
[37] AlmeML, Rhoades C E. A Computational Study Of Projectile Melt in ImpactWith TypicalWhipple Shields. International Journal of Impact Engineering, 1995, 17:1–12.
[38] Souli M, Ouahsine A, Lewin L. ALE formulation for fluid-structure interaction problems.Computer Methods in Applied Mechanics and Engineering, 2000, 190:659–675.
[39] Harlow F H. The particle-in-cell computing method for fluid dynamics. Methods in ComputationalPhysics, 1964, 3:319–345.
[40] 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.
[41] 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.
[42] Lucy L. A numerical approach to the testing of the fission hypothesis. Astrophysical journal,1977, 82:1013.
[43] Gingold R A, Monaghan J J. Smoothed particle hydrodynamics: theory and application tonon-spherical stars. Monthly notices of the Royal Astronomical Society, 1977, 181:375–389.
[44] Monaghan J J. Smoothed particle hydrodynamics. Annual review of astronomy and astrophysics,1992, 30:543–574.
[45] Belytschko T, Lu Y Y, Gu L. Element free Galerkin methods. International Journal forNumerical Methods in Engineering, 1994, 37:229–256.
[46] Belytschko T, Krongauz Y, Organ D, et al. Meshless methods: An overview and recentdevelopments. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4):3–47.
[47] Li S, Liu W K. Meshfree and particle methods and their applications. Applied MechanicsReviws, 2002, 55(1):1–34.
[48]张雄,刘岩,马上.无网格法的理论与应用.力学进展, 2009, 39:1–36.
[49]张雄,刘岩.无网格法.北京:清华大学出版社/Springer, 2004.
[50] Atluri S N. The Meshless Method (MLPG) for Domain & BIE Discretizations. Tech.Science Press, 2004.
[51] Li S, Liu W K. Meshfree Particle Methods. Springer, 2004.
[52] Liu G R, Liu M B. Smoothed Particle Hydrodynamics: a meshfree particle method. WorldScientific, 2003.
[53]李长生,熊尚武, Rodrigues J,等.金属塑性加工过程无网格数值模拟方法.沈阳:东北大学出版社, 2004.
[54]刘更,刘天祥,谢琴.无网格法及其应用.西安:西北工业大学出版社, 2005.
[55] Idelsohn S R, Onate E. To mesh or not to mesh. That is the question... Computer Methodsin Applied Mechanics and Engineering, 2006, 195(37-40):4681–4696.
[56] Idelsohn S R, Onate E, Del Pin F. The particle finite element method: a powerful tool tosolve incompressible flows with free-surfaces and breaking waves. International Journal forNumerical Methods in Engineering, 2004, 61(7):964–989.
[57] Brackbill J U. Particle methods. International Journal for Numerical Methods in Fluids,2005, 47(8-9):693–705.
[58] Randles P W, Libersky L D. Smoothed particle hydrodynamics: Some recent improvementsand applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4):375–408.
[59] 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 ComputationalPhysics, 1993, 109:67–75.
[60] Stellingwerf R, Wingate C. Impact modeling with smooth particle hydrodynamics. Interna-tional Journal of Impact Engineering, 1993, 14:707–718.
[61] Benz W, Asphaug E. Simulations of Brittle Solids Using Smooth Particle Hydrodynamics.Computer Physics Communications, 1995, 87(1-2):253–265.
[62] 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.
[63] Johnson G R, Stryk R A, Beissel S R. SPH for high velocity impact computations. ComputerMethods in Applied Mechanics and Engineering, 1996, 139(1-4):347–373.
[64] Johnson G R, Beissel S R, Stryk R A. A Generalized Particle Algorithm for high velocityimpact computations. Computational Mechanics, 2000, 25(2-3):245–256.
[65] Johnson G R, Beissel S R, Stryk R A. An improved generalized particle algorithm thatincludes boundaries and interfaces. International Journal for Numerical Methods in Engi-neering, 2002, 53(4):875–904.
[66] Johnson G R, Stryk R A. Conversion of 3D distorted elements into meshless particles duringdynamic deformation. International Journal of Impact Engineering, 2003, 28(9):947–966.
[67] Beissel S R, Gerlach C A, Johnson G R. Hypervelocity impact computations with finiteelements and meshfree particles. International Journal of Impact Engineering, 2006, 33(1-12):80–90.
[68] Rabczuk T, Eibl J. Modelling dynamic failure of concrete with meshfree methods. Interna-tional Journal of Impact Engineering, 2006, 32(11):1878–1897.
[69] Riedel W, Nahme H, White D M, et al. Hypervelocity impact damage prediction in compos-ites: Part II - experimental investigations and simulations. International Journal of ImpactEngineering, 2006, 33(1-12):670–680.
[70] Michel Y, Chevalier J M, Durin C, et al. Hypervelocity impacts on thin brittle targets:Experimental data and SPH simulations. International Journal of Impact Engineering, 2006,33(1-12):441–451.
[71] Swegle J W, Attaway S W. On the feasibility of using smoothed particle Hydrodynamics forunderwater explosion calculations. Computational Mechanics, 1995, 17(3):151–168.
[72] Liu M B, Liu G R, Zong Z, et al. Computer simulation of high explosive explosion usingsmoothed particle hydrodynamics methodology. Computers & Fluids, 2003, 32(3):305–322.
[73] Liu M B, Liu G R, Lam K Y, et al. Meshfree particle simulation of the detonation processfor high explosives in shaped charge unlined cavity configurations. Shock Waves, 2003,12(6):509–520.
[74] Wingate C A, Stellingwerf R F. Smooth Particle Hydrodynamics - The SPHINX and SPHCCodes. Technical Report LA-UR-93-1938, Los Alamos National Laboratory, 1993.
[75] Mandell D A, Wingate C A. Prediction of material strength and fracture of glass using theSPHINX smooth particle hydrodynamics code. Technical Report LA-12830, Los AlamosNational Laboratory, 1994.
[76] Hayashida K, Hill S. Comparisons of hydrocode simulation results using CTH and SPHINX.Proceedings of AIAA Space Programs and Technologies Conference, Huntsville, 1995.
[77] Wilson L T, Hertel E, Schwalbe L, et al. Benchmarking the SPHINX and CTH shock physicscodes for three problems in ballistics. Technical Report sand-98-0414c, Sandia NationalLaboratory, 1998.
[78] Fahrenthold E P, Horban B A. An improved hybrid particle-element method for hyperve-locity impact simulation. International Journal of Impact Engineering, 2001, 26(1-10):169–178.
[79] Park Y K, Fahrenthold E P. A kernel free particle-finite element method for hyperveloc-ity impact simulation. International Journal for Numerical Methods in Engineering, 2005,63(5):737–759.
[80] Han Z D, Liu H T, Rajendran A M, et al. The application of Meshless Local Petrov-Galerkin(MLPG) Approaches in High Speed Impact, Penetration and Perforation Problems. CMES:Computer Modeling in Engineering & Science, 2006, 14:119–128.
[81] Brackbill J U, Ruppel H M. FLIP: a method for adaptively zoned, particle-in-cell calcula-tions in two dimensions. Journal of Computational Physics, 1986, 65:314–343.
[82] Brackbill J U, Kothe D B, Ruppel H M. FLIP: a low-dissipation, particle-in-cell method for?uid ?ow. Computer Physics Communications, 1988, 48:25–38.
[83] Sulsky D, Schreyer H L. Axisymmetric form of the material point method with applicationsto upsetting and Taylor impact problems. Computer Methods in Applied Mechanics andEngineering, 1996, 139(1-4):409–429.
[84] Bardenhagen S G, Kober E M. The generalized interpolation material point method. Cmes-Computer Modeling in Engineering & Sciences, 2004, 5(6):477–495.
[85] York A R, Sulsky D, Schreyer H L. The material point method for simulation of thin mem-branes. International Journal for Numerical Methods in Engineering, 1999, 44(10):1429–1456.
[86] Bardenhagen S G, Brackbill J U, Sulsky D. The material-point method for granular materi-als. Computer Methods in Applied Mechanics and Engineering, 2000, 187(3-4):529–541.
[87] Bardenhagen S G, Guilkey J E, Roessig K M, et al. An improved contact algorithm forthe material point method and application to stress propagation in granular material. Cmes-Computer Modeling in Engineering & Sciences, 2001, 2(4):509–522.
[88] Hu W, Chen Z. A multi-mesh MPM for simulating the meshing process of spur gears.Computers & Structures, 2003, 81(20):1991–2002.
[89] Nairn J A. Material point method calculations with explicit cracks. Cmes-Computer Mod-eling in Engineering & Sciences, 2003, 4(6):649–663.
[90] Pan X F, Xu A G, Zhang G C, et al. Three-dimensional multi-mesh material point methodfor solving collision problems. Communications in Theoretical Physics, 2008, 49(5):1129–1138.
[91] Tan H L, Nairn J A. Hierarchical, adaptive, material point method for dynamic energyrelease rate calculations. Computer Methods in Applied Mechanics and Engineering, 2002,191(19-20):2095–2109.
[92] Love E, Sulsky D L. An energy-consistent material-point method for dynamic finite de-formation plasticity. International Journal for Numerical Methods in Engineering, 2006,65(10):1608–1638.
[93] Love E, Sulsky D L. An unconditionally stable, energy-momentum consistent implementa-tion of the material-point method. Computer Methods in Applied Mechanics and Engineer-ing, 2006, 195(33-36):3903–3925.
[94] Sulsky D, Kaul A. Implicit dynamics in the material-point method. Computer Methods inApplied Mechanics and Engineering, 2004, 193(12-14):1137–1170.
[95] Zhang X, Sze K Y, Ma S. An explicit material point finite element method for hyper-velocityimpact. International Journal for Numerical Methods in Engineering, 2006, 66(4):689–706.
[96] Cummins S J, Brackbill J U. An implicit particle-in-cell method for granular materials.Journal of Computational Physics, 2002, 180(2):506–548.
[97] Guilkey J E, Weiss J A. Implicit time integration for the material point method: Quantita-tive and algorithmic comparisons with the finite element method. International Journal forNumerical Methods in Engineering, 2003, 57(9):1323–1338.
[98] York A R, Sulsky D, Schreyer H L. Fluid-membrane interaction based on the material pointmethod. International Journal for Numerical Methods in Engineering, 2000, 48(6):901–924.
[99] Guo Y, Nairn J A. Calculation of J-integral and stress intensity factors using The MaterialPoint Method. Cmes-Computer Modeling in Engineering & Sciences, 2004, 6(3):295–308.
[100] Nairn J A. On the calculation of energy release rates for cracked laminates with residualstresses. International Journal of Fracture, 2006, 139(2):267–293.
[101] Wang B, Karuppiah V, Lu H, et al. Two-dimensional mixed mode crack simulation using thematerial point method. Mechanics of Advanced Materials and Structures, 2005, 12(6):471–484.
[102] Daphalapurkar N P, Lu H, Coker D, et al. Simulation of dynamic crack growth using thegeneralized interpolation material point (GIMP) method. International Journal of Fracture,2007, 143(1):79–102.
[103] Chen Z, Hu W, Shen L, et al. An evaluation of the MPM for simulating dynamic failurewith damage diffusion. Engineering Fracture Mechanics, 2002, 69(17):1873–1890.
[104] Chen Z, Feng R, Xin X, et al. A computational model for impact failure with shear-induceddilatancy. International Journal for Numerical Methods in Engineering, 2003, 56(14):1979–1997.
[105] Chen Z, Shen L, Mai Y W, et al. A bifurcation-based decohesion model for simulatingthe transition from localization to decohesion with the MPM. Zeitschrift Fur AngewandteMathematik Und Physik, 2005, 56(5):908–930.
[106] Shen L M, Chen Z. A multi-scale simulation of tungsten film delamination from siliconsubstrate. International Journal of Solids and Structures, 2005, 42(18-19):5036–5056.
[107] Shen L M, Chen Z. A silent boundary scheme with the material point method for dynamicanalyses. Cmes-Computer Modeling in Engineering & Sciences, 2005, 7(3):305–320.
[108] Schreyer H L, Sulsky D L, Zhou S J. Modeling delamination as a strong discontinuitywith the material point method. Computer Methods in Applied Mechanics and Engineering,2002, 191(23-24):2483–2507.
[109] Sulsky D, Schreyer L. MPM simulation of dynamic material failure with a decohesionconstitutive model. European Journal of Mechanics a-Solids, 2004, 23(3):423–445.
[110] Bardenhagen S G, Brydon A D, Guilkey J E. Insight into the physics of foam densificationvia numerical simulation. Journal of the Mechanics and Physics of Solids, 2005, 53(3):597–617.
[111] Brydon A D, Bardenhagen S G, Miller E A, et al. Simulation of the densification of realopen-celled foam microstructures. Journal of the Mechanics and Physics of Solids, 2005,53(12):2638–2660.
[112] Wieckowski Z, Youn S K, Yeon J H. A particle-in-cell solution to the silo dischargingproblem. International Journal for Numerical Methods in Engineering, 1999, 45(9):1203–1225.
[113] Wieckowski Z. The material point method in large strain engineering problems. ComputerMethods in Applied Mechanics and Engineering, 2004, 193(39-41):4417–4438.
[114] Bardenhagen S G, Brackbill J U, Sulsky D. Numerical study of stress distribution in shearedgranular material in two dimensions. Physical Review E, 2000, 62(3):3882–3890.
[115] Coetzee C J, Basson A H, Vermeer P A. Discrete and continuum modelling of excavatorbucket filling. Journal of Terramechanics, 2007, 44(2):177–186.
[116] Ayton G, Bardenhagen S G, McMurtry P, et al. Interfacing continuum and molecular dy-namics: An application to lipid bilayers. Journal of Chemical Physics, 2001, 114(15):6913–6924.
[117] Ayton G, Smondyrev A M, Bardenhagen S G, et al. Interfacing molecular dynamics andmacro-scale simulations for lipid bilayer vesicles. Biophysical Journal, 2002, 83(2):1026–1038.
[118] Guilkey J E, Hoying J B, Weiss J A. Computational modeling of multicellular constructswith the material point method. Journal of Biomechanics, 2006, 39(11):2074–2086.
[119] Ionescu I, Guilkey J E, Berzins M, et al. Simulation of soft tissue failure using the mate-rial point method. Journal of Biomechanical Engineering-Transactions of the Asme, 2006,128(6):917–924.
[120] Lee W H, Painter J W. Material void-opening computation using particle method. Interna-tional Journal of Impact Engineering, 1999, 22:1–22.
[121] Hu W Q, Chen Z. Model-based simulation of the synergistic effects of blast and fragmenta-tion on a concrete wall using the MPM. International Journal of Impact Engineering, 2006,32(12):2066–2096.
[122] Hu W. A Model-Based Simulation Tool for Impact/Blast-Resistent Structure Design[D].University of Missouri-Columbia, 2004.
[123] Guilkey J E, Harman T B, Banerjee B. An Eulerian-Lagrangian approach for simulatingexplosions of energetic devices. Computers & Structures, 2007, 85(11-14):660–674.
[124] Parker S G, Guilkey J, Harman T. A component-based parallel infrastructure for the simu-lation of ?uid-structure interaction. Engineering with Computers, 2006, 22(3-4):277–292.
[125] Huang P, Zhang X, Ma S, et al. Shared Memory OpenMP Parallelization of Explicit MPMand Its Application to Hypervelocity Impact. CMES: Computer Modeling in Engineering& Science, 2008, 38(2):119–147.
[126] Zhang H W, Wang K P, Chen Z. Material point method for dynamic analysis of saturatedporous media under external contact/impact of solid bodies. Computer Methods in AppliedMechanics and Engineering, 2009, 198(17-20):1456–1472.
[127] Shen Y L, Li W, Sulsky D L, et al. Localization of plastic deformation along grainboundaries in a hardening material. International Journal of Mechanical Sciences, 2000,42(11):2167–2189.
[128] Borodin O, Bedrov D, Smith G D, et al. Multiscale modeling of viscoelastic propertiesof polymer nanocomposites. Journal of Polymer Science Part B-Polymer Physics, 2005,43(8):1005–1013.
[129] Xue L P, Borodin O, Smith G D. Modeling of enhanced penetrant diffusion in nanoparticlepolymercomposite membranes. Journal of Membrane Science, 2006, 286(1-2):293–300.
[130] Xue L P, Borodin O, Smith G D, et al. Micromechanics simulations of the viscoelasticproperties of highly filled composites by the material point method (MPM). Modelling andSimulation in Materials Science and Engineering, 2006, 14(4):703–720.
[131] Zhou S J, Stormont J, Chen Z. Simulation of geomembrane response to settlement in landfillsby using the material point method. International Journal for Numerical and AnalyticalMethods in Geomechanics, 1999, 23(15):1977–1994.
[132] 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.
[133]王宇新,顾元宪,孙明.无网格MPM法在冲击载荷问题中的应用.工程力学, 2006,23(5):46–51.
[134]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.
[135]王宇新,陈震,孙明.滑移爆轰问题无网格MPM法模拟.力学与实践, 2006, 29(3):20–25.
[136]郑勇刚,顾元宪,陈震.薄膜破坏过程数值模拟的MPM方法.力学学报, 2006,38(3):347–355.
[137]马上,张雄,邱信明.超高速碰撞问题的三维物质点法.爆炸与冲击, 2006, 26(3):273–278.
[138]王津龙,刘天云,张楚汉.堆石体柱状试件成型过程的材料点法仿真.清华大学学报（自然科学版）, 2005, 45(12):1604–1607.
[139] Belytschko T, Liu W K, Moran B. Nonlinear Finite Elements for Continua and Structures.John Wiley & Sons, 2000.
[140] Anderson C E Jr. An overview of the theory of hydrocodes. International Journal of ImpactEngineering, 1987, 5:33–59.
[141] Bardenhagen S G. Energy conservation error in the material point method for solid mechanics.Journal of Computational Physics, 2002, 180(1):383–403.
[142] Wallstedt P C, Guilkey J E. Improved velocity projection for the material point method.Cmes-Computer Modeling in Engineering & Sciences, 2007, 19(3):223–232.
[143] Meyers M A. Dynamic Behavior of Materials. John Wiley & Sons, 1994.
[144] Meyers M A原著,张庆明,刘彦,黄风雷,等译.材料的动力学行为.北京:国防工业出版社, 2006.
[145]李翼祺,马素贞.爆炸力学.北京:科学出版社, 1992.
[146] Zukas J A, Walters W P, (eds.). Explosive effects and applications. Springer, 1998.
[147]孙锦山,朱建士.理论爆轰物理.北京:国防工业出版社, 1995.
[148]陈朗,龙新平,冯长根,等.含铝炸药爆轰.北京:国防工业出版社, 2004.
[149]张国伟,韩勇,苟瑞君,编.爆炸作用原理.北京:国防工业出版社, 2006.
[150]汤文辉,张若棋.物态方程理论及计算概论.长沙:国防科技大学出版社, 1999.
[151]王仁,黄文彬,黄筑平.塑性力学引论.北京:北京大学出版社, 1992.
[152] Johnson G R, Holmquist T J. Evaluation of cylinder-impact test data for constitutive modelconstants. Journal of Applied Physics, 1988, 64(8):3901–3910.
[153] Zerilli F J, Armstrong R W. Dislocation-mechanics-based consitutive relations for materialdynamics calculations. Journal of Applied Physics, 1987, 61(5):1816–1825.
[154]彭建祥. Johnson-Cook本构模型和Steinberg本构模型的比较研究[博士学位论文].北京:中国工程物理研究院, 2006.
[155] Steinberg D J, Cochran S G, Guinan M W. A Consitutive model for metals applicable athigh-strain rate. Journal of Applied Physics, 1980, 51(3):1498–1504.
[156] Johnson G R, Cook W H. Fracture characteristics of three metals subjected to variousstrains, strain rates, temperatures and pressures. Engineering fracture mechanics, 1985,21(1):31–48.
[157]王永刚,贺红亮,陈登平,等.延性金属层裂模型比较.爆炸与冲击, 2005, 25(5):467–471.
[158] Liu M B, Liu G R, Lam K Y. Investigation into water mitigations using a meshless particlemethod. Shock Waves, 2002, 12(3):181–195.
[159] Fiserova D. Numerical Analyses of Buried Mine Explosions with Emphasis on Effect ofSoil Properties on Loading[D]. Cranfield University, 2006.
[160] Mader C L. Numerical Modeling of Explosives and Propellants. CRC Press, 1998.
[161] Mason J J, Rosakis A J, Ravichandran G. On the Strain and Strain-Rate Dependence ofthe Fraction of Plastic Work Converted to Heat - an Experimental-Study Using High-SpeedInfrared Detectors and the Kolsky Bar. Mechanics of Materials, 1994, 17(2-3):135–145.
[162] Grandy J. Effecient Computation of Volume of Hexahedral Cells. Technical report,Lawrence Livermore National Laboratory, 1997.
[163] Shin Y S, Chisum J E. Modeling and simulation of underwater shock problems using coupledlagrangian-eulerian analysis approach. Shock and Vibration, 1997, 4(1):1–10.
[164] Sedov L I. Similarity and Dimensional Methods in Mechanics. 10th ed., CRC Press, 1993.
[165] http://flash.uchicago.edu/?ahaque/sedov.html.
[166] Flangan D P, Belytschko T. A uniform strain hexahedron and quadrilaterial with orthogonalhourglass control. International Journal for Numerical Methods in Engineering, 1981,17:679–706.
[167] Anderson C E, Timothy J, Trucano G, et al. Debris cloud dynamics. International Journalof Impact Engineering, 1990, 9(1):89–113.
[168] Moresi L, Dufour F, Muhlhaus H B. A Lagrangian integration point finite element methodfor large deformation modeling of viscoelastic geomaterials. Journal of ComputationalPhysics, 2003, 184(2):476–497.
[169] Knight D D. Elements of Numerical Methods for Compressible Flows. Cambridge UniversityPress, 2006: P.33–36.
[170] Sod G A. A survey of several finite difference methods for systems of nonlinear hyperbolicconservation laws. Journal of Computational Physics, 1978, 27:1–31.
[171] Lee W H. Computer Simulation of Shaped Charge Problems. World Scientific, 2006.
[172] Molinari J F. Finite element simulation of shaped charges. Finite Elements in Analysis andDesign, 2002, 38(10):921–936.
[173] Monaghan J J. Smoothed particle hydrodynamics. Reports on Progress in Physics, 2005,68(8):1703–1759.
[174] Faraud M, Destefanis R, Palmieri D, et al. SPH simulations of debris impacts using twodifferent computer codes. International Journal of Impact Engineering, 1999, 23(1):249–260.
[175] Groenenboom P H L. Numerical simulation of 2D and 3D hypervelocity impact usingthe SPH option in PAM-SHOCK(TM). International Journal of Impact Engineering, 1997,20(1-5):309–323.
[176]马上.超高速碰撞问题的三维物质点法模拟[硕士学位论文].清华大学, 2005.
[177] Libersky L D, Petschek A G. Smooth particle hydrodynamics with strength of materials.Advances in the Free-Lagrange Method, Lecture Notes in Physics, 1990, 395:248–257.
[178] Hernquist L, Katz N. Treesph: a unification of SPH with the hierarchical tree method. TheAstrophysical Journal Supplement Series, 1989, 70:419–446.
[179] Waltz J, Page G L, Milder S D, et al. Aperformance comparison of tree data structuresforN-body simulation. Journal of Computational Physics, 2002, 178:1–14.
[180] Capuzzo-Dolcetta R, Miocchi P. A comparison between the fast multipole algorithm and thetree-code to evaluate gravitational forces in 3-D. Journal of Computational Physics, 1998,143:29–48.
[181] Munjiza A, Andrews K R F. NBS contact detection algorithm for bodies of similar size.International Journal for Numerical Methods in Engineering, 1998, 43:131–149.
[182] Batra R C, Zhang G M. Search algorithm, and simulation of elastodynamic crack propagationby modified smoothed particle hydrodynamics (MSPH) method. ComputationalMechanics, 2007, 40:531–546.
[183] Balsara D S. Von-Neumann Stability Analysis of Smoothed Particle Hydrodynamics - Suggestionsfor Optimal-Algorithms. Journal of Computational Physics, 1995, 121(2):357–372.
[184] Beissel S, Belytschko T. Nodal integration of the element-free Galerkin method. ComputerMethods in Applied Mechanics and Engineering, 1996, 139:49–74.
[185] Morris J P. Analysis of smoothed particle hydrodynamics with applications[D]. MonashUniversity, 1996.
[186] Chen J K, Beraun J E, Jih C J. An improvement for tensile instability in smoothed particlehydrodynamics. Computational Mechanics, 1999, 23:279–287.
[187] Monaghan J J. SPH without a tensile instability. Journal of Computational Physics, 2000,159:290–311.
[188] Dyka C T, Randles PW, Ingel R P. Stress points for tension instability in SPH. InternationalJournal for Numerical Methods in Engineering, 1997, 40(13):2325–2341.
[189] Randles P W, Libersky L D. Normalized SPH with stress points. International Journal forNumerical Methods in Engineering, 2000, 47:1445–1462.
[190] Campbell P M. Some new algorityms for boundary value problems in smoothed particledynamics. DNA Report, 1989, DNA-TR-88-286.
[191] Monaghan J J. Simulating free surface flow with SPH. Journal of Computational Physics,1994, 110:399.
[192] 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.
[193] Oberkampf W L, Trucano T G, Hirsch C. Verification, validation, and predictive capabilityin computational engineering and physics. Applied Mechanics Reviews, 2004, 57(5):345–384.
[194]邓小刚,宗文刚,张来平,等.计算流体力学中的验证与确认.力学进展, 2007,37(2):279–288.109
[2]恽寿榕,赵衡阳.爆炸力学.北京:国防工业出版社, 2005.
[3]王礼立.应力波基础.北京:国防工业出版社, 2005.
[4] Quinn M J. Parallel programming in C with MPI and OpenMP.北京:清华大学出版社,2005.
[5] http://www.top500.org/.
[6] Computational Science: Ensuring America’s Competitiveness. Technical report, President’sInformation Technology Advisory Committee, 2005.
[7]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.
[8] Johnson N L. The Legacy and Future of CFD At Los Alamos. Technical Report LA-UR-96-1426, Los Alamos National Laboratory, 1996.
[9] Zukas J A. Introduction to Hydrocodes. Elsevier Science, 2004.
[10]张雄,王天舒.计算动力学.北京:清华大学出版社, 2007.
[11]洪友士.郑哲敏对应用力学和技术科学的贡献.力学进展, 2005, 35(1):1–4.
[12] Anderson J D. Computational Fluid Dynamics, the Basics with Applications.北京:清华大学出版社, 2002.
[13] McGlaun J M, Thompson S L, Elrick M G. CTH: A three-dimensional shock wave physicscode. International Journal of Impact Engineering, 1990, 10:351–360.
[14] Scheffler D R. Modeling non-eroding perforation of an oblique aluminum target using theEulerian CTH hydrocode. International Journal of Impact Engineering, 2005, 32:461–472.
[15] Huerta M, Vigil M G. Design, analyses, and field test of a 0.7 m conical shaped charge.International Journal of Impact Engineering, 2006, 32(8):1201–1213.
[16] Berger M, Oliger J. Adaptive Mesh Refinement For Hyperbolic Partial-Differential Equations.Journal of Computational Physics, 1984, 53(3):484–512.
[17] Berger M, Colella P. Local Adaptive Mesh Refinement for Shock Hydrodynamics. Journalof Computational Physics, 1989, 82(1):64–84.
[18] MacNeice P, Olson K M, Mobarry C, et al. PARAMESH: A parallel adaptive mesh refinementcommunity toolkit. Computer Physics Communications, 2000, 126:330–354.
[19] Luketa-Hanlin A, Attaway S. Massively parallel computations of damage to a thin-walledstructure from blast. Proceedings of ASME International Mechanical Engineering Congressand Exposition, Seattle, WA: Amer Soc Mechanical Engineers, 2007. 887–891.
[20] http://www.sandia.gov/media/NewsRel/NR2001/cth.htm.
[21] Wilkins M L. Computer Simulation of Dynamic Phenomena. Spinger, 1999.
[22] Wingate C A, Stellingwerf R F, RF D, et al. Models of High Velocity Impact Phenomena.International Journal of Impact Engineering, 1993, 14:819–830.
[23] Meyer H W Jr. A Modified Zerilli-Armstrong Constitutive Model Describing the Strengthand Localizing Behavior of Ti-6Al-4V. Technical Report ARL-CR-0578, Army ResearchLaboratory, 2006.
[24] Attaway S W, Brown M J, Heinstein M W, et al. PRONTO3D User’s Instructions: A TransientDynamic Code for Nonlinear Structural Analysis. Sandia National Laboratory, 1998.
[25] Bessette G C, Bixler N E, Hewson J C, et al. Methodology Assessment and Recommendationsfor the Mars Science Laboratory Launch Safety Analysis. Technical ReportSAND2006-4563, Sandia National Laboratories, 2006.
[26] Hallquist J O. LS-DYNA Theoretical Manual. Livermore Software Technology Corporation,1998.
[27] Zukas J A, (eds.). High Velocity Impact Dynamics. John Wiley & Sons, 1990.
[28]宁建国,刘凯欣,何长江,等.,编.第四届全国计算爆炸力学会议论文集, 2008.
[29]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.
[30] Ma T B, Wang C, Ning J G. Multi-material Eulerian Formulations and Hydrocode for theSimulation of Explosions. CMES-Computer Modeling in Engineering & Sciences, 2008,33(2):155–178.
[31]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.高压物理学报,2008, 22(1):72–78.
[32]冯其京,郝鹏程,杭义洪,等.聚能装药的欧拉数值模拟.爆炸与冲击, 2008, 28:138–143.
[33]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.
[34] Wang G, Zhang D L, Liu K X. An improved CE/SE scheme and its application to detonationpropagation. Chinese Physics Letters, 2007, 24(12):3563–3566.
[35] Wang J, Liu K, Zhang D. An improved CE/SE scheme for multi-material elastic-plasticflows and its applications. Computers & Fluids, 2009, 38(3):544–551.
[36]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.
[37] AlmeML, Rhoades C E. A Computational Study Of Projectile Melt in ImpactWith TypicalWhipple Shields. International Journal of Impact Engineering, 1995, 17:1–12.
[38] Souli M, Ouahsine A, Lewin L. ALE formulation for fluid-structure interaction problems.Computer Methods in Applied Mechanics and Engineering, 2000, 190:659–675.
[39] Harlow F H. The particle-in-cell computing method for fluid dynamics. Methods in ComputationalPhysics, 1964, 3:319–345.
[40] 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.
[41] 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.
[42] Lucy L. A numerical approach to the testing of the fission hypothesis. Astrophysical journal,1977, 82:1013.
[43] Gingold R A, Monaghan J J. Smoothed particle hydrodynamics: theory and application tonon-spherical stars. Monthly notices of the Royal Astronomical Society, 1977, 181:375–389.
[44] Monaghan J J. Smoothed particle hydrodynamics. Annual review of astronomy and astrophysics,1992, 30:543–574.
[45] Belytschko T, Lu Y Y, Gu L. Element free Galerkin methods. International Journal forNumerical Methods in Engineering, 1994, 37:229–256.
[46] Belytschko T, Krongauz Y, Organ D, et al. Meshless methods: An overview and recentdevelopments. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4):3–47.
[47] Li S, Liu W K. Meshfree and particle methods and their applications. Applied MechanicsReviws, 2002, 55(1):1–34.
[48]张雄,刘岩,马上.无网格法的理论与应用.力学进展, 2009, 39:1–36.
[49]张雄,刘岩.无网格法.北京:清华大学出版社/Springer, 2004.
[50] Atluri S N. The Meshless Method (MLPG) for Domain & BIE Discretizations. Tech.Science Press, 2004.
[51] Li S, Liu W K. Meshfree Particle Methods. Springer, 2004.
[52] Liu G R, Liu M B. Smoothed Particle Hydrodynamics: a meshfree particle method. WorldScientific, 2003.
[53]李长生,熊尚武, Rodrigues J,等.金属塑性加工过程无网格数值模拟方法.沈阳:东北大学出版社, 2004.
[54]刘更,刘天祥,谢琴.无网格法及其应用.西安:西北工业大学出版社, 2005.
[55] Idelsohn S R, Onate E. To mesh or not to mesh. That is the question... Computer Methodsin Applied Mechanics and Engineering, 2006, 195(37-40):4681–4696.
[56] Idelsohn S R, Onate E, Del Pin F. The particle finite element method: a powerful tool tosolve incompressible flows with free-surfaces and breaking waves. International Journal forNumerical Methods in Engineering, 2004, 61(7):964–989.
[57] Brackbill J U. Particle methods. International Journal for Numerical Methods in Fluids,2005, 47(8-9):693–705.
[58] Randles P W, Libersky L D. Smoothed particle hydrodynamics: Some recent improvementsand applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4):375–408.
[59] 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 ComputationalPhysics, 1993, 109:67–75.
[60] Stellingwerf R, Wingate C. Impact modeling with smooth particle hydrodynamics. Interna-tional Journal of Impact Engineering, 1993, 14:707–718.
[61] Benz W, Asphaug E. Simulations of Brittle Solids Using Smooth Particle Hydrodynamics.Computer Physics Communications, 1995, 87(1-2):253–265.
[62] 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.
[63] Johnson G R, Stryk R A, Beissel S R. SPH for high velocity impact computations. ComputerMethods in Applied Mechanics and Engineering, 1996, 139(1-4):347–373.
[64] Johnson G R, Beissel S R, Stryk R A. A Generalized Particle Algorithm for high velocityimpact computations. Computational Mechanics, 2000, 25(2-3):245–256.
[65] Johnson G R, Beissel S R, Stryk R A. An improved generalized particle algorithm thatincludes boundaries and interfaces. International Journal for Numerical Methods in Engi-neering, 2002, 53(4):875–904.
[66] Johnson G R, Stryk R A. Conversion of 3D distorted elements into meshless particles duringdynamic deformation. International Journal of Impact Engineering, 2003, 28(9):947–966.
[67] Beissel S R, Gerlach C A, Johnson G R. Hypervelocity impact computations with finiteelements and meshfree particles. International Journal of Impact Engineering, 2006, 33(1-12):80–90.
[68] Rabczuk T, Eibl J. Modelling dynamic failure of concrete with meshfree methods. Interna-tional Journal of Impact Engineering, 2006, 32(11):1878–1897.
[69] Riedel W, Nahme H, White D M, et al. Hypervelocity impact damage prediction in compos-ites: Part II - experimental investigations and simulations. International Journal of ImpactEngineering, 2006, 33(1-12):670–680.
[70] Michel Y, Chevalier J M, Durin C, et al. Hypervelocity impacts on thin brittle targets:Experimental data and SPH simulations. International Journal of Impact Engineering, 2006,33(1-12):441–451.
[71] Swegle J W, Attaway S W. On the feasibility of using smoothed particle Hydrodynamics forunderwater explosion calculations. Computational Mechanics, 1995, 17(3):151–168.
[72] Liu M B, Liu G R, Zong Z, et al. Computer simulation of high explosive explosion usingsmoothed particle hydrodynamics methodology. Computers & Fluids, 2003, 32(3):305–322.
[73] Liu M B, Liu G R, Lam K Y, et al. Meshfree particle simulation of the detonation processfor high explosives in shaped charge unlined cavity configurations. Shock Waves, 2003,12(6):509–520.
[74] Wingate C A, Stellingwerf R F. Smooth Particle Hydrodynamics - The SPHINX and SPHCCodes. Technical Report LA-UR-93-1938, Los Alamos National Laboratory, 1993.
[75] Mandell D A, Wingate C A. Prediction of material strength and fracture of glass using theSPHINX smooth particle hydrodynamics code. Technical Report LA-12830, Los AlamosNational Laboratory, 1994.
[76] Hayashida K, Hill S. Comparisons of hydrocode simulation results using CTH and SPHINX.Proceedings of AIAA Space Programs and Technologies Conference, Huntsville, 1995.
[77] Wilson L T, Hertel E, Schwalbe L, et al. Benchmarking the SPHINX and CTH shock physicscodes for three problems in ballistics. Technical Report sand-98-0414c, Sandia NationalLaboratory, 1998.
[78] Fahrenthold E P, Horban B A. An improved hybrid particle-element method for hyperve-locity impact simulation. International Journal of Impact Engineering, 2001, 26(1-10):169–178.
[79] Park Y K, Fahrenthold E P. A kernel free particle-finite element method for hyperveloc-ity impact simulation. International Journal for Numerical Methods in Engineering, 2005,63(5):737–759.
[80] Han Z D, Liu H T, Rajendran A M, et al. The application of Meshless Local Petrov-Galerkin(MLPG) Approaches in High Speed Impact, Penetration and Perforation Problems. CMES:Computer Modeling in Engineering & Science, 2006, 14:119–128.
[81] Brackbill J U, Ruppel H M. FLIP: a method for adaptively zoned, particle-in-cell calcula-tions in two dimensions. Journal of Computational Physics, 1986, 65:314–343.
[82] Brackbill J U, Kothe D B, Ruppel H M. FLIP: a low-dissipation, particle-in-cell method for?uid ?ow. Computer Physics Communications, 1988, 48:25–38.
[83] Sulsky D, Schreyer H L. Axisymmetric form of the material point method with applicationsto upsetting and Taylor impact problems. Computer Methods in Applied Mechanics andEngineering, 1996, 139(1-4):409–429.
[84] Bardenhagen S G, Kober E M. The generalized interpolation material point method. Cmes-Computer Modeling in Engineering & Sciences, 2004, 5(6):477–495.
[85] York A R, Sulsky D, Schreyer H L. The material point method for simulation of thin mem-branes. International Journal for Numerical Methods in Engineering, 1999, 44(10):1429–1456.
[86] Bardenhagen S G, Brackbill J U, Sulsky D. The material-point method for granular materi-als. Computer Methods in Applied Mechanics and Engineering, 2000, 187(3-4):529–541.
[87] Bardenhagen S G, Guilkey J E, Roessig K M, et al. An improved contact algorithm forthe material point method and application to stress propagation in granular material. Cmes-Computer Modeling in Engineering & Sciences, 2001, 2(4):509–522.
[88] Hu W, Chen Z. A multi-mesh MPM for simulating the meshing process of spur gears.Computers & Structures, 2003, 81(20):1991–2002.
[89] Nairn J A. Material point method calculations with explicit cracks. Cmes-Computer Mod-eling in Engineering & Sciences, 2003, 4(6):649–663.
[90] Pan X F, Xu A G, Zhang G C, et al. Three-dimensional multi-mesh material point methodfor solving collision problems. Communications in Theoretical Physics, 2008, 49(5):1129–1138.
[91] Tan H L, Nairn J A. Hierarchical, adaptive, material point method for dynamic energyrelease rate calculations. Computer Methods in Applied Mechanics and Engineering, 2002,191(19-20):2095–2109.
[92] Love E, Sulsky D L. An energy-consistent material-point method for dynamic finite de-formation plasticity. International Journal for Numerical Methods in Engineering, 2006,65(10):1608–1638.
[93] Love E, Sulsky D L. An unconditionally stable, energy-momentum consistent implementa-tion of the material-point method. Computer Methods in Applied Mechanics and Engineer-ing, 2006, 195(33-36):3903–3925.
[94] Sulsky D, Kaul A. Implicit dynamics in the material-point method. Computer Methods inApplied Mechanics and Engineering, 2004, 193(12-14):1137–1170.
[95] Zhang X, Sze K Y, Ma S. An explicit material point finite element method for hyper-velocityimpact. International Journal for Numerical Methods in Engineering, 2006, 66(4):689–706.
[96] Cummins S J, Brackbill J U. An implicit particle-in-cell method for granular materials.Journal of Computational Physics, 2002, 180(2):506–548.
[97] Guilkey J E, Weiss J A. Implicit time integration for the material point method: Quantita-tive and algorithmic comparisons with the finite element method. International Journal forNumerical Methods in Engineering, 2003, 57(9):1323–1338.
[98] York A R, Sulsky D, Schreyer H L. Fluid-membrane interaction based on the material pointmethod. International Journal for Numerical Methods in Engineering, 2000, 48(6):901–924.
[99] Guo Y, Nairn J A. Calculation of J-integral and stress intensity factors using The MaterialPoint Method. Cmes-Computer Modeling in Engineering & Sciences, 2004, 6(3):295–308.
[100] Nairn J A. On the calculation of energy release rates for cracked laminates with residualstresses. International Journal of Fracture, 2006, 139(2):267–293.
[101] Wang B, Karuppiah V, Lu H, et al. Two-dimensional mixed mode crack simulation using thematerial point method. Mechanics of Advanced Materials and Structures, 2005, 12(6):471–484.
[102] Daphalapurkar N P, Lu H, Coker D, et al. Simulation of dynamic crack growth using thegeneralized interpolation material point (GIMP) method. International Journal of Fracture,2007, 143(1):79–102.
[103] Chen Z, Hu W, Shen L, et al. An evaluation of the MPM for simulating dynamic failurewith damage diffusion. Engineering Fracture Mechanics, 2002, 69(17):1873–1890.
[104] Chen Z, Feng R, Xin X, et al. A computational model for impact failure with shear-induceddilatancy. International Journal for Numerical Methods in Engineering, 2003, 56(14):1979–1997.
[105] Chen Z, Shen L, Mai Y W, et al. A bifurcation-based decohesion model for simulatingthe transition from localization to decohesion with the MPM. Zeitschrift Fur AngewandteMathematik Und Physik, 2005, 56(5):908–930.
[106] Shen L M, Chen Z. A multi-scale simulation of tungsten film delamination from siliconsubstrate. International Journal of Solids and Structures, 2005, 42(18-19):5036–5056.
[107] Shen L M, Chen Z. A silent boundary scheme with the material point method for dynamicanalyses. Cmes-Computer Modeling in Engineering & Sciences, 2005, 7(3):305–320.
[108] Schreyer H L, Sulsky D L, Zhou S J. Modeling delamination as a strong discontinuitywith the material point method. Computer Methods in Applied Mechanics and Engineering,2002, 191(23-24):2483–2507.
[109] Sulsky D, Schreyer L. MPM simulation of dynamic material failure with a decohesionconstitutive model. European Journal of Mechanics a-Solids, 2004, 23(3):423–445.
[110] Bardenhagen S G, Brydon A D, Guilkey J E. Insight into the physics of foam densificationvia numerical simulation. Journal of the Mechanics and Physics of Solids, 2005, 53(3):597–617.
[111] Brydon A D, Bardenhagen S G, Miller E A, et al. Simulation of the densification of realopen-celled foam microstructures. Journal of the Mechanics and Physics of Solids, 2005,53(12):2638–2660.
[112] Wieckowski Z, Youn S K, Yeon J H. A particle-in-cell solution to the silo dischargingproblem. International Journal for Numerical Methods in Engineering, 1999, 45(9):1203–1225.
[113] Wieckowski Z. The material point method in large strain engineering problems. ComputerMethods in Applied Mechanics and Engineering, 2004, 193(39-41):4417–4438.
[114] Bardenhagen S G, Brackbill J U, Sulsky D. Numerical study of stress distribution in shearedgranular material in two dimensions. Physical Review E, 2000, 62(3):3882–3890.
[115] Coetzee C J, Basson A H, Vermeer P A. Discrete and continuum modelling of excavatorbucket filling. Journal of Terramechanics, 2007, 44(2):177–186.
[116] Ayton G, Bardenhagen S G, McMurtry P, et al. Interfacing continuum and molecular dy-namics: An application to lipid bilayers. Journal of Chemical Physics, 2001, 114(15):6913–6924.
[117] Ayton G, Smondyrev A M, Bardenhagen S G, et al. Interfacing molecular dynamics andmacro-scale simulations for lipid bilayer vesicles. Biophysical Journal, 2002, 83(2):1026–1038.
[118] Guilkey J E, Hoying J B, Weiss J A. Computational modeling of multicellular constructswith the material point method. Journal of Biomechanics, 2006, 39(11):2074–2086.
[119] Ionescu I, Guilkey J E, Berzins M, et al. Simulation of soft tissue failure using the mate-rial point method. Journal of Biomechanical Engineering-Transactions of the Asme, 2006,128(6):917–924.
[120] Lee W H, Painter J W. Material void-opening computation using particle method. Interna-tional Journal of Impact Engineering, 1999, 22:1–22.
[121] Hu W Q, Chen Z. Model-based simulation of the synergistic effects of blast and fragmenta-tion on a concrete wall using the MPM. International Journal of Impact Engineering, 2006,32(12):2066–2096.
[122] Hu W. A Model-Based Simulation Tool for Impact/Blast-Resistent Structure Design[D].University of Missouri-Columbia, 2004.
[123] Guilkey J E, Harman T B, Banerjee B. An Eulerian-Lagrangian approach for simulatingexplosions of energetic devices. Computers & Structures, 2007, 85(11-14):660–674.
[124] Parker S G, Guilkey J, Harman T. A component-based parallel infrastructure for the simu-lation of ?uid-structure interaction. Engineering with Computers, 2006, 22(3-4):277–292.
[125] Huang P, Zhang X, Ma S, et al. Shared Memory OpenMP Parallelization of Explicit MPMand Its Application to Hypervelocity Impact. CMES: Computer Modeling in Engineering& Science, 2008, 38(2):119–147.
[126] Zhang H W, Wang K P, Chen Z. Material point method for dynamic analysis of saturatedporous media under external contact/impact of solid bodies. Computer Methods in AppliedMechanics and Engineering, 2009, 198(17-20):1456–1472.
[127] Shen Y L, Li W, Sulsky D L, et al. Localization of plastic deformation along grainboundaries in a hardening material. International Journal of Mechanical Sciences, 2000,42(11):2167–2189.
[128] Borodin O, Bedrov D, Smith G D, et al. Multiscale modeling of viscoelastic propertiesof polymer nanocomposites. Journal of Polymer Science Part B-Polymer Physics, 2005,43(8):1005–1013.
[129] Xue L P, Borodin O, Smith G D. Modeling of enhanced penetrant diffusion in nanoparticlepolymercomposite membranes. Journal of Membrane Science, 2006, 286(1-2):293–300.
[130] Xue L P, Borodin O, Smith G D, et al. Micromechanics simulations of the viscoelasticproperties of highly filled composites by the material point method (MPM). Modelling andSimulation in Materials Science and Engineering, 2006, 14(4):703–720.
[131] Zhou S J, Stormont J, Chen Z. Simulation of geomembrane response to settlement in landfillsby using the material point method. International Journal for Numerical and AnalyticalMethods in Geomechanics, 1999, 23(15):1977–1994.
[132] 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.
[133]王宇新,顾元宪,孙明.无网格MPM法在冲击载荷问题中的应用.工程力学, 2006,23(5):46–51.
[134]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.
[135]王宇新,陈震,孙明.滑移爆轰问题无网格MPM法模拟.力学与实践, 2006, 29(3):20–25.
[136]郑勇刚,顾元宪,陈震.薄膜破坏过程数值模拟的MPM方法.力学学报, 2006,38(3):347–355.
[137]马上,张雄,邱信明.超高速碰撞问题的三维物质点法.爆炸与冲击, 2006, 26(3):273–278.
[138]王津龙,刘天云,张楚汉.堆石体柱状试件成型过程的材料点法仿真.清华大学学报（自然科学版）, 2005, 45(12):1604–1607.
[139] Belytschko T, Liu W K, Moran B. Nonlinear Finite Elements for Continua and Structures.John Wiley & Sons, 2000.
[140] Anderson C E Jr. An overview of the theory of hydrocodes. International Journal of ImpactEngineering, 1987, 5:33–59.
[141] Bardenhagen S G. Energy conservation error in the material point method for solid mechanics.Journal of Computational Physics, 2002, 180(1):383–403.
[142] Wallstedt P C, Guilkey J E. Improved velocity projection for the material point method.Cmes-Computer Modeling in Engineering & Sciences, 2007, 19(3):223–232.
[143] Meyers M A. Dynamic Behavior of Materials. John Wiley & Sons, 1994.
[144] Meyers M A原著,张庆明,刘彦,黄风雷,等译.材料的动力学行为.北京:国防工业出版社, 2006.
[145]李翼祺,马素贞.爆炸力学.北京:科学出版社, 1992.
[146] Zukas J A, Walters W P, (eds.). Explosive effects and applications. Springer, 1998.
[147]孙锦山,朱建士.理论爆轰物理.北京:国防工业出版社, 1995.
[148]陈朗,龙新平,冯长根,等.含铝炸药爆轰.北京:国防工业出版社, 2004.
[149]张国伟,韩勇,苟瑞君,编.爆炸作用原理.北京:国防工业出版社, 2006.
[150]汤文辉,张若棋.物态方程理论及计算概论.长沙:国防科技大学出版社, 1999.
[151]王仁,黄文彬,黄筑平.塑性力学引论.北京:北京大学出版社, 1992.
[152] Johnson G R, Holmquist T J. Evaluation of cylinder-impact test data for constitutive modelconstants. Journal of Applied Physics, 1988, 64(8):3901–3910.
[153] Zerilli F J, Armstrong R W. Dislocation-mechanics-based consitutive relations for materialdynamics calculations. Journal of Applied Physics, 1987, 61(5):1816–1825.
[154]彭建祥. Johnson-Cook本构模型和Steinberg本构模型的比较研究[博士学位论文].北京:中国工程物理研究院, 2006.
[155] Steinberg D J, Cochran S G, Guinan M W. A Consitutive model for metals applicable athigh-strain rate. Journal of Applied Physics, 1980, 51(3):1498–1504.
[156] Johnson G R, Cook W H. Fracture characteristics of three metals subjected to variousstrains, strain rates, temperatures and pressures. Engineering fracture mechanics, 1985,21(1):31–48.
[157]王永刚,贺红亮,陈登平,等.延性金属层裂模型比较.爆炸与冲击, 2005, 25(5):467–471.
[158] Liu M B, Liu G R, Lam K Y. Investigation into water mitigations using a meshless particlemethod. Shock Waves, 2002, 12(3):181–195.
[159] Fiserova D. Numerical Analyses of Buried Mine Explosions with Emphasis on Effect ofSoil Properties on Loading[D]. Cranfield University, 2006.
[160] Mader C L. Numerical Modeling of Explosives and Propellants. CRC Press, 1998.
[161] Mason J J, Rosakis A J, Ravichandran G. On the Strain and Strain-Rate Dependence ofthe Fraction of Plastic Work Converted to Heat - an Experimental-Study Using High-SpeedInfrared Detectors and the Kolsky Bar. Mechanics of Materials, 1994, 17(2-3):135–145.
[162] Grandy J. Effecient Computation of Volume of Hexahedral Cells. Technical report,Lawrence Livermore National Laboratory, 1997.
[163] Shin Y S, Chisum J E. Modeling and simulation of underwater shock problems using coupledlagrangian-eulerian analysis approach. Shock and Vibration, 1997, 4(1):1–10.
[164] Sedov L I. Similarity and Dimensional Methods in Mechanics. 10th ed., CRC Press, 1993.
[165] http://flash.uchicago.edu/?ahaque/sedov.html.
[166] Flangan D P, Belytschko T. A uniform strain hexahedron and quadrilaterial with orthogonalhourglass control. International Journal for Numerical Methods in Engineering, 1981,17:679–706.
[167] Anderson C E, Timothy J, Trucano G, et al. Debris cloud dynamics. International Journalof Impact Engineering, 1990, 9(1):89–113.
[168] Moresi L, Dufour F, Muhlhaus H B. A Lagrangian integration point finite element methodfor large deformation modeling of viscoelastic geomaterials. Journal of ComputationalPhysics, 2003, 184(2):476–497.
[169] Knight D D. Elements of Numerical Methods for Compressible Flows. Cambridge UniversityPress, 2006: P.33–36.
[170] Sod G A. A survey of several finite difference methods for systems of nonlinear hyperbolicconservation laws. Journal of Computational Physics, 1978, 27:1–31.
[171] Lee W H. Computer Simulation of Shaped Charge Problems. World Scientific, 2006.
[172] Molinari J F. Finite element simulation of shaped charges. Finite Elements in Analysis andDesign, 2002, 38(10):921–936.
[173] Monaghan J J. Smoothed particle hydrodynamics. Reports on Progress in Physics, 2005,68(8):1703–1759.
[174] Faraud M, Destefanis R, Palmieri D, et al. SPH simulations of debris impacts using twodifferent computer codes. International Journal of Impact Engineering, 1999, 23(1):249–260.
[175] Groenenboom P H L. Numerical simulation of 2D and 3D hypervelocity impact usingthe SPH option in PAM-SHOCK(TM). International Journal of Impact Engineering, 1997,20(1-5):309–323.
[176]马上.超高速碰撞问题的三维物质点法模拟[硕士学位论文].清华大学, 2005.
[177] Libersky L D, Petschek A G. Smooth particle hydrodynamics with strength of materials.Advances in the Free-Lagrange Method, Lecture Notes in Physics, 1990, 395:248–257.
[178] Hernquist L, Katz N. Treesph: a unification of SPH with the hierarchical tree method. TheAstrophysical Journal Supplement Series, 1989, 70:419–446.
[179] Waltz J, Page G L, Milder S D, et al. Aperformance comparison of tree data structuresforN-body simulation. Journal of Computational Physics, 2002, 178:1–14.
[180] Capuzzo-Dolcetta R, Miocchi P. A comparison between the fast multipole algorithm and thetree-code to evaluate gravitational forces in 3-D. Journal of Computational Physics, 1998,143:29–48.
[181] Munjiza A, Andrews K R F. NBS contact detection algorithm for bodies of similar size.International Journal for Numerical Methods in Engineering, 1998, 43:131–149.
[182] Batra R C, Zhang G M. Search algorithm, and simulation of elastodynamic crack propagationby modified smoothed particle hydrodynamics (MSPH) method. ComputationalMechanics, 2007, 40:531–546.
[183] Balsara D S. Von-Neumann Stability Analysis of Smoothed Particle Hydrodynamics - Suggestionsfor Optimal-Algorithms. Journal of Computational Physics, 1995, 121(2):357–372.
[184] Beissel S, Belytschko T. Nodal integration of the element-free Galerkin method. ComputerMethods in Applied Mechanics and Engineering, 1996, 139:49–74.
[185] Morris J P. Analysis of smoothed particle hydrodynamics with applications[D]. MonashUniversity, 1996.
[186] Chen J K, Beraun J E, Jih C J. An improvement for tensile instability in smoothed particlehydrodynamics. Computational Mechanics, 1999, 23:279–287.
[187] Monaghan J J. SPH without a tensile instability. Journal of Computational Physics, 2000,159:290–311.
[188] Dyka C T, Randles PW, Ingel R P. Stress points for tension instability in SPH. InternationalJournal for Numerical Methods in Engineering, 1997, 40(13):2325–2341.
[189] Randles P W, Libersky L D. Normalized SPH with stress points. International Journal forNumerical Methods in Engineering, 2000, 47:1445–1462.
[190] Campbell P M. Some new algorityms for boundary value problems in smoothed particledynamics. DNA Report, 1989, DNA-TR-88-286.
[191] Monaghan J J. Simulating free surface flow with SPH. Journal of Computational Physics,1994, 110:399.
[192] 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.
[193] Oberkampf W L, Trucano T G, Hirsch C. Verification, validation, and predictive capabilityin computational engineering and physics. Applied Mechanics Reviews, 2004, 57(5):345–384.
[194]邓小刚,宗文刚,张来平,等.计算流体力学中的验证与确认.力学进展, 2007,37(2):279–288.109