物质点法的理论和应用

姓名
邮箱
手机号码
标题
留言内容
验证码

doi:10.6052/1000-0992-12-122

清华大学航天航空学院, 北京 100084

基金项目:国家自然科学基金项目(11272180, 11102097)和国家重点基础研究发展计划项目(2010CB832701)资助

详细信息

作者简介:
张雄, 清华大学航天航空学院教授、博士生导师. 2004 年入选教育部首批新世纪优秀人才支持计划, 获教育部自然科学奖二等奖(2009, 第一获奖人) 和一等奖(2008, 第六获奖人)、北京市教育创新标兵(2003)、北京市高等教育教学成果奖二等奖(2004)、ICACM Fellows Award (2011, 台北) 等奖励.

通讯作者:
张雄

中图分类号:O242
计量
- 文章访问数:6223
- HTML全文浏览量:503
- PDF下载量:4913
- 被引次数:0
出版历程
- 收稿日期:2012-12-24
- 修回日期:2013-03-21
- 刊出日期:2013-03-25

Material point method and its applications

School of Aerospace, Tsinghua University, Beijing 100084, China

Funds:This project was supported by National Nature Science Foundation of China (11272180,11102097), and National Basic Research Program of China (2010CB832701)

More Information

Corresponding author:ZHANG Xiong

摘要

摘要:物质点法采用质点离散材料区域, 用背景网格计算空间导数和求解动量方程,避免了网格畸变和对流项处理, 兼具拉格朗日和欧拉算法的优势, 非常适合模拟涉及材料特大变形和断裂破碎的问题. 本文详细论述了物质点法在基本理论、算法和软件开发方面的进展, 包括广义插值物质点法、接触算法、自适应算法、并行算法、与其他算法的杂交和耦合等. 系统地总结了物质点法在超高速碰撞、冲击侵彻、爆炸、动态断裂、流固耦合、多尺度分析、颗粒材料流动和岩土失效等一系列涉及材料特大变形问题中的应用,展示了其相对于传统数值计算方法的优势.
- 无网格法/
- 物质点法/
- 冲击侵彻/
- 爆炸/
- 特大变形
Abstract:Material point method (MPM) discretizes the material domain by particles, and solves the momentum equations on a predefined background mesh. MPM avoids mesh entanglement and involving convection term, by taking advantages of both the Lagrangian and the Eulerian methods. So it is very promising in the numerical simulation of problems involving extreme material deformation and fracture. The state of the art of the theory, the algorithm development and implementation, and the software development of material point method are reviewed in detail. The generalized material point method, the contact algorithm, the adaptive algorithm, the parallel algorithm, and the coupling with other methods are included. Applications of MPM to the problems involving extreme material deformation, such as hypervelocity impact, penetration, explosion, dynamic fracture, fluid-structure interaction, multiscale analysis, and granular material flow and rock and soil failure, are investigated systematically. The applications demonstrate the advantages of MPM over conventional numerical methods.
- meshless/meshfree method/
- material point method/
- impact and penetration/
- explosion/
- extreme deformation

HTML全文

参考文献 (153)

[1]	Ambati R, Pan X F, Yuan H. 2012. Application of material point method for cutting process simulations. Computational Materials Science, 57: 102-110
[2]	Andersen S, Andersen L. 2010. Modelling of landslides with the material-point method. Computational Geosciences, 14: 137-147.
[3]	Anvar G, Sumanta A. 2008. A hybrid immersed boundary and material point method for simulating 3d fluid-structure interaction problems. International Journal for Numerical Methods in Fluids, 56: 2151-2177%
[4]	Ayton G, Bardenhagen S G, McMurtry P, et al. 2001. Interfacing continuum and molecular dynamics: An application to lipid bilayers. Journal of Chemical Physics, 114 (15): 6913-6924
[5]	Bardenhagen S G, Brackbill J U, Sulsky D. 2000. The material-point method for granular materials. Computer Methods in Applied Mechanics and Engineering, 187 (3-4): 529-541
[6]	Bardenhagen S G, Brydon A D, Guilkey J E. 2005. Insight into the physics of foam densification via numerical simulation. Journal of the Mechanics and Physics of Solids, 53 (3): 597-617
[7]	Bardenhagen S G, Guilkey J E, Roessig K M, et al. 2001. An improved contact algorithm for the material point method and application to stress propagation in granular material. Computer Modeling in Engineering & Sciences, 2 (4): 509-522
[8]	Bardenhagen S G, Kober E M. 2004. The generalized interpolation material point method. Computer Modeling in Engineering & Sciences, 5 (6): 477-495
[9]	Bardenhagen S G. 2002. Energy conservation error in the material point method for solid mechanics. Journal of Computational Physics, 180: 383-403
[10]	Belytschko T, Krongauz Y, Organ D, et al. 1996. Meshless methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering, 139 (1-4): 3-47
[11]	Belytschko T, Liu W K, Moran B. 2000. Nonlinear Finite Elements for Continua and Structures. London:John Wiley & Sons Ltd.
[12]	Benioff M R, Lazowska E D. 2005. Computational science: ensuring america's competitiveness. Technical report, President's Information Technology Advisory Committee
[13]	Borodin O, Bedrov D, Smith G D, et al. 2005. Multiscale modeling of viscoelastic properties of polymer nanocomposites. Journal of Polymer Science: Part B: Polymer Physics, 43: 1005-1013
[14]	Brackbill J U, Kothe D B, Ruppel H M. 1988. FLIP : A low-dissipation, particle-in-cell method for fluid flow. Computer Physics Communications, 48: 25-38
[15]	Brackbill J U, Ruppel H M. 1986. FLIP : A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. Journal of Computational Physics, 65: 314-343
[16]	Chen H W, Hagiwara I, Tieu A K. 2011. A seamless coupling between molecular dynamics and material point method. Japan Journal of Industrial and Applied Mathematics. , 28: 55-67
[17]	Chen J K, Beraun J E, Jih C J. 1999. An improvement for tensile instability in smoothed particle hydrodynamics. Computational Mechanics, 23 (4): 279-287
[18]	Chen W D, Zhang F, Yang W M. 2012. Simulation of spall fracture based on material point method. In: 11th International Conference on Fracture and Damage Mechanics
[19]	Chen Z, Feng R, Xin X, et al. 2003. A computational model for impact failure with shear-induced dilatancy. International Journal for Numerical Methods in Engineering, 56: 1979-1997
[20]	Chen Z, Gan Y, Chen J K. 2008. A coupled thermo-mechanical model for simulating the material failure evolution due to localized heating. Computer Modeling in Engineering & Sciences, 26 (2): 123-137
[21]	Chen Z, Hu W, Shen L M, et al. 2002. An evaluation of the MPM for simulating dynamic failure with damage diffusion. Engineering Fracture Mechanics, 69: 1873-1890
[22]	Chen Z, Shen L M, Mai Y W, et al. 2005. A bifurcation-based decohesion model for simulating the transition from localization to decohesion with the MPM. Zeitschrift fur Angewandte Mathematik und Physick ZAMP, 56: 908-930
[23]	Chiang W F, DeLisi M, Hummel T, et al. 2010. GPU acceleration of the generalized interpolation material point method.
[24]	Coetzee C J, Basson A H, Vermeer P A. 2007. Discrete and continuum modelling of excavator bucket filling. Journal of Terramechanics, 44 (2): 177-186
[25]	Coetzee C J, Vermeer P A, Basson A H. 2005. The modelling of anchors using the material point method. International Journal for Numerical and Analytical Methods in Geomechanics, 29: 879-895
[26]	Colom A. 2011. Solving hydro-mechanical problems with the material point method. In: Proceedings of the 21st European Young Geotechnical Engineers' Conference Geotechnical Engineering: New Horizons. Rotterdam 2011
[27]	Cummins S J, Brackbill J U. 2002. An implicit particle-in-cell method for granular materials. Journal of Computational Physics, 180: 506-548
[28]	Daphalapurkar N P, Hanan J C, Phelps N B, et al. 2008. Tomography and simulation of microstructure evolution of a closed-cell polymer foam in compression. Mechanics of Advanced Materials and Structures, 15: 594-611
[29]	Daphalapurkar N P, Lu H, Coker D, et al. 2007. Simulation of dynamic crack growth using the generalized interpolation material point (GIMP ) method. International Journal of Fracture, 143 (1): 79-102
[30]	Dyka C T, Randles P W, Ingel R P. 1997. Stress points for tension instability in SPH. International Journal for Numerical Methods in Engineering, 40: 2325-2341
[31]	Fluid Dynamics Group Theoretical Division. 2007. CartaBlanca Theory Manual: Multiphase Flow Equations and Numerical Methods
[32]	Gan Y, Chen Z, Montgomery-Smith S. 2011. Improved material point method for simulating the zona failure response in piezo-assisted intracytoplasmic sperm injection. Computer Modeling in Engineering & Sciences, 73 (1): 45-76
[33]	Gilabert F A, Cantavella V C, Sanchez E, et al. 2011. Modelling fracture process in ceramic materials using the material point method. A Letters Journal Exploring the Frontiers of Physics, 96:24002, 1-6
[34]	Gilmanov A, Acharya S. 2008a. A computational strategy for simulating heat transfer and flow past deformable objects. International Journal of Heat and Mass Transfer, 51: 4415-4426
[35]	Gilmanov A, Acharya S. 2008b. A hybrid immersed boundary and material point method for simulating 3D fluid-structure interaction problems. International Journal for Numerical Methods in Engineering, 56: 2151-2177
[36]	Gingold R A, Monaghan J J. 1977. Smoothed particle hydrodynamics: theory and application to nonspherical stars. Monthly notices of the Royal Astronomical Society, 18: 375-389
[37]	Gong W W, Liu Y, Zhang X, et al. 2012. Numerical investigation on dynamical response of aluminum foam subject to hypervelocity impact with material point method. Computer Modeling in Engineering & Sciences, 83 (5): 527-545
[38]	Gong W W, Zhang X, Qiu X M. 2011. Numerical study of dynamic compression process of aluminum foam with material point method. Computer Modeling in Engineering & Sciences, 82 (3-4): 195-213
[39]	宫伟伟. 2012. 泡沫铝动态力学性能的物质点法研究:[博士论文]. 北京:清华大学 (Gong W W. 2012. Numerical study of dynamical behaviors of aluminum foam using material point method: [Ph. D. Thesis]. Beijing:Tsinghua University (in Chinese))
[40]	Guilkey J E, Hoying J B, Weiss J A. 2006. Computational modeling of multicellular constructs with the material point method. Journal of Biomechanics, 39: 2074-2086
[41]	Guilkey J E, Weiss J A. 2003. Implicit time integration for the material point method: Quantitative and algorithm comparisons with the finite element method. International Journal for Numerical Methods in Engineering, 57:1323-1338
[42]	Guillkey J E, Harman T B, Banerjee B. 2007. An eulerian-lagrangian approach for simulating explosions of energetic devices. Computers & Structures, 85: 660-674
[43]	Guo Y J, Nairn J A. 2006. Three-dimensional dynamic fracture analysis using the material point method. Computer Modeling in Engineering & Sciences, 16 (3): 141-155
[44]	Guo Y, Nairn J A. 2004. Calculation of $J$ integration and stress intensity factors using the material point method. Computer Modeling in Engineering & Sciences, 6: 295-308
[45]	Guo Z, Yang W. 2006a. MPM /MD handshaking method for multiscale simulation and its application to high energy cluster impacts. International Journal of Mechanical Sciences, 48: 145-159
[46]	Gupta V, Rajagopal S, Gupta N. 2011. A comparative study of meshfree methods for fracture. International Journal of Damage Mechanics, 20: 729-751
[47]	Harlow F H. 1964. The particle-in-cell computing method for fluid dynamics. Methods in Computational Physics, 3: 319-43
[48]	Hornung R D, Kohn S R. 2002. Managing application complexity in the samrai object-oriented framework. Concurrency and Computation: Practice and Experience, 14: 347-368
[49]	黄鹏, 张雄, 马上, 等. 2010a. 基于OpenMP 的三维显式物质点法并行化研究. 计算力学学报, 27: 21-27 (Huang P, Zhang X, Ma S, et al. 2010. Parallelization of 3Dexplicit material point method using OpenMP. Chinese Journal of Computational Mechanics, 27: 21-27 (in Chinese))
[50]	黄鹏. 2010b. 金属及岩土冲击动力学问题的物质点法研究:[博士论文]. 北京:清华大学 (Huang P. 2010. Material point method for metal and soil impact dynamics problems:[Ph. D. Thesis]. Beijing:Tsinghua University (in Chinese))
[51]	Htike H, Chen W, Gu Y, et al. 2011. Material point method with rbf interpolation. Computer Modeling in Engineering & Sciences, 72: 247-272
[52]	Hu P, Xue L, Mao S, et al. 2010. Material point method applied to fluid-structure interaction (FSI )/aeroelasticity problems. In: Proceedings of 8th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010-1464
[53]	Hu P, Xue L, Qu K, et al. 2009. Unified solver for modeling and simulation of nonlinear aeroelasticity and fluid-structure interactions. In: Proceedings of AIAA Atmospheric Flight Mechanics Conference, AIAA-2009-6148. Chicago
[54]	Hu W Q, Chen Z. 2006. Model-based simulation of the synergistic effects of blast and fragmentation on a concrete wall using the MPM. International Journal of Impact Engineering, 32 (12): 2066-2096
[55]	Hu W, Chen Z. 2003. A multi-mesh MPM for simulating the meshing process of spur gears. Computers & Structures, 81: 1991-2002
[56]	Huang P, Zhang X, Ma S, et al. 2008. Shared memory openmp parallelization of explicit MPM and its application to hypervelocity impact. Computer Modeling in Engineering & Sciences, 38: 119-147
[57]	Huang P, Zhang X, Ma S, et al. 2011. Contact algorithms for the material point method in impact and penetration simulation. International Journal for Numerical Methods in Engineering, 85 (4): 498-517.
[58]	Humphrey A, Meng Q Y, Berzins M, et al. 2012. Radiation modeling using the uintah heterogeneous CPU/GPU runtime system.
[59]	Idelsohn S R, Marti J, Limache A, et al. 2008. Unified lagrangian formulation for elastic solids and incompressible fluids: Application to fluid-structure interaction problems via the pfem. Computer Methods in Applied Mechanics and Engineering, 197 (19-20): 1762-1776
[60]	Ionescu I, Guilkey J E, Berzins M, et al. 2006. Simulation of soft tissue failure using the material point method. Journal of Biomechanical Engineering, 128: 917-924
[61]	Johnson G R, Stryk R A, Beissel S R. 1996. SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering, 139 (1-4): 347-373
[62]	Lemiale V, Nairn J, Hurmane A. 2010. material point method simulation of equal channel angular pressing involving large plastic strain and contact through sharp corners. Computer Modeling in Engineering & Sciences, 70: 41-46
[63]	Lenardic A, Moresi L, Muhlhaus H. 2000. The role of mobile belts for the longevity of deep cratonic lithosphere: the crumpled zone model. Geophys. Res. Lett. , 27: 1235-1238
[64]	Li F, Pan J Z, Sinka C. 2011a. Modelling brittle impact failure of disc particles using material point method. International Journal of Impact Engineering, 38: 653-660
[65]	Li F, Pan J Z, Sinka S. 2011b. Modelling adhesive contact between fine particles using material point method. Mechanics of Materials, 43: 157-167
[66]	Lian Y P, Zhang X, Liu Y. 2011c. Coupling of finite element method with material point method by local multi-mesh contact method. Computer Methods in Applied Mechanics and Engineering, 200: 3482-3494
[67]	Lian Y P, Zhang X, Liu Y. 2012a. An adaptive finite element material point method and its application in extreme deformation problems. Computer Methods in Applied Mechanics and Engineering, 241-244 (1): 275-285
[68]	Lian Y P, Zhang X, Liu Y. 2012b. Coupling between finite element and material point method for problems with extreme deformation. Theoretical & Applied Mechanics Letters, 2: 021003
[69]	Lian Y P, Zhang X, Zhou X, et al. 2011a. Numerical simulation of explosively driven metal by material point method. International Journal of Impact Engineering, 38: 237-245
[70]	Lian Y P, Zhang X, Zhou X, et al. 2011b. A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading. Computer Methods in Applied Mechanics and Engineering, 200 (17-20): 1659-1670
[71]	廉艳平. 2012. 自适应物质点有限元法及其在冲击侵彻问题中的应用:[博士论文]. 北京:清华大学 (Lian Y P 2012. An adaptive material point finite element method and its application in impact/penetration problems:[Ph. D. Thesis]. Beijing:Tsinghua University (in Chinese))
[72]	Liu G R, Liu M B. 2003. Smoothed Particle Hydrodynamics: A Meshfree Particle Method. Singapore: World Scientific
[73]	Liu M B, Liu G R, Lam K Y. 2002. Investigation into water mitigations using a meshles particle method. Shock Waves, 12 (3): 181-195
[74]	Liu Y, Wang H K, Zhang X. 2013. A multiscale framework for high-velocity impact process with combined material point method and molecular dynamics. International Journal of Mechanics and Materials in Design, in press
[75]	Liu Y, Zhang X, Lu M W. 2005. A meshless method based on least-squares approach for steady- and unsteady-state heat conduction problems. Numerical Heat Transfer, Part B, 47: 257-275
[76]	刘欣. 2011. 无网格方法. 北京:科学出版社 (Liu X. 2011. Meshfree Method Beijing: Science Press (in Chinese))
[77]	Love E, Sulsky D L. 2006. An unconditionally stable, energy-momentum consistent implementation of the material point method. Computer Methods in Applied Mechanics and Engineering, 195 (33-36): 3903-3925
[78]	Lu H, Daphalapurkar N P, Wang B, et al. 2006. Multiscale simulation form atomistic to continuum - coupling molecular dynamics (MD ) with the material point method (MPM ). Philosophical Magazine, 86 (20): 2971-2994
[79]	Lucy L B. 1977. A numerical approach to the testing of the fission hypothesis. The Astrophysical Journal, 8 (12): 1013-1024
[80]	Lysmer J, Kuhlemeyer R L. 1969. Finite dynamic model for infinite media. Journal of the Engineering Mechanics Division ASCE, 95: 859-877
[81]	Ma J, Lu H, Wang B, Roy S, et al. 2005. Multiscale simulations using generalized interpolation material point (GIMP ) method and samrai parallel processing. Computer Modeling in Engineering & Sciences, 8 (2): 135-152
[82]	Ma J. 2006. Multiscale simulation using the generalized interpolation material point method, discrete dislocations and molecular dynamics:[Ph. D. Thesis]. Oklahoma:Oklahoma State University
[83]	Ma S, Zhang X, Lian Y P et al. 2009a. Simulation of high explosive explosion using adaptive material point method. Computer Modeling in Engineering & Sciences, 39 (2): 101-123
[84]	Ma S, Zhang X, Qiu X M. 2009b. Comparison study of MPM and SPH in modeling hypervelocity impact problems. International Journal of Impact Engineering, 36: 272-282
[85]	马上, 张雄, 邱信明. 2006. 超高速碰撞问题的三维物质点法. 爆炸与冲击, 26 (3): 273-278 (Ma S, Zhang X, Qiu X M. 2006. Three dimensional material point method for hypervelocity impact. Explosion and Shock Waves, 26 (3): 273-278 (in Chinese))
[86]	马上, 张雄. 2009b. 聚能装药射流形成的自适应物质点法模拟. 固体力学学报, 30 (5): 504-508 (Ma S, Zhang X. 2009. Adaptive material point method for shaped charge jet formation. Chinese Journal of Solid Mechanics, 30 (5): 504-508 (in Chinese))
[87]	马上. 2005. 超高速碰撞问题的三维物质点法模拟:[硕士论文]. 北京:清华大学 ( Ma S. 2005. Material point method for 3D hypervelocity impact simulation:[Master Thesis]. Beijing:Tsinghua University (in Chinese))
[88]	马上. 2009a. 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 (Ma S. 2009. Material point meshfree methods for impact and explosion problems:[Ph. D. Thesis]. Beijing:Tsinghua University (in Chinese))
[89]	Ma Z T, Zhang X, Huang P. 2010. An object-oriented MPM framework for simulation of large deformation and contact of numerous grains. Computer Modeling in Engineering & Sciences, 55 (1): 61-87
[90]	Matsumoto N, Nairn J A. 2009. The fracture toughness of medium density fiberboard (MDF ) including the effects of fiber bridging and crack--plane interference. Engineering Fracture Mechanics, 76: 2748-2757
[91]	Monaghan J J. 2000. SPH without a tensile instability. Journal of Computational Physics, 159: 290-311
[92]	Nairn J A . 2003. Material point method calculations with explicit cracks. Computer Modeling in Engineering & Sciences, 4: 649-663
[93]	Nairn J A. 2006. On the calculation of energy release rates for cracked laminates with residual stresses. International Journal of Fracture, 139: 267-293
[94]	Nairn J A. 2007. Numerical implementation of imperfect interfaces. Computational Materials Science, 40: 525-536
[95]	Pan X F, Xu A G, Zhang G C, et al. 2008. Generalized interpolation material point approach to high melting explosive with cavities under shock. Journal of Physics D: Applied Physics, 41 (1): 1-9
[96]	Parker S G, Guilkey J, Harman T. 2006. A component-based parallel infrastructure for simulation of fluid-structure interaction. Engineering with Computers, 22: 277-292
[97]	Parker S G. 2006. A component-based architecture for parallel multi-physics pde simulaiton. Future Generation Computer Systems, 22: 204-216
[98]	Purdue University. 2009. Nnsa center for prediction of reliability, integrity and survivability of microsystems annual report. Technical report, Purdue University
[99]	Sadeghirad A, Brannon R M, Burghardt J. 2011. A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations. International Journal for Numerical Methods in Engineering, 86: 1435-1456
[100]	Schreyer H L, Sulsky D, Zhou S J. 2002. Modeling delamination as a strong discontinuity with the material point method. Computer Methods in Applied Mechanics and Engineering, 191: 2483-2507
[101]	Shen L M, Chen Z. 2005. A silent boundary scheme with the material point method for dynamic analyses. Computer Modeling in Engineering & Sciences, 7 (3): 305-320
[102]	Shen L M. 2009. A rate-dependent damage/decohesion model for simulating glass fragmentation under impact using the material point method. Computer Modeling in Engineering & Sciences, 49 (1): 23-45
[103]	Shen L, Chen Z. 2005. A multi-scale simulation of tungsten film delamination from silicon substrate. International Journal of Solids and Structures, 42: 5036-5056
[104]	Shen Y L, Li W, Sulsky D L, et al. 2000. Localization of plastic deformation along grain boundaries in a hardening material. International Journal of Mechanical Sciences, 42: 2167-2189
[105]	Shin W, Miller G R, Arduino P, et al. 2010. Dynamic meshing for material point method computations. World Academy of Science, Engineering and Technology I: Mathematical and Computational Sciences
[106]	Smolinski P, Palmer T. 2000. Procedures for multi-time step integration of element-free galerkin methods for diffusion problems. Computers and Structures, 77: 171-183%
[107]	Steffen M, Kirby R M, Berzins M. 2010. Decoupling and balancing of space and time errors in the material point method (MPM ). International Journal for Numerical Methods in Engineering, 82: 1207-1243
[108]	Sulsky D, Schreyer H L. 1996. Axisymmetric form of the material point method with applications to upsetting and taylor impact problems. Computer Methods in Applied Mechanics and Engineering, 139 (1-4): 409-429
[109]	Sulsky D, Chen Z, Schreyer H L. 1994. A particle method for history-dependent materials. Computer Methods in Applied Mechanics and Engineering, 118 (1-2): 179-196
[110]	Sulsky D, Kaul A. 2004a. Implicit dynamic in the material-point-method. Computer Methods in Applied Mechanics and Engineering, 193 (12-14): 1137-1170
[111]	Sulsky D, Peterson K. 2011. Toward a new elastic--decohesive model of arctic sea ice. Physica D, 240: 1674-1683
[112]	Sulsky D, Schreyer L. 2004b. MPM simulation of dynamic material failure with a decohesion constitutive model. European Journal of Mechanics A/Solids, 23: 423-445
[113]	Sulsky D, Zhou S J, Schreyer H L. 1995. Application of a particle-in-cell method to solid mechanics. Computer Physics Communications, 87 (1-2): 236-252
[114]	Sun L, Mathur S R, Murthy J Y. 2010. An unstructured finite-volume method for incompressible flows with complex immersed boundaries. Numerical Heat Transfer, Part B: Fundamentals, 58: 217-241
[115]	Tan H L, Nairn J A. 2002. Hierarchical, adaptive, material point method for dynamic energy release rate calculations. Computer Methods in Applied Mechanics and Engineering, 191 (19-20):2095-2109
[116]	Wallstedt P C, Guilkey J E. 2007. Improved velocity projection for the material point method. Computer Modeling in Engineering & Sciences, 19 (3): 223-232
[117]	Wallstedt P C, Guilkey J E. 2008. An evaluation of explicit time integration schemes for use with the generalized interpolation material point method. Journal of Computational Physics, 227: 9628-9642
[118]	Wang B, Karuppiah V, Lu H, et al. 2005. Two-dimensional mixed mode crack simulaiton using the material point method. Mechanics of Advanced Materials and Structures, 12: 471-484
[119]	Wang H K, Liu Y Zhang X. 2012. Numerical simulation of carbon nanotube reinforced composite by material point method. Computational Materials Science, 57: 23-29
[120]	Wang Y X, Beom H G, Sun M, et al. 2011. Numerical simulation of explosive welding using the material point method. International Journal of Impact Engineering, 38: 51-60
[121]	王汉奎. 2011. 金属及碳管复合材料力学行为物质点类方法研究:[博士论文]. 北京:清华大学 (Wang H K. 2011. Material point method for metal and carbon nanotube composite materials:[Ph. D. Thesis]. Beijing:Tsinghua University (in Chinese))
[122]	王津龙, 刘天云, 张楚汉. 2005. 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), 45 (12): 1604-1607 (Wang J L, Liu T Y, Zhang C H. 2005. Simulation of cylindrical stone pile based on the material point method. Journal of Tsinghua University (Science and Technology), 45 (12): 1604-1607 (in Chinese))
[123]	王宇新, 陈震, 孙明. 2006a. 滑移爆轰问题无网格MPM 法数值模拟. 力学与实践, 29 (3): 20-25 (Wang Y X, Chen Z, S M. 2006. Numerical simulation of slippage detonation by material point method--MPM. Mechanics in Engineering, 29 (3): 20-25 (in Chinese))
[124]	王宇新, 孙明, 张建臣. 2008. 无网格MPM 法三维前处理系统设计. 计算力学学报, 25: 392-396 (Wang Y X, Sun M, Zhang J. 2008. Implementation of 3D preprocessing program for material point method. Chinese Journal of Computational Mechanics, 25: 392-396 (in Chinese))
[125]	王宇新. 2006b. 多相介质爆炸冲击响应物质点法分析:[博士论文]. 大连:大连理工大学 (Wang Y X. 2006. Numerical analysis of explosion/impact response involved multiple materials using the material point method: [Ph. D. Thesis]. Dalian:Dalian University of Technology (in Chinese))
[126]	Wieckowski Z, Youn S K, Yeon J H. 1999. A particle-in-cell solution to the silo discharging problem. International Journal for Numerical Methods in Engineering, 45: 1203-1225
[127]	Wieckowski Z. 2004. The material point method in large strain engineering problems. Computer Methods in Applied Mechanics and Engineering, 193 (39-41): 4417-4438
[128]	Xu A G, Zhang G C, Li H, et al. 2011. Dynamical similarity in shock wave response of porous material: From the view of pressure. Computers and Mathematics with Applications, 61: 3618-3627
[129]	许爱国, 张广财, 应阳君, 等. 2010. 多孔材料冲击特性的数值研究. 力学学报, 42 (6):1138-1148 (Xu A G, Zhang G C, Ying Y J. 2010. Numerical study on porous materials under shock. Chinese Journal of Theoretical and Applied Mechanics, 42 (6): 1138-1148 (in Chinese))%
[130]	Xue L P, Borodin O, Smith G D, et al. 2006. Micromechanics simulations of the viscoelastic properties of highly filled composites by the material point method (MPM ). Modelling and Simulation in Materials Science and Engineering, 14 (4): 703-720
[131]	York II A R, Sulsky D, Schreyer H L. 1999. The material point method for simulation of thin membranes. International Journal for Numerical Methods in Engineering, 44: 1429-1456
[132]	York II A R, Sulsky D, Schreyer H L. 2000. Fluid-membrane interaction based on the material point method. International Journal for Numerical Methods in Engineering, 48: 901-924
[133]	Zhang D Z, Ma X, Giguere P T. 2011. Material point method enhanced by modified gradient of shape function. Journal of Computational Physics, 230: 6379-6398%
[134]	Zhang D Z, Ma X, Giguere P. 2009c. Computation of multi-material interactions using material point method. In: International Conference on Particle Based Methods
[135]	Zhang D Z, Zou Q, Ma X, et al. 2008a. Simulation of large deformation of materials using multiphase flow methods.%
[136]	Zhang D Z, Zou Q, VanderHeyden W B, et al. 2008b. Material point method applied to multiphase flows. Journal of Computational Physics, 227: 3159-3173
[137]	Zhang H W, Wang K P, Chen Z. 2009. Material point method for dynamic analysis of saturated porous media under external contact/impact of solid bodies. Computer Methods in Applied Mechanics and Engineering, 198: 1456-1472
[138]	Zhang X, Sze K Y, Ma S. 2006. An explicit material point finite element method for hyper-velocity impact. International Journal for Numerical Methods in Engineering, 66 (4): 689-706
[139]	Zhang Y T, Zhang X, Liu Y. 2010. An alternated grid updating parallel algorithm for material point method using openmp. Computer Modeling in Engineering & Sciences, 69 (2): 143-165
[140]	张洪武, 王鲲鹏, 陈震. 2009a. 基于物质点方法饱和多孔介质动力学模拟 (I): 耦合物质点方法. 岩土工程学报, 31 (10): 1505-1011 (Zhang H W, Wang K P, Chen Z. 2009. Material point method for dynamic analysis of saturated porous media (I): coupling material point method, Chinese Journal of Geotechnical Engineering. Chinese Journal of Geotechnical Engineering, 31 (10): 1505-1011 (in Chinese))
[141]	张洪武, 王鲲鹏, 陈震. 2009b. 基于物质点方法饱和多孔介质动力学模拟 (II): 饱和多孔介质与固体间动力接触分析. 岩土工程学报, 31 (11): 1672-1679 (Zhang H W, Wang K P, Chen Z. 2009. Material point method for dynamic analysis of saturated porous media (II): dynamic contact analysis between saturated porous media and solid bodies. Chinese Journal of Geotechnical Engineering, 31 (11): 1672-1679 (in Chinese))
[142]	张洪武, 王鲲鹏. 2010. 基于物质点方法饱和多孔介质动力学模拟 (III): 两相物质点方法. 岩土工程学报, 32 (4): 507-513 (Zhang H W, Wang K P. 2010. Material point method for dynamic analysis of saturated porous media (III): two-phase material point method. Chinese Journal of Geotechnical Engineering, 2010, 32 (4): 507-513 (in Chinese))
[143]	张雄, 廉艳平, 杨鹏飞, 等. 2011. 冲击爆炸问题的三维物质点法数值仿真. 计算机辅助工程, 20 (4): 29-37 (Zhang X, Lian Y P, Yang P F et al. 2011. 3D simulation based on material point method for impact and explosion problems Computer Aided Engineering, 20 (4): 29-37 (in Chinese))
[144]	张雄, 刘岩, 马上. 2009. 无网格法的理论及应用. 力学进展, 39 (1): 1-36 (Zhang X, Liu Yan, Ma S. 2009. Meshfree methods and their applications. Advances in Mechanics, 39 (1): 1-36 (in Chinese))
[145]	张雄, 刘岩. 2004. 无网格法. 北京: 清华大学出版社/Springer (Zhang X, Liu Y. 2004. Meshless Methods Beijing: Tsinghua University Press/Springer (in Chinese))
[146]	张雄, 王天舒. 2007. 计算动力学. 北京:清华大学出版社 (Zhang X, Wang T S, 2007. Computational Dynamics. Beijing:Tsinghua University Press (in Chinese))
[147]	张忠, 陈卫东, 杨文淼. 2011. 非均匀固体炸药冲击起爆的物质点法. 爆炸与冲击, 31 (1): 25-30 (Zhang Z, Chen W D, Yang W M. 2011. The material point method for shock-to-detonation transition of heterogeneous solid explosive. Explosion and Shock Waves, 31 (1): 25-30 (in Chinese))
[148]	郑勇刚, 顾元宪, 陈震. 2006. 薄膜破坏过程数值模拟的MPM 方法. 力学学报, 38: 347-355 (Zheng Y G, Gu Y X, Chen Z. 2006. Numerical simulation of thin film failure with MPM. Chinese Journal of Theoretical and Applied Mechanics, 38: 347-355 (in Chinese))
[149]	Zhou S Z, Zhang Z, Ma H L. 2012. Numerical simulation of human head impact using the material point method. International Journal of Computational Methods, Accepted.
[150]	周双珍, 张雄, 马红磊. 2013a. 不同骨密度下人体脊柱着陆冲击响应的数值模拟. 医用生物力学, Accepted (Zhou S Z, Zhang X, Ma H L. 2013. Numerical simulation of human spine to landing impact loading with different bone mineral density. Journal of medical Biomechanics, Accepted (in Chinese))
[151]	周双珍, 张雄, 马红磊. 2013b. 利用物质点法研究不同头部模型对头部碰撞动态响应的影响. 医用生物力学, 28 (1): 74-79 (Zhou S Z, Zhang X, Ma H L. 2013. Effects from different head models on dynamic responses of the head impact using material point method. Journal of Medical Biomechanics, 28 (1): 74-79 (in Chinese))
[152]	Zou Q, Zhang D Z, VanderHeyden W B et al. 2004. Application of a FLIP -MPM -MFM method for simulating weapon-target interaction. In: 75th Shock & Vibration Symposium
[153]	Zou Q, Zhang D Z, VanderHeyden W B. 2005. The application of an MPM -MFM method for simulating weapon-target interaction. In: 12th International Symposium on Interaction of the Effects of Munitions with Structures