Simulation of elastic-plastic impact with modified smoothed particle hydrodynamics method

[1] Gingold R A, Monaghan J J. Smoothed particle hydrodynamics:theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society,1977, 181:375-389 [2] Libersky L D, Petschek A G. Smoothed particle hydrodynamics with strength of materials Trease H, Fritts J, Crowley W. Proceedings, The Next Free Lagrange Conf. NY:Springer-Verlag, 1991, 395:248-257 [3] 张锁春.光滑质点流体动力学(SPH)方法(综述)[J].计算物理,1996, 13(4):385-397 Zhang Suochun. Smoothed particle hydrodynamics (SPH) method(a review)[J]. Chinese Journal of Computational Physics,1996, 13(4):385-397 (in Chinese) [4] Swegle J W, Hicks D L, Attaway S W. Smoothed particle hydrodynamics stability analysis[J]. J Comput Phys, 1995, 116:123-134 [5] Randles P W, Liberskey L D. Smoothed particle hydrodynamics:some recently improvements and applications[J]. Comput Methods Appl Mech Engrg, 1996,139:375-408  [6] Johnson G R, Beissel S R. Normalized smoothing functions for SPH impact computations[J]. Int J Numer Methods Engrg, 1996,39:S.2725-S.2741 [7] Krongauz Y, Belytschko T. Consistent pseudo derivatives in meshless methods[J]. Comput Methods Appl Mech Engrg, 1997,146:371-386  [8] Randles P W, Libersky L D. Recent improvements in SPH modeling of hypervelocity impact[J]. Int J Impact Engrg, 1997,20:525-532  [9] Gary A Dilts.Moving-least-squares-particle hydrodynamics -I:consistency and stability[J]. Int J Numer Methods Engrg, 1999,44:1115-1155 [10] Gary A Dilts. Moving least-squares particle hydrodynamics II:conservation and boundaries[J]. Int J Numer Methods Engrg ,2000,48:1503-1524 [11] Liu W K, Jun S, Zhang Y F. Reproducing kernel particle methods[J].Int J Numer Methods Engrg, 1995,20:1081-1106 [12] Chen J S, Pan C, Wu C T,et al. Reproducing kernel particle methods for large deformation analysis of non-linear structures[J]. Comput Methods Appl Mech Engrg, 1996,139:195-227 [13] Chen J K, Beraun J E, Jih C J. Completeness of corrective smoothed particle method for linear elastodynamics[J]. Computational Mechanics , 1999, 24:273-285 [14] Chen J K, Beraun J E. A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems[J]. Comput Methods Appl Mech Engrg,2000,19:225-239 [15] 刘鹏,刘更,刘天祥,等.光滑粒子动力学方法及其应用[J].机械科学与技术,2005, 24(9):1126-1130 Liu Peng, Liu Geng, Liu Tianxiang, et al. On smoothed particle hydrodynamics method and its application[J]. Mechanical Science and Technology, 2005, 24(9):1126-1130(in Chinese)