[1] LIU Q L, SUBHASH G, GAO X L. A parametric study on crushability of open-cell structural polymeric foams [J]. Journal of Porous Materials, 2005, 12(3): 233-248.
[2] CHEN C, LU T J, FLECK N A. Effect of inclusions and holes on the stiffness and strength of honeycombs [J]. International Journal of Mechanical Sciences, 2001, 43(2): 487-504.
[3] OZTURK U E, ANLAS G. Hydrostatic compression of anisotropic low density polymeric foams under multiple loadings and unloading [J]. Polymer Testing, 2011, 30(7): 737-742.
[4] GIBSON L J, ASHBY M F. Cellular solids: structure and properties [M]. Cambridge: Cambridge University Press, 2001: 30-60.
[5] FABRICE S, LAURENT C, JEAN-YVES C, et al. Mechanical properties of high density polyurethane foams: I. effect of the density [J]. Composite Science and Technology, 2006, 66(15): 2700-2708.
[6] THOMAS T, MAHMUZ H, CARLSSON L A, et al. Dynamic compression of cellular cores: temperature and strain rate effects [J]. Composite Structures, 2002, 58(4): 505-512.
[7] MAHFUZ H, THOMAS T, RANGARI V, et al. On the dynamic response of sandwich composites and their core materials [J]. Composites Science and Technology, 2006, 66(14): 2465-2472.
[8] GRACE I, PILIPCHUK V, IBRAHIM R, et al. Temperature effect on non-stationary compressive loading response of polymethacrylimide solid foam [J]. Composite Structures, 2012, 94(10): 3052-3063.
[9]CHEN W, LU F, WINFREE N. High-strain-rate compressive behavior of a rigid polyurethane foam with various densities [J]. Experimental Mechanics, 2002, 42(1): 65-73.
[10] SONG B, CHEN W W, DOU S, et al. Strain-rate effects on elastic and early cell-collapse responses of a polystyrene foam [J]. International Journal of Impact Engineering, 2005, 31(5): 509-521.
[11] SAHA M C, MAHFUZ H, CHAKRAVARTY U K, et al. Effect of density, microstructure, and strain rate on compression behavior of polymeric foams [J]. Materials Science and Engineering A, 2005, 406 (1/2): 328-336.
[12]VIOT P, BEANI F, LATAILLADE L J. Polymeric foam behavior under dynamic compressive loading [J]. Journal of Materials Science, 2005, 40(22): 5829-5837.
[13] ZHANG J, LIN Z, WANG A, et al. Constitutive modeling and material characterization of polymeric foams[J]. Journal of Engineering Materials and Technology,1997,119(3):284-291.
[14] DI L L, SALA G, OLIVIERI D. Deformation mechanisms and energy absorption of polystyrene foams for protective helmets [J]. Polymer Testing, 2002, 21(2): 217-228.
[15] SWETHA C, KUMAR R. Quasi-static uniaxial compression behaviour of hollow glass microspheres/epoxy based syntactic foams [J]. Materials and Design, 2011, 32(8/9): 4152-4163.
[16] LORENZO P, MARTINA S, MASSIMILIANO A. Dynamic mechanical behavior of syntactic iron foams with glass microspheres [J]. Materials Science and Engineering A, 2012, 552(1): 364-375.
[17] MONTANINI R. Measurement of strain rate sensitivity of aluminium foams for energy dissipation [J]. Journal of Mechanical Sciences, 2005, 47(1): 26-42.
[18] CADY C M, GRAY G T, LIU C, et al. Compressive properties of a closed-cell aluminum foam as a function of strain rate and temperature [J]. Materials Science Engineering A, 2009, 525(1/2): 16.
[19] HALL I W, GUDEN M, YU C J. Crushing of aluminum closed cell foams: density and strain rate effects [J]. Scripta Materialia, 2000, 43(6): 515-521.
[20]VIOT P. Hydrostatic compression on polypropylene foam [J]. International Journal of Impact Engineering, 2009, 36 (7): 975-989.
[21] MOREU Y M, MILLS N J. Rapid hydrostatic compression of low-density polymeric foams [J]. Polymer Testing, 2004, 23(3): 313-322.
[22] SRIVASTAVA V, SRIVASTAVA R. On the polymeric foams: modeling and properties [J]. Journal of Material Science, 2014, 49(7): 2681-2692.
[23] KIM Y, KANG S. Development of experimental method to characterize pressure-dependent yield criteria for polymeric foams [J]. Polymer Testing, 2003, 22(2): 197-202.
[24]LI B, GU Y D, EHGLISH R, et al. Characterization of nonlinear material parameters of foams based on indentation tests [J]. Materials and Design, 2009, 30(7): 2708-2714.
[25] ABRAMOWICZ W, JONES N. Dynamic progressive buckling of circular and square tubes [J]. International Journal of Impact Engineering, 1986, 4(4): 243-270.
[26]GIGLIO M, MANES A, GILIOLI A. Investigations on sandwich core properties through an experimental-numerical approach [J]. Composites Part B, 2012, 43(2): 361-374.
[27] HU L, YOU F F, YU T X. Effect of cell-wall angle on the in-plane crushing behaviour of hexagonal honeycombs [J]. Materials and Design, 2013, 46: 511-523.
[28] XU S Q, BEYNON J H, RUAN D, et al. Experimental study of the out-of-plane dynamic compression of hexagonal honeycombs [J]. Composite Structures, 2012, 94( 8): 2326-2336.
[29]RUAN D, LU G, WANG B, et al. In-plane dynamic crushing of honeycombs: a finite element study [J]. International Journal of Impact Engineering, 2003, 28(2): 161-182.
[30]WANG A J, MCDOWELL D L. In-plane stiffness and yield strength of periodic metal honeycombs [J]. Journal of Engineering Materials and Technology, 2004, 126(2): 137-156.
[31]LIU Q, SUBHASH G. A phenomenological constitutive model for foams under large deformation [J]. Polymer Engineering and Science, 2004, 44 (5): 463-473.
[32] LIU Q, TOOLE B O. Behavior pattern and parametric characterization for low density crushable foams [J]. Journal of Materials Processing Technology, 2007, 191(1/2/3): 73-76.
[33] AVALLE M, BELINGARDI G, IBBA A. Mechanical models of cellular solids: parameters identification from experimental tests [J]. International Journal of Impact Engineering, 2007, 34(1): 327.
[34] SHERWOOD J A, FROST C C. Constitutive modeling and simulation of energy absorbing polyurethane foam under impact loading [J]. Polymer Engineering and Science, 1992, 32(16): 1138-1146.
[35] ZHANG J, KIKUCHI N, LI V, et al. Constitutive modeling of polymeric foam material subjected to dynamic crash loading [J]. International Journal of Impact Engineering, 1998, 21(5): 369-386.
[36] JEBUR Q H, HARRISON P, GUO Z Y, et al. Characterization and modeling of a transversely isotropic melt-extruded low-density polyethylene closed cell foam under uniaxial compression [J]. Journal of Mechanical Engineering Science, 2012, 226(9): 2168-2177.
[37] MILLS N J, FITZGERALD C, GILCHRIST A, et al. Polymer foams for personal protection: cushions, shoes and helmets [J]. Composites Science and Technology, 2003, 63(16): 2389-2400.
[38] SHIM V P W, TU Z H, LIM C T. Two-dimensional response of crushable polyurethane foam to low velocity impact [J]. International Journal of Impact Engineering, 2000, 24(6/7): 703-731.
[39] UMUD E O, GUNAY A. Finite element analysis of expanded polystyrene foam under multiple compressive loading and unloading [J]. Materials and Design, 2011, 32(2): 773-780.
[40] BROTHERS A H, DUNAND D C. Mechanical properties of a density-graded replicated aluminum foam [J]. Materials Science and Engineering A, 2008, 489 (1/2): 439-443.
[41] DESHPANDE V S, FLECK N A. Isotropic constitutive models for metallic foams [J]. Journal of the Mechanics and Physics of Solids, 2000, 48(6/7): 1253-1283.
[42] HANSSEN A G, HOPPERSTAD O S, LANGSETH M, et al. Validation of constitutive models applicable to aluminium foam [J]. International Journal of Mechanical Sciences, 2002, 44(2): 359-406.
[43]MEGUID S A, STRANART J C, HEYERMAN J. On the layered micromechanical three-dimensional finite element modeling of foam-filled columns [J]. Finite Elements Analysis and Design, 2004, 40(9/10): 1035-1057.
[44] REYES A, HOPPERSTAD O S, BERSTAD T, et al. Constitutive modeling of aluminum foam including fracture and statistical variation of density [J]. European Journal of Mechanics Solids, 2003, 22(6): 815-835.
[45] GONG L, KYRIAKIDES S, TRIANTAFYLLIDIS N. On the stability of Kelvin cell foams under compressive loads [J]. Journal of the Mechanics and Physics of Solids, 2005, 53(4): 771-794.
[46]MILLS N J. Modeling the dynamic crushing of closed-cell polyethylene and polystyrene foams [J]. Journal of Cellular Plastics, 2011, 47(2): 173-197.
[47] ALVAREZ P, MENDIZABAL A, PETITE M M. Finite element modelling of compressive mechanical behaviour of high and low density polymeric foams [J]. Material Wissenschaft und Werkstofftechnik, 2009, 40(3): 126-132.
[48] NAMMI S K, MYLER P, EDWARDS G. Finite element analysis of closed-cell aluminium foam under quasi-static loading [J]. Materials and Design, 2010, 31(2): 712-722.
[49] SULLIVAN R M, GHOSN L J, LERCH B A. A general tetrakaidecahedron model for open-celled foams [J]. International Journal of Solids and Structures, 2008, 45(6): 1754-1765.
[50] SONG Y Z, WANG Z H, ZHAO L M. Dynamic crushing behavior of 3D closed-cell foams based on Voronoi random model [J]. Materials and Design, 2010, 31(9): 4281-4289.
[51] ATTIA M S, MEGUID S A, TAN K T, et al. Influence of cellular imperfections on mechanical response of metallic foams [J]. International Journal of Crashworthiness, 2010,15(4): 357-367.
[52] 卢富德,高德. 考虑蜂窝纸板箱缓冲作用的产品包装系统跌落冲击研究[J].振动工程学报,2012, 25(3): 335-341.
LU Fu-de, GAO De. Study on drop impact of packaging system considering the cushioning action of honeycomb paperboard box [J]. Journal of Vibration Engineering, 2012, 25(3): 335-341.
[53] 卢富德, 高德. C楞瓦楞纸板动态缓冲模型及应用[J]. 功能材料, 2012, 43(1): 39-41.
LU Fu-de, GAO De. Cushion model and its application of C-flute corrugated paperboard [J]. Journal of Functional Materials, 2012, 43(1): 39-41.
[54] ZHAO H, GARY G. Crushing behaviour of aluminium honeycombs under impact loading [J]. International Journal of Impact Engineering, 1998, 21(10): 827-836.
[55]张绍云,储火,卢富德,等.蜂窝-泡沫缓冲系统动力学有限元分析[J].振动与冲击,2014,33(2):5254.
ZHANG Shao-yun, CHU Huo, LU Fu-de, et al. Finite element analysis for dynamic response of cushioning system made out of honeycomb paperboard and foam [J]. Journal of Vibration and Shock, 2014, 33(2): 52-54.
[56] HANSSEN A G, HOPPERSTAD O S, LANGSETH M. Design of aluminium foam-filled crash boxes of square and circular cross-sections [J]. International Journal of Crashworthiness, 2001, 6(2): 177-188.
[57] HANSSEN A G,STOBENER K, RAUSCH G, et al. Optimization of energy absorption of an A-pillar by metal foam insert [J]. International Journal of Crashworthiness, 2006, 11(3): 231-241.
[58] KIM H S, CHEN W, WIERZBICKI T. Weight and crash optimization of foam-filled three-dimensional "S" frame [J]. Computational Mechanics, 2002, 28(5): 417-424.
[59] ZAREI H R, KROEGER M. Crashworthiness optimization of empty and filled aluminum crash boxes [J]. International Journal of Crashworthiness, 2007, 12(3): 255-264.
[60] ZAREI H R, KROEGER M. Multiobjective crashworthiness optimization of circular aluminum tubes [J]. Thin-Walled Structures, 2006, 44(3): 301-308.
[61] ZAREI H R, KROEGER M. Optimization of the foam-filled aluminum tubes for crush box application [J]. Thin-Walled Structures, 2008, 46(2): 214-221.
[62] HOU S J, LI Q, LONG S Y, et al. Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria [J]. Finite Elements in Analysis and Design, 2007, 43(6/7): 555-565.
[63] NARIMAN-ZADEH N, DARVIZEH A, JAMALI A. Pareto optimization of energy absorption of square aluminium columns using multi-objective genetic algorithms [J]. Journal of Engineering Manufacture, 2006, 220(2): 213-224.
[64]CHEN W G. Optimisation for minimum weight of foam-filled tubes under large twisting rotation [J]. International Journal of Crashworthiness, 2001, 6(2): 223-241.
[65] SUN G Y, LI G, HOU S J. Crashworthiness design for functionally graded foam-filled thin-walled structures [J]. Materials Science and Engineering A, 2010, 527(7/8): 1911-1919.
[66] ZHANG Y, SUN G, LI G, et al. Optimization of foam-flled bitubal structures for crashworthiness criteria [J]. Material and Design, 2012, 38(1): 99-109.
[67]YANG S, CHANG Q. Multiobjective optimization for empty and foam-filled square columns under oblique impact loading [J].International Journal of Impact Engineering, 2013, 54(1): 177-191.
[68] SANTOSA S, WIERZBICKI T. Crash behavior of box columns filled with aluminum honeycomb or foam [J]. Computers Structures,1998, 68(4): 343-367.
[69]ZARE H, KROEGER M. Optimum honeycomb filled crash absorber design [J]. Materials and Design, 2008, 29(1): 193-204.
[70] SUN G, LI G, STONE M, et al. A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials [J]. Computational Materials Science, 2010, 49(3): 500-511.
[71]YIN H F, WEN G L, HOU S J, et al. Crushing analysis and multiobjective crashworthiness optimization of honeycomb-filled single and bitubular polygonal tubes [J]. Materials and Design, 2011, 32(8/9): 4449-4460.
[72]NAGEL G M, THAMBIRATNAM D P. Computer simulation and energy absorption of tapered thin-walled rectangular tubes [J]. Thin-Walled Structures, 2005, 43(8): 1225-1242.
[73]QI C, YANG S, DONG F. Crushing analysis and multiobjective crashworthiness optimization of tapered square tubes under oblique impact loading [J]. Thin-Walled Structures, 2012, 59(1): 103-119.
[74]TINARD V, DECK C, WILLINGER R. Modeling and validation of motorcyclist helmet with composite shell [J]. International Journal of Crashworthiness, 2012, 17(2): 209215.
[75] LONG B T, KWONG-MING L, HEOW- PUEH L, et al. Performance of an advanced combat helmet with different interior cushioning systems in ballistic impact: experiments and finite element simulations [J]. International Journal of Impact Engineering, 2012, 50(1): 99-112.
[76]GAETANO G D, LANNUCCI L, GALVANETTO U. Shock absorption performance of a motorbike helmet with honeycomb reinforced liner [J]. Composite Structures, 2011, 93(11): 2748-2759.
[77] COELHO R M, ALVES D, SOUSA R J, et al.New composite liners for energy absorption purposes [J]. Materials and Design, 2013, 43: 384-392.
[78] RUEDA M A F, CUI L, GILCHRIST M D. Optimization of energy absorbing liner for equestrian helmets. Part I: layered foam liner [J]. Materials and Design, 2009, 30(9): 3405-3413.
[79] CUI L, RUEDA M A F,GILCHRIST M D. Optimization of energy absorbing liner for equestrian helmets. Part II: functionally graded foam liner [J]. Materials and Design, 2009, 30(9): 3414-3419.
[80] ZHOU J, GUAN Z W, CANTWELL W J. The impact response of graded foam sandwich structures [J]. Composite Structures, 2013, 97(1): 370-377.
[81] HANSSEN A G, GIRARD Y, OLOVSSON L, et al. A numerical model for bird strike of aluminium foam-based sandwich panels [J]. International Journal of Impact Engineering, 2006, 32(7): 1127-1144.
[82]SEK M, ROUILLARD V, TARASH H, et al. Enhancement of cushioning performance with paperboard crumple inserts [J]. Packaging Technology and Science, 2005, 18(5): 273-278.
[83] LU F D, TAO W M, GAO D. Virtual mass method for solution of dynamic response of composite cushion packaging system [J]. Packaging Technology and Science, 2013, 26(suppl.1): 32-42.
[84] 卢富德,陶伟明,高德. 串联缓冲系统冲击响应与结构优化分析 [J]. 浙江大学学报:工学版,2012,46(10): 1773-1777.
LU Fu-de, TAO Wei-ming, GAO De. Impact response of series cushioning system and structure optimization analysis [J]. Journal of Zhejiang University: Engineering Science, 2012, 46(10): 1773-1777.
[85] 卢富德,陶伟明,高德. 串联缓冲结构压缩响应虚拟质量分析方法[J]. 浙江大学学报:工学版, 2012,46(8): 1431-1436.
LU Fu-de, TAO Wei-ming, GAO De. Compression responses of series cushioning structures by a virtual mass method [J]. Journal of Zhejiang University: Engineering Science, 2012, 46(8): 14311436.2 |