多孔金属材料率效应的数值分析与动态压缩行为的理论研究
|
摘要
多孔金属材料由于其微结构的特殊性和多样性,从而具有相当优异的力学特性和能量吸收能力。因此,多孔材料作为功能结构材料已在众多的工程实践中得到了广泛的应用。关于多孔金属材料的静态及准静态力学行为已经有了大量的研究和系统的认识,而对其动态力学行为的研究却相对较少。目前文献中对泡沫金属的动态行为和率敏感性效应有了较多的实验研究,但在对泡沫金属的应变率效应和惯性效应的相关认识中,尚存在着一些矛盾的结果。本论文中,为弄清多孔金属材料的率效应,我们通过数值模拟的手段,揭示了惯性效应、基体材料的应变强化效应和应变率效应对泡沫金属动态力学行为的影响。另外,为进一步理解多孔材料的变形传播行为,我们还提出了两种对应于不同变形模式下的理论模型来说明其中出现的冲击波现象。
利用二维随机Voronoi技术,我们建立了不规则蜂窝的有限元模型。当蜂窝基体材料为弹性理想塑性时,有限元模拟的结果表明,蜂窝在不同的冲击速度之下将会发生三种变形模式。当冲击速度比较低时,蜂窝剪切变形带随机分布,其整体的宏观变形基本均匀,我们称之为准静态模式。当冲击速度足够高时,蜂窝的胞元几乎是逐层崩塌,在冲击面一侧形成很窄的剪切带,我们称之为动态模式或冲击模式。而当冲击速度介于准静态模式和冲击模式之间时,蜂窝的剪切变形带相对来说集中于冲击侧,形成较为局部的变形,并在整体上表现出梯度化,此时我们称之为过渡模式。经研究表明,当改变蜂窝的密度和基体材料的力学属性时,蜂窝仍然会发生上述三种变形模式,有所不同的是,对应不同变形模式的临界冲击速度将发生变化。
为了揭示惯性效应对多孔金属材料力学行为的影响,我们人为地改变了蜂窝试件基体材料的密度。数值试验的结果表明,当蜂窝的变形模式处于准静态均匀模式时,对于不同的冲击速度和基体材料密度,试件的名义应力应变曲线基本上是一致的。因此惯性效应并没有导致蜂窝应力应变关系的应变率敏感性。而在过渡模式和冲击模式之下,蜂窝平台应力将随着冲击速度的增大而显著增加。当降低蜂窝基体材料的密度时,三种变形模式之间的临界速度将明显提高,相对来说均匀的变形容易发生。此时在过渡模式和冲击模式下,蜂窝平台应力强度的增长会明显减小。由此可知,在中高冲击速度之下,惯性导致了蜂窝变形出现明显的局部化,促使平台应力的提高。因此多孔金属材料出现的率效应主要是由惯性引起的。与此同时,我们还研究了微惯性的影响,结果表明蜂窝微惯性的影响相对来说是可以忽略不计的。
为了进一步认清多孔金属材料的力学行为,我们还考察了基体材料属性对蜂窝动态压缩响应的影响,其中包括基体材料的应变强化效应和两种强度不同的应变率强化效应。基体材料的应变率效应对变形模式之间的临界速度影响不大,其引起的增幅大约在10%之内,但对蜂窝的平台应力会有所提高。在相同的应变率之下,蜂窝平台应力的相对增长要小于蜂窝基体材料屈服应力的相对增长。不同冲击速度下的平台应力的相对增长变化基本不大,且随着冲击速度的提高有减小的趋势。因此相对于惯性效应来说,应变率效应是可以忽略不计的。同时我们也考虑了基体材料应变强化效应对压缩行为的影响,相对于基体材料为弹性理想塑性的蜂窝来说,在不同冲击速度之下,由应变强化效应引起的平台应力的相对增长大约在5%左右,可见应变强化对蜂窝动态力学行为的影响是很微弱的。最后关于不同变形模式之间的临界速度也做了讨论,并且我们也估算了蜂窝在压缩时变形传播的冲击波波速。
本文还探讨了多孔材料在冲击压缩时变形会出现类似冲击波传播的现象。一方面,在众多的有关多孔金属材料高速冲击下的动态力学响应的研究中,都存在着一个共同的现象,即在试件的压缩波前处会出现大约只有一个胞元宽度大小的不连续区域,在此区域的两侧,应力、应变和质点速度都有明显地跳跃。此时多孔材料试件的冲击部分逐渐地被压垮几乎达到密实状态。另一方面,当多孔材料在中等速度冲击下,同样也在试件中压缩波前处存在一不连续区域,此刻多孔材料试件被压缩部分的名义应变会逐渐变小。为了能更好的解释这种现象存在的内在机理,基于应力波理论中的刚性卸载假设,对应于上述两种情况,我们建立了两个理论模型,分别为冲击模式模型和过渡模式模型。利用模型中冲击面处的位移连续条件,我们给出了两个模型的显式解。理论解结果表明,当多孔材料处于冲击模式时,模型中泡沫杆冲击端处的初始应力大小与冲击速度的平方成比例关系,而当多孔材料处于过渡模式时,初始应力将随着冲击速度成线性增长。根据理论模型,我们还给出了冲击模式发生的临界速度和从冲击模式到过渡模式的转变时间。最后,为了验证理论模型的正确性,我们进行了相关的数值验证,数值计算的结果与理论预测值符合得很好。
Cellular metals have considerably excellent mechanical properties and energy absorption capacity because of the specialty and variability of their micro structures. Therefore, cellular metals are widely used as advanced structural components in many engineering applications. The static and quasi-static mechanical behaviors of cellular metals have been studied substantially and systematically while the dynamic mechanical responses of them are relatively less researched. Although many experimental researches on the dynamic behavior and rate sensitivity of cellular metals have been reported in the literature, there are some conflicting conclusions on the strain-rate effect and the inertia effect of metallic foams. In order to know the role of rate effect in this paper, we conduct some numerical tests to explore the influence of inertia effect and strain hardening, strain-rate hardening of metal matrix on the behavior of cellular metals under impact compression. Moreover, for a deep understanding of the deformation propagating behavior, two theoretical models corresponding to different deformation modes are presented to reveal the inherent mechanism of this shock wave phenomenon.
Finite element model of irregular honeycomb samples is constructed using the 2D random Voronoi technique. When elastic-perfectly plastic model is adopted for the cell wall material, numerical simulations show that three types of deformation modes are observed. At a low impact velocity, the deformation of the honeycomb is macroscopically homogeneous with multiple random weak shear bands (the quasi-static mode). At a high impact velocity, the deformation mode is layer wise collapse near the impact surface (the shock or dynamic mode). A transition mode with gradual change of macroscopic strain exists for an intermediate impact velocity. It is also shown that when the density and cell-wall material properties of the honeycomb are changed, these three types of deformation modes are still happened, but the corresponding critical velocities are different.
To explore the effect of inertia, the density of the wall material is artificially reduced and it is found that when the honeycomb deformed in quasi-static mode, the stress-strain curves are nearly the same, regardless of the impact velocity and the matrix density. Hence the inertia effect will not cause strain-rate sensitivity of the stress-strain relation of the honeycomb. Nevertheless, the plateau stress in transition mode and shock mode increase significantly with the increase of impact velocity. As the matrix density decreases, the critical impact velocities of mode transition increase significantly, and the increase in plateau stress under the same impact velocity for both transition mode and shock mode reduces remarkably. It will be seen form this that due to the inertial effect, the deformation becomes inhomogeneous and localized, and the plateau stress on the impact interface increases rapidly when the impact velocity is moderate or high. So the rate effect of the cellular metals exhibited under high-velocity impact is mainly because of an inertia effect, rather than the strain-rate effect. Meanwhile, the effect of micro inertia is also studied and the results show that this effect is almost neglectable.
In order to further understand the mechanical behavior of cellular metals, we also study the influence of cell-wall material properties on their dynamic responses, including strain hardening effect and strain-rate hardening effect. It is found that strain-rate hardening effect of base metal has little influence to the mode transition velocities (increasing about 10%), and will cause a slight increase in the plateau stress. The relative increase in the plateau stress is less than the relative increase in yield stress of the matrix under the same strain rate. The increase in the plateau stress for different impact velocity is nearly the same, and usually decreases gradually with the increasing velocity, thus the influence at high impact velocities is neglectable, in comparison with the inertia effect. Meanwhile, the strain hardening effect of metal matrix is taken into account. In comparison with the elastic-perfectly plastic material, the relative increase in the plateau stress caused by the strain hardening effect is about 5%, so it is found that this effect has minor influence on the plateau stress under dynamic cases. Finally, the critical velocities between the three different deformation modes are discussed and we also evaluate the shock front propagation velocity during the compaction process.
On the one hand, among extensive studies of the dynamic responses of cellular materials under high impact velocity, there is a common phenomenon that a zone almost only one single-layer width of cell at the compaction front exists, across which the physical quantities such as stress, strain and velocity are apparently discontinuous. In this case, the compressed part of the cellular material is progressively crushed and almost densified. On the other hand, when the impact velocity is moderate, there also exists a discontinuity at the compaction front while the nominal strain of the compressed portion of the cellular metal is gradually getting smaller. To explore the inherent mechanism of this phenomenon, two models, viz. Transition-Mode model and Shock-Mode model, based on stress wave theory with a'rigid unloading' assumption are established, and their explicit solutions are obtained by using a supplemental relationship of the continuous condition at impact interface. The theoretical results show that the initial stress at the impact end of the foam rod is proportional to the square of the impact velocity when the cellular metal is deformed in Shock Mode but increases linearly with the increasing impact velocity in Transition Mode. The critical velocity for the occurrence of Shock Mode and the transition time when the deformation mode transformed from Shock Mode to Transition Mode are presented. Finally, numerical verifications based on finite element method were carried out and the results are compared well with the theoretical predictions by both the models.
利用二维随机Voronoi技术,我们建立了不规则蜂窝的有限元模型。当蜂窝基体材料为弹性理想塑性时,有限元模拟的结果表明,蜂窝在不同的冲击速度之下将会发生三种变形模式。当冲击速度比较低时,蜂窝剪切变形带随机分布,其整体的宏观变形基本均匀,我们称之为准静态模式。当冲击速度足够高时,蜂窝的胞元几乎是逐层崩塌,在冲击面一侧形成很窄的剪切带,我们称之为动态模式或冲击模式。而当冲击速度介于准静态模式和冲击模式之间时,蜂窝的剪切变形带相对来说集中于冲击侧,形成较为局部的变形,并在整体上表现出梯度化,此时我们称之为过渡模式。经研究表明,当改变蜂窝的密度和基体材料的力学属性时,蜂窝仍然会发生上述三种变形模式,有所不同的是,对应不同变形模式的临界冲击速度将发生变化。
为了揭示惯性效应对多孔金属材料力学行为的影响,我们人为地改变了蜂窝试件基体材料的密度。数值试验的结果表明,当蜂窝的变形模式处于准静态均匀模式时,对于不同的冲击速度和基体材料密度,试件的名义应力应变曲线基本上是一致的。因此惯性效应并没有导致蜂窝应力应变关系的应变率敏感性。而在过渡模式和冲击模式之下,蜂窝平台应力将随着冲击速度的增大而显著增加。当降低蜂窝基体材料的密度时,三种变形模式之间的临界速度将明显提高,相对来说均匀的变形容易发生。此时在过渡模式和冲击模式下,蜂窝平台应力强度的增长会明显减小。由此可知,在中高冲击速度之下,惯性导致了蜂窝变形出现明显的局部化,促使平台应力的提高。因此多孔金属材料出现的率效应主要是由惯性引起的。与此同时,我们还研究了微惯性的影响,结果表明蜂窝微惯性的影响相对来说是可以忽略不计的。
为了进一步认清多孔金属材料的力学行为,我们还考察了基体材料属性对蜂窝动态压缩响应的影响,其中包括基体材料的应变强化效应和两种强度不同的应变率强化效应。基体材料的应变率效应对变形模式之间的临界速度影响不大,其引起的增幅大约在10%之内,但对蜂窝的平台应力会有所提高。在相同的应变率之下,蜂窝平台应力的相对增长要小于蜂窝基体材料屈服应力的相对增长。不同冲击速度下的平台应力的相对增长变化基本不大,且随着冲击速度的提高有减小的趋势。因此相对于惯性效应来说,应变率效应是可以忽略不计的。同时我们也考虑了基体材料应变强化效应对压缩行为的影响,相对于基体材料为弹性理想塑性的蜂窝来说,在不同冲击速度之下,由应变强化效应引起的平台应力的相对增长大约在5%左右,可见应变强化对蜂窝动态力学行为的影响是很微弱的。最后关于不同变形模式之间的临界速度也做了讨论,并且我们也估算了蜂窝在压缩时变形传播的冲击波波速。
本文还探讨了多孔材料在冲击压缩时变形会出现类似冲击波传播的现象。一方面,在众多的有关多孔金属材料高速冲击下的动态力学响应的研究中,都存在着一个共同的现象,即在试件的压缩波前处会出现大约只有一个胞元宽度大小的不连续区域,在此区域的两侧,应力、应变和质点速度都有明显地跳跃。此时多孔材料试件的冲击部分逐渐地被压垮几乎达到密实状态。另一方面,当多孔材料在中等速度冲击下,同样也在试件中压缩波前处存在一不连续区域,此刻多孔材料试件被压缩部分的名义应变会逐渐变小。为了能更好的解释这种现象存在的内在机理,基于应力波理论中的刚性卸载假设,对应于上述两种情况,我们建立了两个理论模型,分别为冲击模式模型和过渡模式模型。利用模型中冲击面处的位移连续条件,我们给出了两个模型的显式解。理论解结果表明,当多孔材料处于冲击模式时,模型中泡沫杆冲击端处的初始应力大小与冲击速度的平方成比例关系,而当多孔材料处于过渡模式时,初始应力将随着冲击速度成线性增长。根据理论模型,我们还给出了冲击模式发生的临界速度和从冲击模式到过渡模式的转变时间。最后,为了验证理论模型的正确性,我们进行了相关的数值验证,数值计算的结果与理论预测值符合得很好。
Cellular metals have considerably excellent mechanical properties and energy absorption capacity because of the specialty and variability of their micro structures. Therefore, cellular metals are widely used as advanced structural components in many engineering applications. The static and quasi-static mechanical behaviors of cellular metals have been studied substantially and systematically while the dynamic mechanical responses of them are relatively less researched. Although many experimental researches on the dynamic behavior and rate sensitivity of cellular metals have been reported in the literature, there are some conflicting conclusions on the strain-rate effect and the inertia effect of metallic foams. In order to know the role of rate effect in this paper, we conduct some numerical tests to explore the influence of inertia effect and strain hardening, strain-rate hardening of metal matrix on the behavior of cellular metals under impact compression. Moreover, for a deep understanding of the deformation propagating behavior, two theoretical models corresponding to different deformation modes are presented to reveal the inherent mechanism of this shock wave phenomenon.
Finite element model of irregular honeycomb samples is constructed using the 2D random Voronoi technique. When elastic-perfectly plastic model is adopted for the cell wall material, numerical simulations show that three types of deformation modes are observed. At a low impact velocity, the deformation of the honeycomb is macroscopically homogeneous with multiple random weak shear bands (the quasi-static mode). At a high impact velocity, the deformation mode is layer wise collapse near the impact surface (the shock or dynamic mode). A transition mode with gradual change of macroscopic strain exists for an intermediate impact velocity. It is also shown that when the density and cell-wall material properties of the honeycomb are changed, these three types of deformation modes are still happened, but the corresponding critical velocities are different.
To explore the effect of inertia, the density of the wall material is artificially reduced and it is found that when the honeycomb deformed in quasi-static mode, the stress-strain curves are nearly the same, regardless of the impact velocity and the matrix density. Hence the inertia effect will not cause strain-rate sensitivity of the stress-strain relation of the honeycomb. Nevertheless, the plateau stress in transition mode and shock mode increase significantly with the increase of impact velocity. As the matrix density decreases, the critical impact velocities of mode transition increase significantly, and the increase in plateau stress under the same impact velocity for both transition mode and shock mode reduces remarkably. It will be seen form this that due to the inertial effect, the deformation becomes inhomogeneous and localized, and the plateau stress on the impact interface increases rapidly when the impact velocity is moderate or high. So the rate effect of the cellular metals exhibited under high-velocity impact is mainly because of an inertia effect, rather than the strain-rate effect. Meanwhile, the effect of micro inertia is also studied and the results show that this effect is almost neglectable.
In order to further understand the mechanical behavior of cellular metals, we also study the influence of cell-wall material properties on their dynamic responses, including strain hardening effect and strain-rate hardening effect. It is found that strain-rate hardening effect of base metal has little influence to the mode transition velocities (increasing about 10%), and will cause a slight increase in the plateau stress. The relative increase in the plateau stress is less than the relative increase in yield stress of the matrix under the same strain rate. The increase in the plateau stress for different impact velocity is nearly the same, and usually decreases gradually with the increasing velocity, thus the influence at high impact velocities is neglectable, in comparison with the inertia effect. Meanwhile, the strain hardening effect of metal matrix is taken into account. In comparison with the elastic-perfectly plastic material, the relative increase in the plateau stress caused by the strain hardening effect is about 5%, so it is found that this effect has minor influence on the plateau stress under dynamic cases. Finally, the critical velocities between the three different deformation modes are discussed and we also evaluate the shock front propagation velocity during the compaction process.
On the one hand, among extensive studies of the dynamic responses of cellular materials under high impact velocity, there is a common phenomenon that a zone almost only one single-layer width of cell at the compaction front exists, across which the physical quantities such as stress, strain and velocity are apparently discontinuous. In this case, the compressed part of the cellular material is progressively crushed and almost densified. On the other hand, when the impact velocity is moderate, there also exists a discontinuity at the compaction front while the nominal strain of the compressed portion of the cellular metal is gradually getting smaller. To explore the inherent mechanism of this phenomenon, two models, viz. Transition-Mode model and Shock-Mode model, based on stress wave theory with a'rigid unloading' assumption are established, and their explicit solutions are obtained by using a supplemental relationship of the continuous condition at impact interface. The theoretical results show that the initial stress at the impact end of the foam rod is proportional to the square of the impact velocity when the cellular metal is deformed in Shock Mode but increases linearly with the increasing impact velocity in Transition Mode. The critical velocity for the occurrence of Shock Mode and the transition time when the deformation mode transformed from Shock Mode to Transition Mode are presented. Finally, numerical verifications based on finite element method were carried out and the results are compared well with the theoretical predictions by both the models.
引文
[1]Gibson LJ, Ashby ME 1997. Cellular solids:Structure and Properties.2nd ed. UK: Cambridge University Press.
[2]Ashby MF. 1983. The mechanical properties of cellular solids. Metallurgical Transactions, 14A:1755-1769.
[3]Bellet D, Dolino G.1994. X-ray observation of porous-silicon wetting. Physical Review, B50:17-162.
[4]Bodig J, Jayne BA.1982. Mechanics of Wood and Wood Composites. New York:Van Nostrand Reinhold.
[5]Cunningham A, Sparrow DJ, Rosbotham ID, Nazelle D, Cauze GMR.1989. A fundamental study of the thermal conductivity ageing of rigid PUR foam blown with HFA-141b/CO2 and HFA-123/CO2 mixtures. Proceedings of the SPI 32nd Annual Conference, San Francisco,56-60.
[6]Lauriks W.1994. Acoustic characteristics of low density foams//Hilyard NC, Cunningham A, Chapman, Hall. Low Density Cellular Plastics. London.
[7]Kollman FFP, Cote WAJ.1968. Principles of Wood Science and Technology. Germany: Springer-Verlag, Berlin.
[8]Mills NJ.1994. Chapter 9//Hilyard NC, Cunningham A, Chapman, Hall. Low Density Cellular Plastics & Physical Basis of Behavior. London.
[9]奚正平,汤慧萍,张健,董领峰,王建永,汪强兵,朱纪磊.2009.烧结金属多孔材料.北京：冶金工业出版社.
[10]Wang XL, Lu TJ.1999. Optimized acoustic properties of cellular solids. Journal of Acoustical Society of America,106:756-765.
[11]Gu S, Lu TJ, Evans AG.2001. On the design of two-dimensional cellular metals for combined heat dissipation and structural load capacity. Journal of Heat and Mass Transfer, 44:2163-2175.
[12]Kim T, Zhao CY, Lu TJ, Hodson H.2004. Convective heat dissipation with lattice-frame materials. Mechanics of Materials,36:767-780.
[13]Lu TJ, Hess A, Ashby ME 1999. Sound absorption in metallic foams. Journal of Applied Physics,85:8528-7539.
[14]卢天健,何德坪,陈常青,赵长颖,方岱宁,王晓林.2006.超轻多孔金属材料的多功能特性及应用.力学进展,36(4)：517-535.
[15]Papka SD, Kyriakides S.1999. Biaxial crushing of honeycombs—Part Ⅰ:Experiments.
International Journal of Solids and Structures,36:4367-4396.
[16]Wallash JC, Gibson LJ.2001. Defect sensitivity of a 3D truss material. Scripta Materialia, 45:639-644.
[17]Sugimura Y, Meyer J, He MY, Bart-Smith H, Grenstedt J, Evans AG.1997. On the mechanical performance of closed cell Al alloy foams. Acta Materials,45(12):5245-5259.
[18]Chen C, Fleck NA, Lu TJ.2001. The mode I crack growth of metallic foams. Journal of the Mechanics and Physics of Solids,49:231-259.
[19]McCullough KYG, Fleck NA, Ashby MF. 1999. Toughness of aluminum alloy foams. Acta Materials,47:2331-2343.
[20]Ashby MF, Lu TJ.2003. Metal foams:a survey. Science in China (B),46(6):521-532.
[21]Wu CL, Sun CT.1996. Low velocity impact damage in composite sandwich beams. Composite Structures,34:21-27.
[22]Shuaeib FM, Soden PD.1997. Indentation failure of composite sandwich beams. Composite Science and Technology,57:1249-1259.
[23]Kim HS, Wierzbicki T.2000. Numerical and analytical study on deep biaxial bending collapse of thin-walled beams. International Journal of Mechanical Sciences,42: 1947-1970.
[24]Sokolinsky VS, Shen HB, Vaikhanski L, Nutt SR.2003. Experimental and analytical study of nonlinear bending response of sandwich beams. Composite Structures,60:219-229.
[25]Fleck NA, Deshpande VS.2004. The resistance of clamped sandwich beams to shock loading. Journal of Applied Mechanics,71:386-401.
[26]Yu JL, Wang EH, Li JR, Zheng ZJ.2008. Static and low-velocity impact behavior of sandwich beams with closed-cell aluminum-foam core in three-point bending. International Journal of Impact Engineering,35:885-894.
[27]Shim VPW, Yap KY.1997. Modeling impact deformation of foam-plate sandwich systems. International Journal of Impact Engineering,19(7):615-636.
[28]Meunier M, Shenoi RA.2001. Dynamic analysis of composite sandwich plates with damping modeled using high-order shear deformation theory. Composite Structures,54: 243-254.
[29]Bart-Smith H, Hutchinson JW, Fleck NA, Evans AG.2002. Influence of imperfections on the performance of metal foam core sandwich panels. International Journal of Solids and Structures,39:4999-5012.
[30]Pokharel N, Mahendran M.2004. Finite element analysis and design of sandwich panels subject to local buckling effects. Thin-walled Structures,42:589-611.
[31]Radford DD, McShane GJ, Deshpande VS, Fleck NA.2006. The response of clamped sandwich plates with metallic foam cores to simulated blast loading. International Journal of Solids and Structures,43:2243-2259.
[32]Dharmasena KP, Wadley HNG, Xue ZY, Hutchinson JW.2008. Mechanical response of metallic honeycomb panel structures to high-intensity dynamic loading. International Journal of Impact Engineering,35:1063-1074.
[33]Seitzberger M, Rammerstorfer FG, Degischer HP, Vienna, Gradinger R, Ranshofen, Austria.1997. Crushing of axially compressed steel tubes filled with aluminum foam. Acta Mechanica,125:93-105.
[34]Santosa SP, Wierzbicki T, Hanssen AG, Langseth M.2000. Experimental and numerical studies of foam-filled sections. International Journal of Impact Engineering,24:509-534.
[35]Mantena PR, Mann R.2003. Impact and dynamic response of high-density structural foams used as filler inside circular steel tube. Composite Structures,61:291-302.
[36]Aktay L, Toksoy AK, Guden M.2006. Quasi-static axial crushing of extruded polystyrene foam-filled thin-walled aluminum tubes:Experimental and numerical analysis. Materials and Design,27:556-565.
[37]Zhang X, Cheng GD.2007. A comparative study of energy absorption characteristics of foam-filled and multi-cell square columns. International Journal of Impact Engineering, 34:1739-1752.
[38]Mirfendereski L, Salimi M, Ziaei-Rad S.2008. Parametric study and numerical analysis of empty and foam-filled thin-walled tubes under static and dynamic loadings. International Journal of Mechanical Sciences,50:1042-1057.
[39]Wubben T, Stanzick H, Banhart J, Odenbach S.2003. Stability of metallic foams studied under microgravity. Journal of Physics:Condensed Matter,15:S427-S433.
[40]Feng Y, Zheng HW, Zhu ZG, Zu FQ.2002. The microstructures and electrical conductivity of aluminum alloy foams. Materials Chemistry and Physics,78:196-201.
[41]Norman A, Fleck NA.2004. An overview of the mechanical properties of foams and periodic lattice materials, the 4th International Conference on Fracture:Symposium on Cellular Metals and Polymers. Germany.
[42]Roberts AP, Garboczi EJ.2002. Computation of the linear elastic properties of random porous materials with a wide variety of microstructure. Mathematical Physical and Engineering Sciences, A458(2021):1033-1054.
[43]Elzey DM, Wadley HNG.2001. The limits of solid state foaming. Acta Materials,49: 849-859.
[44]Banhart J, Bellmann D, Clemens H.2001. Investigation of metal foam formation by microscopy and ultra small-angle neutron scattering. Acta materials,49:3409-3420.
[45]Sanders WS, Gibson LJ.2003. Mechanics of BBC and FCC hollow-sphere foams. Materials Science and Engineering, A352:150-161.
[46]Banhart J, Stanzick H.2001. Metal foam evolution studied by synchrotron radioscopy. Applied Physics Letters,78(8):1152-1154.
[47]Hutchinson JW, He MY.2000. Buckling of cylindrical sandwich shells with metal foam core. International Journal of Solids and Structures,37:6777-6794.
[48]Neugebaver R, Hipke T.2006. Machine tools with metal foams. Advanced Engineering Materials,8(9):858-863.
[49]Schwingel D, Seeliger HW, Vecchionacci C, Alwes D, Dittrich J.2007. Aluminium foam sandwich structures for space applications. Acta Astronautica,61:326-330.
[50]Rajendran R, Prem Sai K, Chandrasekar B, Gokhale A, Basu S.2008. Preliminary investigation of aluminum foam as an energy absorber for nuclear transportation cask. Materials and Design,29:1732-1739.
[51]Stobener K, Rausch G.2009. Aluminium foam-polymer composites:processing and characteristics. Journal of Materials Science,44:1506-1511.
[52]Banhart J, Baumeister MW.1995. Powder metallurgical technology for the production of metallic foams. Proceedings of the powder Metallurgy European Congress Euro PM95, 201-208.
[53]Banhart J.2001. Manufacture, characterization and application of cellular metals and metal foams. Progress in Materials Science,46:559-632.
[54]Evan AG.1999. Multi-functional of cellular metal systems. Progress in Materials Science, 43:171-221.
[55]Lu TJ, Vaide vit L, Evans AG.2005. Active cooling by metallic sandwich structures with periodic cores. Progress in Material Science,50:789-815.
[56]Ashby MF, Evans AG, Fleck NA, Gibson LJ, Hutchinson JW, Wadley HNG.2000. Metal Foam:a design guide. Wobum:Butterworth-Heinemann.
[57]Banhart J. Fleck NA, Ashby MF.2000. Metal foams special issue. Advanced Engineering Materials,2(4).
[58]Degischer HP, Kriszt B.2002. Handbook of cellular metals:Production, Processing, Applications. KGaA:Wiley-VCH Verlag GmbH & Company.
[59]Crowson C.1998. Materials issues in impact engineering, the 3rd International Symposium on Impact Engineering, Singapore.
[60]Zhu HX, Knott JF, Mills NJ.1997. Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells. Journal of the Mechanics and Physics of Solids,45: 319-325.
[61]Zhu HX, Mills NJ, Knott JF.1997. Analysis of the high strain compression of open-cell foams. Journal of the Mechanics and Physics of Solids,45:326-343.
[62]Warren WE, Kraynik AM.1997. Linear elastic behavior of a low-density Kelvin foam with open cells. ASME Journal of Applied Mechanics,64:787-794.
[63]Warren WE, Kraynik AM.1987. Foam mechanics:the linear elastic response of two-dimensional spatially periodic cellular materials. Mechanics of Materials,6:27-37.
[64]Roberts Ap, Garboczi EJ.2001. Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Materialia,49:189-197.
[65]Grenestedt JL.1998. Influence of wavy imperfections in cell walls on elastic stiffness of cellular solids. Journal of the Mechanics and Physics of Solids,46:29-50.
[66]Deshpande VS, Fleck NA, Ashby MF.2001. Effective properties of the octet-truss material. Journal of the Mechanics and Physics of Solids,49:1747-1769.
[67]Hutchinson RG, Wicks N, Evans AG, Fleck NA, Hutchinson JW.2003. Kagome plate structures for actuation. International Journal of Solids and Structures,40:6969-6980.
[68]Gan YX, Chen C, Shen YP.2005. Three dimensional modeling of the mechanical property of elastomeric open cell foams. International Journal of Solids and Structures,42: 6628-6642.
[69]Gong L, Kyriakides S.2005 Compressive response of open-cell foams. Part II:Initiation and spreading of crushing. International Journal of Solids and Structures,42:1381-1399.
[70]Roberts AP, Garboczi EJ.2002. Elastic properties of model random three-dimensional open-ell solids. Journal of the Mechanics and Physics of Solids,50:33-55.
[71]Bart-Smith H, Bastawros AF, Mumm DR, Evans AG, Sypeck DJ, Wadley HNG.1998. Compression deformation and yielding mechanisms in cellular AL alloys determined using X-ray tomography and surface strain mapping. Acta materialia,46(10):3583-3592.
[72]Grenestedt JL.1998. Influence of cell shape variations on elastic stiffness of closed cell cellular solids. Scripta Materialia,40(1):71-77.
[73]Andrews EW, Sanders W, Gibson LJ.1999. Compressive and tensile behavior of aluminum foams. Materials Science and Engineering A,270(2):113-124.
[74]Miyoshi T, Itoh M, Mukai T, Kanahashi H, Kohzu S, Tanabe S, Higashi K.1999. Enhancement of energy absorption in a closed-cell aluminum by the modification of cellular structures. Scripta Materialia,41(10):1055-1060.
[75]Andrews EW, Gioux G, Onck P, Gibson LJ.2001. Size effects in ductile cellular solids, Part II:Experimental results. International Journal of Mechanical Sciences,43:701-713.
[76]Onck PR, Andrews EW, Gibson LJ.2001. Size effects in ductile cellular solids Part I: modeling. International Journal of Mechanical Sciences,43:681-699.
[77]Li JR, Cheng HF, Yu JL, Han FS.2003. Effect of dual-size cell mix on the stiffness and strength of open-cell aluminum foams. Materials Science and Engineering, A362: 240-248.
[78]Klocker T.1999. Image analysis of metallic foams:[Ph. D.]. Austria:Vienna University of Technology.
[79]Chan KC, Xie LS.2003. Dependency of densification properties on cell topology of metal foams. Scripta Materialia,48:1147-1152.
[80]Ableidinger A.2000. Some aspects of the fracture behavior of metal foams:[Ph. D.]. Austria:Vienna University of Technology.
[81]Silva MJ, Hayes WC, Gibson LJ.1995. The effect of non-periodic microstructure on the elastic properties of two-dimensional cellular solids. International Journal of Mechanical Sciences,37:1161-1177.
[82]Chen C, Lu TJ, Fleck NA.1999. Effect of imperfections on the yielding of two-dimensional foams. Journal of the Mechanics and Physics of Solids,47:2235-2272.
[83]Zhu HX, Hobdell JR, Windle AH.2000. Effects of cell irregularity on the elastic properties of open-cell foams. Acta Materialia,48:4893-4900.
[84]Deshpande VS, Fleck NA.2000. Isotropic constitutive models for metallic foams. Journal of the Mechanics and Physics of Solids,48:1253-1283.
[85]Gibson LJ, Ashby MF, Zhang J, Triantafillou TC.1989. Failure surface for cellular materials under multiaxial loads:I modeling. International Journal of Mechanical Sciences, 31:635-663.
[86]Miller RE.2000. A continuum plasticity model for the constitutive and indentation behavior of foamed metals. International Journal of Mechanical Sciences,42:729-754.
[87]Chen C, Lu TJ.2000. A phenomenological framework of constitutive modeling for incompressible and compressible elastoplasctic solids. International Journal of Solids and Structures,37:7769-7786.
[88]Hanssen AG, Hopperstad OS, Langseth M, Ilstad H.2002. Validation of constitutive models applicable to aluminium foams. International Journal of Mechanical Sciences,44: 359-406.
[89]Chen C, Fleck NA.2002. Size effect in the constrained deformation of metallic foams.
Journal of the Mechanics and Physics of Solids,50:955-977.
[90]Chen JY, Huang Y, Ortiz M.1998. Fracture analysis of cellular materials:a strain gradient model. Journal of the Mechanics and Physics of Solids,46:789-828.
[91]Wang XL, Stronge WJ.1999. Micropolar theory for two-dimensional stresses in elastic honeycomb. Proceedings of the Royal Society of London, A455:2091-2116.
[92]Kumar RS, McDowell DL.2004. Generalized continuum modeling of 2-D periodic cellular solids. International Journal of Solids and Structures,41:7399-7422.
[93]Lu GX, Yu TX.2003. Energy absorption of structures and materials. UK:Woodhead Publishing Limited.
[94]Wang ZP.1994. Growth of voids in porous ductile materials at high strain rate. Journal of Applied Physics,67(3):1535-1542.
[95]Reid SR, Peng C.1997. Dynamic uniaxial crushing of wood. International Journal of Impact Engineering,19(5-6):531-570.
[96]Mukai T, Kanahashi H, Miyoshi T, Mabuchi M, Nieh TG, Higashi K.1999. Experimental study of energy absorption in a close-celled aluminum foam under dynamic loading. Scripta Materialia,40(8):921-927.
[97]Harrigan JJ, Reid SR, Peng C.1999. Inertia effects in impact energy absorbing materials and structures. International Journal of Impact Engineering,22:955-979.
[98]Hall IW, Guden M, Yu CJ.2000. Crushing of aluminum closed cell foams:density and strain rate effects. Scripta Materialia,43:515-521.
[99]Deshpande VS, Fleck NA.1999. High strain rate compressive behavior of aluminium alloy foams. International Journal of Impact Engineering,24:277-298.
[100]Dannemann KA, Lankford JJ.2000. High strain rate compression of closed-cell aluminium foams. Materials Science and Engineering, A239:157-164.
[101]Paul A, Ramamurty U.2000. Strain rate sensitivity of a closed-cell aluminum foam. Materials Science and Engineering, A281:1-7.
[102]Lopatnikov SL, Gama BA, Haque MJ, Krauthauser C, Guden M, Hall IW, Gillespie JW. 2003. Dynamics of metal foam deformation during Taylor Cylinder-Hopkinson bar impact experiment. Composite Structures,61:61-71.
[103]Lopatnikov SL, Gama BA, Haque MJ, Krauthauser C, Gillespie JW.2004. High-velocity plate impact of metal foams. International Journal of Impact Engineering,30:421-445.
[104]Yi F, Zhu ZG.2001. Dynamic compressive behavior of aluminum alloy foams. Journal of Materials Science Letters,20:1667-1668.
[105]Yi F, Zhu ZG, Zu FQ, Hu SS, Yi P.2001. Strain rate effects on the compressive property
and the energy-absorbing capacity of aluminum alloy foams. Material Characterization,47: 417-422.
[106]Kanahashi H, Mukai T, Yamada Y, Shimojima K, Mabuchi M, Aizawa T, Higashi K.2001. Experimental study for the improvement of crashworthiness in AZ91 magnesium foam controlling its microstructure. Materials Science and Engineering, A308:283-287.
[107]Ruan D, Lu G, Chen FL, Siores E.2002. Compressive behavior of aluminium foams at low and medium strain rates. Composite Structures,57:331-336.
[108]Zhang YF, Tang YZ, Zhou G, Wei JN, Han FS.2002. Dynamic compressin properties of porous aluminum. Materials Letters,56:728-731.
[109]Park C, Nutt SR.2002. Strain rate sensitivity and defects in steel foam. Materials Science and Engineering, A323:358-366.
[110]Zhao H, Elnasri I, Abdennadher S.2005. An experimental study on the behavior under impact loading of metallic cellular materials. International Journal of Mechanical Sciences, 47:757-774.
[111]Bartl F, Dallner R, Meyer W.2005. Experimental and numerical investigations of selected cellular solids at higher strain rates. KGaA:Wiley-VCH Verlag GmbH & Company,36(6): 254-263.
[112]Kitazono K, Takiguchi Y.2006. Strain rate sensitivity and energy absorption of Zn-22A1 foams. Scripta Materialia,55:501-504.
[113]Sadot O, Anteby I, Harush S, Levintant O, Nizri E, Ostraich B, Schenker A, Gal E, Kivity Y, Ben-Dor G.2005. Experimental investigation of dynamic properties of aluminum foams. ASCE Journal of Structural Engineering,131(8):1226-1232.
[114]Cao XQ, Wang ZH, Ma HW, Zhao LM, Yang GT.2006. Effects of cell size on compressive properties of aluminum foam. Transaction of Nonferrous Metals Society of China,16:351-356.
[115]Wang ZH, Ma HE, Zhao LM, Yang GT.2006. Studies on the dynamic compressive properties of open-cell aluminum alloy foams. Scripta Materialia,54:83-87.
[116]Han FS, Cheng HF, Li ZH, Wang Q.2005. The strain rate effect of an open cell aluminum foam. Metallurgical and Materials Transaction, A36:645-650.
[117]Lee S, Barthelat F, Moldovan N, Espinosa HD, Wadley HNG.2006. Deformation rate effects on failure modes of open-cell Al foams and textile cellular materials. International Journal of Solids and Structures,43:53-73.
[118]Tan PJ, Harrigan JJ, Reid SR.2002. Inertia effects in uniaxial dynamic compression of a closed cell aluminum alloy foam. Materials Science and Technology,18:480-488.
[119]Tan PJ, Reid SR, Harrigan JJ, Zou Z, Li S.2005. Dynamic compressive strength properties of aluminum foams. Part I—experimental data and observations. Journal of the Mechanics and Physics of Solids,53:2174-2205.
[120]Tan PJ, Reid SR, Harrigan JJ, Zou Z, Li S.2005. Dynamic compressive strength properties of aluminum foams. Part II—‘shock’theory and comparison with experimental data and numerical models. Journal of the Mechanics and Physics of Solids,53: 2206-2230.
[121]Yu JL, Wang EH, Li JR.2008. An experimental study on the quasi-static and dynamic behavior of aluminum foams under multi-axial compression//Fan JH, Chen HB. Advances in Heterogeneous Material Mechanics. Lancaster:DEStech Publications, 879-882.
[122]Zhao H, Gary G, Klepaczko JR.1997. On the use of a viscoelastic split hopkinson pressure bar. International Journal of Impact Engineering,19:319-330.
[123]Daxner T, Bohm HJ, Rammerstorfer FG.1999. Mesoscopic simulation of inhomogeneous metallic foams with respect to energy absorption. Computational Materials Science,16: 61-69.
[124]Mukai T, Miyoshi T, Nakano S, Somekawa H, Higashi K.2005. Compressive response of a closed-cell aluminum foam at high strain rate. Scripta Materialia,54:533-537.
[125]Lankford J, Dannemann KA.1998. Strain rate effects in porous materials//Swartz DS, Shih DS, Evans AG, Wadley HNG. Porous and Cellular Materials for Structural Applications. Materials Research Society Proceedings,521:103-108.
[126]Kanahashi H, Mukai T, Yamada Y, Shimojima K, Mabuchi M, Nieh TG, Higashi K.2000. Dynamic compression of an ultra-low density aluminium foam. Materials Science and Engineering, A280:349-353.
[127]Zhu HX, Thorpe SM, Windle AH.2001. The geometrical properties of irregular two-dimensional Voronoi tessellations. Philosophy Magazine, A81(12):2765-2783.
[128]Zheng ZJ, Yu JL, Li JR.2005. Dynamic crushing of 2D cellular structures:A finite element study. International Journal of Impact Engineering,32(1-4):650-664.
[129]Calladine CR.1983. An investigation of impact scaling theory//Jones N, Wierzbicki T. Structural Crashworthiness. London:Butterworths,169-174.
[130]Booth E, Collier D, Miles J.1983. Impact scalability of plated steel structures//Jones N, Wierzbicki T. Structural Crashworthiness. London:Butterworths,136-175.
[131]Zhang TG, Yu TX.1989. A note on a'velocity sensitive'energy-absorbing structure. International Journal of Impact Engineering,8:43-51.
[132]Zhu HX, Hobdell JR, Windle AH.2001. Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs. Journal of the Mechanics and Physics of Solids,49: 857-870.
[133]Tekoglu C, Onck PR.2005. Size effects in the mechanical behavior of cellular materials. Journal of Materials Science,40:5911-5917.
[134]Tekoglu C, Onck PR.2008. Size effects in two-dimensional Voronoi foams:A comparison between generalized continua and discrete models. Journal of the Mechanics and Physics of Solids,56:3541-3564.
[135]Ruan D, Lu G, Wang B, Yu TX.2003. In-plane dynamic crushing of honeycombs—a finite element study. International Journal of Impact Engineering,28:161-182.
[136]Zou Z, Reid SR, Tan PJ, Li S, Harrigan JJ.2009. Dynamic crushing of honeycombs and features of shock fronts. International Journal of Impact Engineering,36:165-176.
[137]Ma GW, Ye ZQ, Shao ZS.2009. Modeling loading rate effect on crushing stress of metallic cellular materials. International Journal of Impact Engineering,36:775-782.
[138]Johnson GR, Cook WH.1983. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the Seventh International Symposium on Ballistics. Netherlands:the Hague,541-547.
[139]Li K, Gao XL, Wang J.2007. Dynamic crushing behavior of honeycomb structures with irregular cell shapes and non-uniform cell wall thickness. International Journal of Solids and Structures,44:5003-5026.
[140]Pattofatto S, Elnasri I, Zhao H, Tsitsiris H, Hild F, Girard Y.2007. Shock enhancement of cellular structures under impact loading:Part II analysis. Journal of the Mechanics and Physics of Solids,55:2672-2686.
[141]Li QM, Reid SR.2006. About one-dimensional shock propagation in a cellular material. International Journal of Impact and Engineering,32:1898-1906.
[142]Zhao H, Gary G.1998. Crushing behavior of aluminium honeycombs under impact loadings. International Journal of Impact Engineering,21:827-836.
[143]Montanini R.2005. Measurement of strain rate sensitivity of aluminium foams for energy dissipation. International Journal of Mechanical Sciences,47:26-42.
[144]Reid SR, Bell WW, Barr RA.1983. Structural plastic shock model for one-dimensional ring system. International Journal of Impact and Engineering,1:175-191.
[145]Shim VP, Tay BY, Stronge WJ.1990. Dynamic crushing of strain-softening cellular structures—a one-dimensional analysis. ASME Journal of Engineering Materials and Technology,112:398-405.
[146]Li QM, Meng H.2002. Attenuation or enhancement —a one-dimensional analysis on shock transmission in the solid phase of cellular material. International Journal of Impact and Engineering,27:1049-1065.
[147]Harrigan JJ, Reid SR, Yaghoubi AS.2009. The correct analysis of shocks in a cellular material. International Journal of Impact and Engineering, In Press.
[148]Liu YD, Yu JL, Zheng ZJ, Li JR.2009. A numerical study on the rate sensitivity of cellular metals. International Journal of Solids and Structures,46:3988-3998.
[149]Wang LL.2007. Foundations of stress waves. Amsterdam:Elsevier Science Limited.
[150]Papka SD, Kyriakides S.1994. In-plane compressive response and crushing of honeycomb. Journal of Mechanics and Physics of Solids,42:1499-1532.
[151]Papka SD, Kyriakides S.1998. Experiments and full-scale numerical simulations of in-plane crushing of a honeycomb. Acta Materialia,46:2765-2776.
[152]Gao ZY, Yu TX, Lu G.2005. A study on type Ⅱ structures, part I:a one-dimensional model. International Journal of Impact Engineering,31(7):895-910.
[153]Gao ZY, Yu TX, Lu G.2005. A study on type II structures, part II:behavior of a chain of pre-bent plates. International Journal of Impact Engineering,31(7):911-926.
[2]Ashby MF. 1983. The mechanical properties of cellular solids. Metallurgical Transactions, 14A:1755-1769.
[3]Bellet D, Dolino G.1994. X-ray observation of porous-silicon wetting. Physical Review, B50:17-162.
[4]Bodig J, Jayne BA.1982. Mechanics of Wood and Wood Composites. New York:Van Nostrand Reinhold.
[5]Cunningham A, Sparrow DJ, Rosbotham ID, Nazelle D, Cauze GMR.1989. A fundamental study of the thermal conductivity ageing of rigid PUR foam blown with HFA-141b/CO2 and HFA-123/CO2 mixtures. Proceedings of the SPI 32nd Annual Conference, San Francisco,56-60.
[6]Lauriks W.1994. Acoustic characteristics of low density foams//Hilyard NC, Cunningham A, Chapman, Hall. Low Density Cellular Plastics. London.
[7]Kollman FFP, Cote WAJ.1968. Principles of Wood Science and Technology. Germany: Springer-Verlag, Berlin.
[8]Mills NJ.1994. Chapter 9//Hilyard NC, Cunningham A, Chapman, Hall. Low Density Cellular Plastics & Physical Basis of Behavior. London.
[9]奚正平,汤慧萍,张健,董领峰,王建永,汪强兵,朱纪磊.2009.烧结金属多孔材料.北京：冶金工业出版社.
[10]Wang XL, Lu TJ.1999. Optimized acoustic properties of cellular solids. Journal of Acoustical Society of America,106:756-765.
[11]Gu S, Lu TJ, Evans AG.2001. On the design of two-dimensional cellular metals for combined heat dissipation and structural load capacity. Journal of Heat and Mass Transfer, 44:2163-2175.
[12]Kim T, Zhao CY, Lu TJ, Hodson H.2004. Convective heat dissipation with lattice-frame materials. Mechanics of Materials,36:767-780.
[13]Lu TJ, Hess A, Ashby ME 1999. Sound absorption in metallic foams. Journal of Applied Physics,85:8528-7539.
[14]卢天健,何德坪,陈常青,赵长颖,方岱宁,王晓林.2006.超轻多孔金属材料的多功能特性及应用.力学进展,36(4)：517-535.
[15]Papka SD, Kyriakides S.1999. Biaxial crushing of honeycombs—Part Ⅰ:Experiments.
International Journal of Solids and Structures,36:4367-4396.
[16]Wallash JC, Gibson LJ.2001. Defect sensitivity of a 3D truss material. Scripta Materialia, 45:639-644.
[17]Sugimura Y, Meyer J, He MY, Bart-Smith H, Grenstedt J, Evans AG.1997. On the mechanical performance of closed cell Al alloy foams. Acta Materials,45(12):5245-5259.
[18]Chen C, Fleck NA, Lu TJ.2001. The mode I crack growth of metallic foams. Journal of the Mechanics and Physics of Solids,49:231-259.
[19]McCullough KYG, Fleck NA, Ashby MF. 1999. Toughness of aluminum alloy foams. Acta Materials,47:2331-2343.
[20]Ashby MF, Lu TJ.2003. Metal foams:a survey. Science in China (B),46(6):521-532.
[21]Wu CL, Sun CT.1996. Low velocity impact damage in composite sandwich beams. Composite Structures,34:21-27.
[22]Shuaeib FM, Soden PD.1997. Indentation failure of composite sandwich beams. Composite Science and Technology,57:1249-1259.
[23]Kim HS, Wierzbicki T.2000. Numerical and analytical study on deep biaxial bending collapse of thin-walled beams. International Journal of Mechanical Sciences,42: 1947-1970.
[24]Sokolinsky VS, Shen HB, Vaikhanski L, Nutt SR.2003. Experimental and analytical study of nonlinear bending response of sandwich beams. Composite Structures,60:219-229.
[25]Fleck NA, Deshpande VS.2004. The resistance of clamped sandwich beams to shock loading. Journal of Applied Mechanics,71:386-401.
[26]Yu JL, Wang EH, Li JR, Zheng ZJ.2008. Static and low-velocity impact behavior of sandwich beams with closed-cell aluminum-foam core in three-point bending. International Journal of Impact Engineering,35:885-894.
[27]Shim VPW, Yap KY.1997. Modeling impact deformation of foam-plate sandwich systems. International Journal of Impact Engineering,19(7):615-636.
[28]Meunier M, Shenoi RA.2001. Dynamic analysis of composite sandwich plates with damping modeled using high-order shear deformation theory. Composite Structures,54: 243-254.
[29]Bart-Smith H, Hutchinson JW, Fleck NA, Evans AG.2002. Influence of imperfections on the performance of metal foam core sandwich panels. International Journal of Solids and Structures,39:4999-5012.
[30]Pokharel N, Mahendran M.2004. Finite element analysis and design of sandwich panels subject to local buckling effects. Thin-walled Structures,42:589-611.
[31]Radford DD, McShane GJ, Deshpande VS, Fleck NA.2006. The response of clamped sandwich plates with metallic foam cores to simulated blast loading. International Journal of Solids and Structures,43:2243-2259.
[32]Dharmasena KP, Wadley HNG, Xue ZY, Hutchinson JW.2008. Mechanical response of metallic honeycomb panel structures to high-intensity dynamic loading. International Journal of Impact Engineering,35:1063-1074.
[33]Seitzberger M, Rammerstorfer FG, Degischer HP, Vienna, Gradinger R, Ranshofen, Austria.1997. Crushing of axially compressed steel tubes filled with aluminum foam. Acta Mechanica,125:93-105.
[34]Santosa SP, Wierzbicki T, Hanssen AG, Langseth M.2000. Experimental and numerical studies of foam-filled sections. International Journal of Impact Engineering,24:509-534.
[35]Mantena PR, Mann R.2003. Impact and dynamic response of high-density structural foams used as filler inside circular steel tube. Composite Structures,61:291-302.
[36]Aktay L, Toksoy AK, Guden M.2006. Quasi-static axial crushing of extruded polystyrene foam-filled thin-walled aluminum tubes:Experimental and numerical analysis. Materials and Design,27:556-565.
[37]Zhang X, Cheng GD.2007. A comparative study of energy absorption characteristics of foam-filled and multi-cell square columns. International Journal of Impact Engineering, 34:1739-1752.
[38]Mirfendereski L, Salimi M, Ziaei-Rad S.2008. Parametric study and numerical analysis of empty and foam-filled thin-walled tubes under static and dynamic loadings. International Journal of Mechanical Sciences,50:1042-1057.
[39]Wubben T, Stanzick H, Banhart J, Odenbach S.2003. Stability of metallic foams studied under microgravity. Journal of Physics:Condensed Matter,15:S427-S433.
[40]Feng Y, Zheng HW, Zhu ZG, Zu FQ.2002. The microstructures and electrical conductivity of aluminum alloy foams. Materials Chemistry and Physics,78:196-201.
[41]Norman A, Fleck NA.2004. An overview of the mechanical properties of foams and periodic lattice materials, the 4th International Conference on Fracture:Symposium on Cellular Metals and Polymers. Germany.
[42]Roberts AP, Garboczi EJ.2002. Computation of the linear elastic properties of random porous materials with a wide variety of microstructure. Mathematical Physical and Engineering Sciences, A458(2021):1033-1054.
[43]Elzey DM, Wadley HNG.2001. The limits of solid state foaming. Acta Materials,49: 849-859.
[44]Banhart J, Bellmann D, Clemens H.2001. Investigation of metal foam formation by microscopy and ultra small-angle neutron scattering. Acta materials,49:3409-3420.
[45]Sanders WS, Gibson LJ.2003. Mechanics of BBC and FCC hollow-sphere foams. Materials Science and Engineering, A352:150-161.
[46]Banhart J, Stanzick H.2001. Metal foam evolution studied by synchrotron radioscopy. Applied Physics Letters,78(8):1152-1154.
[47]Hutchinson JW, He MY.2000. Buckling of cylindrical sandwich shells with metal foam core. International Journal of Solids and Structures,37:6777-6794.
[48]Neugebaver R, Hipke T.2006. Machine tools with metal foams. Advanced Engineering Materials,8(9):858-863.
[49]Schwingel D, Seeliger HW, Vecchionacci C, Alwes D, Dittrich J.2007. Aluminium foam sandwich structures for space applications. Acta Astronautica,61:326-330.
[50]Rajendran R, Prem Sai K, Chandrasekar B, Gokhale A, Basu S.2008. Preliminary investigation of aluminum foam as an energy absorber for nuclear transportation cask. Materials and Design,29:1732-1739.
[51]Stobener K, Rausch G.2009. Aluminium foam-polymer composites:processing and characteristics. Journal of Materials Science,44:1506-1511.
[52]Banhart J, Baumeister MW.1995. Powder metallurgical technology for the production of metallic foams. Proceedings of the powder Metallurgy European Congress Euro PM95, 201-208.
[53]Banhart J.2001. Manufacture, characterization and application of cellular metals and metal foams. Progress in Materials Science,46:559-632.
[54]Evan AG.1999. Multi-functional of cellular metal systems. Progress in Materials Science, 43:171-221.
[55]Lu TJ, Vaide vit L, Evans AG.2005. Active cooling by metallic sandwich structures with periodic cores. Progress in Material Science,50:789-815.
[56]Ashby MF, Evans AG, Fleck NA, Gibson LJ, Hutchinson JW, Wadley HNG.2000. Metal Foam:a design guide. Wobum:Butterworth-Heinemann.
[57]Banhart J. Fleck NA, Ashby MF.2000. Metal foams special issue. Advanced Engineering Materials,2(4).
[58]Degischer HP, Kriszt B.2002. Handbook of cellular metals:Production, Processing, Applications. KGaA:Wiley-VCH Verlag GmbH & Company.
[59]Crowson C.1998. Materials issues in impact engineering, the 3rd International Symposium on Impact Engineering, Singapore.
[60]Zhu HX, Knott JF, Mills NJ.1997. Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells. Journal of the Mechanics and Physics of Solids,45: 319-325.
[61]Zhu HX, Mills NJ, Knott JF.1997. Analysis of the high strain compression of open-cell foams. Journal of the Mechanics and Physics of Solids,45:326-343.
[62]Warren WE, Kraynik AM.1997. Linear elastic behavior of a low-density Kelvin foam with open cells. ASME Journal of Applied Mechanics,64:787-794.
[63]Warren WE, Kraynik AM.1987. Foam mechanics:the linear elastic response of two-dimensional spatially periodic cellular materials. Mechanics of Materials,6:27-37.
[64]Roberts Ap, Garboczi EJ.2001. Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Materialia,49:189-197.
[65]Grenestedt JL.1998. Influence of wavy imperfections in cell walls on elastic stiffness of cellular solids. Journal of the Mechanics and Physics of Solids,46:29-50.
[66]Deshpande VS, Fleck NA, Ashby MF.2001. Effective properties of the octet-truss material. Journal of the Mechanics and Physics of Solids,49:1747-1769.
[67]Hutchinson RG, Wicks N, Evans AG, Fleck NA, Hutchinson JW.2003. Kagome plate structures for actuation. International Journal of Solids and Structures,40:6969-6980.
[68]Gan YX, Chen C, Shen YP.2005. Three dimensional modeling of the mechanical property of elastomeric open cell foams. International Journal of Solids and Structures,42: 6628-6642.
[69]Gong L, Kyriakides S.2005 Compressive response of open-cell foams. Part II:Initiation and spreading of crushing. International Journal of Solids and Structures,42:1381-1399.
[70]Roberts AP, Garboczi EJ.2002. Elastic properties of model random three-dimensional open-ell solids. Journal of the Mechanics and Physics of Solids,50:33-55.
[71]Bart-Smith H, Bastawros AF, Mumm DR, Evans AG, Sypeck DJ, Wadley HNG.1998. Compression deformation and yielding mechanisms in cellular AL alloys determined using X-ray tomography and surface strain mapping. Acta materialia,46(10):3583-3592.
[72]Grenestedt JL.1998. Influence of cell shape variations on elastic stiffness of closed cell cellular solids. Scripta Materialia,40(1):71-77.
[73]Andrews EW, Sanders W, Gibson LJ.1999. Compressive and tensile behavior of aluminum foams. Materials Science and Engineering A,270(2):113-124.
[74]Miyoshi T, Itoh M, Mukai T, Kanahashi H, Kohzu S, Tanabe S, Higashi K.1999. Enhancement of energy absorption in a closed-cell aluminum by the modification of cellular structures. Scripta Materialia,41(10):1055-1060.
[75]Andrews EW, Gioux G, Onck P, Gibson LJ.2001. Size effects in ductile cellular solids, Part II:Experimental results. International Journal of Mechanical Sciences,43:701-713.
[76]Onck PR, Andrews EW, Gibson LJ.2001. Size effects in ductile cellular solids Part I: modeling. International Journal of Mechanical Sciences,43:681-699.
[77]Li JR, Cheng HF, Yu JL, Han FS.2003. Effect of dual-size cell mix on the stiffness and strength of open-cell aluminum foams. Materials Science and Engineering, A362: 240-248.
[78]Klocker T.1999. Image analysis of metallic foams:[Ph. D.]. Austria:Vienna University of Technology.
[79]Chan KC, Xie LS.2003. Dependency of densification properties on cell topology of metal foams. Scripta Materialia,48:1147-1152.
[80]Ableidinger A.2000. Some aspects of the fracture behavior of metal foams:[Ph. D.]. Austria:Vienna University of Technology.
[81]Silva MJ, Hayes WC, Gibson LJ.1995. The effect of non-periodic microstructure on the elastic properties of two-dimensional cellular solids. International Journal of Mechanical Sciences,37:1161-1177.
[82]Chen C, Lu TJ, Fleck NA.1999. Effect of imperfections on the yielding of two-dimensional foams. Journal of the Mechanics and Physics of Solids,47:2235-2272.
[83]Zhu HX, Hobdell JR, Windle AH.2000. Effects of cell irregularity on the elastic properties of open-cell foams. Acta Materialia,48:4893-4900.
[84]Deshpande VS, Fleck NA.2000. Isotropic constitutive models for metallic foams. Journal of the Mechanics and Physics of Solids,48:1253-1283.
[85]Gibson LJ, Ashby MF, Zhang J, Triantafillou TC.1989. Failure surface for cellular materials under multiaxial loads:I modeling. International Journal of Mechanical Sciences, 31:635-663.
[86]Miller RE.2000. A continuum plasticity model for the constitutive and indentation behavior of foamed metals. International Journal of Mechanical Sciences,42:729-754.
[87]Chen C, Lu TJ.2000. A phenomenological framework of constitutive modeling for incompressible and compressible elastoplasctic solids. International Journal of Solids and Structures,37:7769-7786.
[88]Hanssen AG, Hopperstad OS, Langseth M, Ilstad H.2002. Validation of constitutive models applicable to aluminium foams. International Journal of Mechanical Sciences,44: 359-406.
[89]Chen C, Fleck NA.2002. Size effect in the constrained deformation of metallic foams.
Journal of the Mechanics and Physics of Solids,50:955-977.
[90]Chen JY, Huang Y, Ortiz M.1998. Fracture analysis of cellular materials:a strain gradient model. Journal of the Mechanics and Physics of Solids,46:789-828.
[91]Wang XL, Stronge WJ.1999. Micropolar theory for two-dimensional stresses in elastic honeycomb. Proceedings of the Royal Society of London, A455:2091-2116.
[92]Kumar RS, McDowell DL.2004. Generalized continuum modeling of 2-D periodic cellular solids. International Journal of Solids and Structures,41:7399-7422.
[93]Lu GX, Yu TX.2003. Energy absorption of structures and materials. UK:Woodhead Publishing Limited.
[94]Wang ZP.1994. Growth of voids in porous ductile materials at high strain rate. Journal of Applied Physics,67(3):1535-1542.
[95]Reid SR, Peng C.1997. Dynamic uniaxial crushing of wood. International Journal of Impact Engineering,19(5-6):531-570.
[96]Mukai T, Kanahashi H, Miyoshi T, Mabuchi M, Nieh TG, Higashi K.1999. Experimental study of energy absorption in a close-celled aluminum foam under dynamic loading. Scripta Materialia,40(8):921-927.
[97]Harrigan JJ, Reid SR, Peng C.1999. Inertia effects in impact energy absorbing materials and structures. International Journal of Impact Engineering,22:955-979.
[98]Hall IW, Guden M, Yu CJ.2000. Crushing of aluminum closed cell foams:density and strain rate effects. Scripta Materialia,43:515-521.
[99]Deshpande VS, Fleck NA.1999. High strain rate compressive behavior of aluminium alloy foams. International Journal of Impact Engineering,24:277-298.
[100]Dannemann KA, Lankford JJ.2000. High strain rate compression of closed-cell aluminium foams. Materials Science and Engineering, A239:157-164.
[101]Paul A, Ramamurty U.2000. Strain rate sensitivity of a closed-cell aluminum foam. Materials Science and Engineering, A281:1-7.
[102]Lopatnikov SL, Gama BA, Haque MJ, Krauthauser C, Guden M, Hall IW, Gillespie JW. 2003. Dynamics of metal foam deformation during Taylor Cylinder-Hopkinson bar impact experiment. Composite Structures,61:61-71.
[103]Lopatnikov SL, Gama BA, Haque MJ, Krauthauser C, Gillespie JW.2004. High-velocity plate impact of metal foams. International Journal of Impact Engineering,30:421-445.
[104]Yi F, Zhu ZG.2001. Dynamic compressive behavior of aluminum alloy foams. Journal of Materials Science Letters,20:1667-1668.
[105]Yi F, Zhu ZG, Zu FQ, Hu SS, Yi P.2001. Strain rate effects on the compressive property
and the energy-absorbing capacity of aluminum alloy foams. Material Characterization,47: 417-422.
[106]Kanahashi H, Mukai T, Yamada Y, Shimojima K, Mabuchi M, Aizawa T, Higashi K.2001. Experimental study for the improvement of crashworthiness in AZ91 magnesium foam controlling its microstructure. Materials Science and Engineering, A308:283-287.
[107]Ruan D, Lu G, Chen FL, Siores E.2002. Compressive behavior of aluminium foams at low and medium strain rates. Composite Structures,57:331-336.
[108]Zhang YF, Tang YZ, Zhou G, Wei JN, Han FS.2002. Dynamic compressin properties of porous aluminum. Materials Letters,56:728-731.
[109]Park C, Nutt SR.2002. Strain rate sensitivity and defects in steel foam. Materials Science and Engineering, A323:358-366.
[110]Zhao H, Elnasri I, Abdennadher S.2005. An experimental study on the behavior under impact loading of metallic cellular materials. International Journal of Mechanical Sciences, 47:757-774.
[111]Bartl F, Dallner R, Meyer W.2005. Experimental and numerical investigations of selected cellular solids at higher strain rates. KGaA:Wiley-VCH Verlag GmbH & Company,36(6): 254-263.
[112]Kitazono K, Takiguchi Y.2006. Strain rate sensitivity and energy absorption of Zn-22A1 foams. Scripta Materialia,55:501-504.
[113]Sadot O, Anteby I, Harush S, Levintant O, Nizri E, Ostraich B, Schenker A, Gal E, Kivity Y, Ben-Dor G.2005. Experimental investigation of dynamic properties of aluminum foams. ASCE Journal of Structural Engineering,131(8):1226-1232.
[114]Cao XQ, Wang ZH, Ma HW, Zhao LM, Yang GT.2006. Effects of cell size on compressive properties of aluminum foam. Transaction of Nonferrous Metals Society of China,16:351-356.
[115]Wang ZH, Ma HE, Zhao LM, Yang GT.2006. Studies on the dynamic compressive properties of open-cell aluminum alloy foams. Scripta Materialia,54:83-87.
[116]Han FS, Cheng HF, Li ZH, Wang Q.2005. The strain rate effect of an open cell aluminum foam. Metallurgical and Materials Transaction, A36:645-650.
[117]Lee S, Barthelat F, Moldovan N, Espinosa HD, Wadley HNG.2006. Deformation rate effects on failure modes of open-cell Al foams and textile cellular materials. International Journal of Solids and Structures,43:53-73.
[118]Tan PJ, Harrigan JJ, Reid SR.2002. Inertia effects in uniaxial dynamic compression of a closed cell aluminum alloy foam. Materials Science and Technology,18:480-488.
[119]Tan PJ, Reid SR, Harrigan JJ, Zou Z, Li S.2005. Dynamic compressive strength properties of aluminum foams. Part I—experimental data and observations. Journal of the Mechanics and Physics of Solids,53:2174-2205.
[120]Tan PJ, Reid SR, Harrigan JJ, Zou Z, Li S.2005. Dynamic compressive strength properties of aluminum foams. Part II—‘shock’theory and comparison with experimental data and numerical models. Journal of the Mechanics and Physics of Solids,53: 2206-2230.
[121]Yu JL, Wang EH, Li JR.2008. An experimental study on the quasi-static and dynamic behavior of aluminum foams under multi-axial compression//Fan JH, Chen HB. Advances in Heterogeneous Material Mechanics. Lancaster:DEStech Publications, 879-882.
[122]Zhao H, Gary G, Klepaczko JR.1997. On the use of a viscoelastic split hopkinson pressure bar. International Journal of Impact Engineering,19:319-330.
[123]Daxner T, Bohm HJ, Rammerstorfer FG.1999. Mesoscopic simulation of inhomogeneous metallic foams with respect to energy absorption. Computational Materials Science,16: 61-69.
[124]Mukai T, Miyoshi T, Nakano S, Somekawa H, Higashi K.2005. Compressive response of a closed-cell aluminum foam at high strain rate. Scripta Materialia,54:533-537.
[125]Lankford J, Dannemann KA.1998. Strain rate effects in porous materials//Swartz DS, Shih DS, Evans AG, Wadley HNG. Porous and Cellular Materials for Structural Applications. Materials Research Society Proceedings,521:103-108.
[126]Kanahashi H, Mukai T, Yamada Y, Shimojima K, Mabuchi M, Nieh TG, Higashi K.2000. Dynamic compression of an ultra-low density aluminium foam. Materials Science and Engineering, A280:349-353.
[127]Zhu HX, Thorpe SM, Windle AH.2001. The geometrical properties of irregular two-dimensional Voronoi tessellations. Philosophy Magazine, A81(12):2765-2783.
[128]Zheng ZJ, Yu JL, Li JR.2005. Dynamic crushing of 2D cellular structures:A finite element study. International Journal of Impact Engineering,32(1-4):650-664.
[129]Calladine CR.1983. An investigation of impact scaling theory//Jones N, Wierzbicki T. Structural Crashworthiness. London:Butterworths,169-174.
[130]Booth E, Collier D, Miles J.1983. Impact scalability of plated steel structures//Jones N, Wierzbicki T. Structural Crashworthiness. London:Butterworths,136-175.
[131]Zhang TG, Yu TX.1989. A note on a'velocity sensitive'energy-absorbing structure. International Journal of Impact Engineering,8:43-51.
[132]Zhu HX, Hobdell JR, Windle AH.2001. Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs. Journal of the Mechanics and Physics of Solids,49: 857-870.
[133]Tekoglu C, Onck PR.2005. Size effects in the mechanical behavior of cellular materials. Journal of Materials Science,40:5911-5917.
[134]Tekoglu C, Onck PR.2008. Size effects in two-dimensional Voronoi foams:A comparison between generalized continua and discrete models. Journal of the Mechanics and Physics of Solids,56:3541-3564.
[135]Ruan D, Lu G, Wang B, Yu TX.2003. In-plane dynamic crushing of honeycombs—a finite element study. International Journal of Impact Engineering,28:161-182.
[136]Zou Z, Reid SR, Tan PJ, Li S, Harrigan JJ.2009. Dynamic crushing of honeycombs and features of shock fronts. International Journal of Impact Engineering,36:165-176.
[137]Ma GW, Ye ZQ, Shao ZS.2009. Modeling loading rate effect on crushing stress of metallic cellular materials. International Journal of Impact Engineering,36:775-782.
[138]Johnson GR, Cook WH.1983. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the Seventh International Symposium on Ballistics. Netherlands:the Hague,541-547.
[139]Li K, Gao XL, Wang J.2007. Dynamic crushing behavior of honeycomb structures with irregular cell shapes and non-uniform cell wall thickness. International Journal of Solids and Structures,44:5003-5026.
[140]Pattofatto S, Elnasri I, Zhao H, Tsitsiris H, Hild F, Girard Y.2007. Shock enhancement of cellular structures under impact loading:Part II analysis. Journal of the Mechanics and Physics of Solids,55:2672-2686.
[141]Li QM, Reid SR.2006. About one-dimensional shock propagation in a cellular material. International Journal of Impact and Engineering,32:1898-1906.
[142]Zhao H, Gary G.1998. Crushing behavior of aluminium honeycombs under impact loadings. International Journal of Impact Engineering,21:827-836.
[143]Montanini R.2005. Measurement of strain rate sensitivity of aluminium foams for energy dissipation. International Journal of Mechanical Sciences,47:26-42.
[144]Reid SR, Bell WW, Barr RA.1983. Structural plastic shock model for one-dimensional ring system. International Journal of Impact and Engineering,1:175-191.
[145]Shim VP, Tay BY, Stronge WJ.1990. Dynamic crushing of strain-softening cellular structures—a one-dimensional analysis. ASME Journal of Engineering Materials and Technology,112:398-405.
[146]Li QM, Meng H.2002. Attenuation or enhancement —a one-dimensional analysis on shock transmission in the solid phase of cellular material. International Journal of Impact and Engineering,27:1049-1065.
[147]Harrigan JJ, Reid SR, Yaghoubi AS.2009. The correct analysis of shocks in a cellular material. International Journal of Impact and Engineering, In Press.
[148]Liu YD, Yu JL, Zheng ZJ, Li JR.2009. A numerical study on the rate sensitivity of cellular metals. International Journal of Solids and Structures,46:3988-3998.
[149]Wang LL.2007. Foundations of stress waves. Amsterdam:Elsevier Science Limited.
[150]Papka SD, Kyriakides S.1994. In-plane compressive response and crushing of honeycomb. Journal of Mechanics and Physics of Solids,42:1499-1532.
[151]Papka SD, Kyriakides S.1998. Experiments and full-scale numerical simulations of in-plane crushing of a honeycomb. Acta Materialia,46:2765-2776.
[152]Gao ZY, Yu TX, Lu G.2005. A study on type Ⅱ structures, part I:a one-dimensional model. International Journal of Impact Engineering,31(7):895-910.
[153]Gao ZY, Yu TX, Lu G.2005. A study on type II structures, part II:behavior of a chain of pre-bent plates. International Journal of Impact Engineering,31(7):911-926.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |