负泊松比蜂窝材料的动力学响应及能量吸收特性
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摘要
针对传统正方形蜂窝,通过用更小的双向内凹结构胞元替代原蜂窝材料的结构节点,得到了一种具有负泊松比特性的节点层级蜂窝材料模型。利用显式动力有限元方法,研究了冲击荷载作用下该负泊松比蜂窝结构的动力学响应及能量吸收特性。研究结果表明,除了冲击速度和相对密度,负泊松比蜂窝材料的动力学性能亦取决于胞元微结构。与正方形蜂窝相比,该负泊松比层级蜂窝材料的动态承载能力和能量吸收能力明显增强。在中低速冲击下,试件表现为拉胀材料明显的"颈缩"现象,并展示出负泊松比材料独特的平台应力增强效应。基于能量吸收效率方法和一维冲击波理论,给出了负泊松比蜂窝材料的密实应变和动态平台应力的经验公式,以预测该蜂窝材料的动态承载能力。本文的研究将为负泊松比多胞材料冲击动力学性能的多目标优化设计提供新的设计思路。
In this work,for the traditional square honeycombs,we obtained a joint-based hierarchical honeycomb model with the negative Poisson's ratio( NPR) by replacing the structural nodes of the original honeycombs having smaller inner concave structures. We numerically investigated the dynamic responses and energy absorption characteristics of these honeycombs with NPR under in-plane crushing using the explicit dynamic finite element analysis( DFEA),revealing that,apart from the impact velocity and the relative density,the inplane dynamic properties of the honeycombs also depend upon the cell micro-structure. Compared with those of the square honeycombs,the dynamic strengths and energy absorption abilities of these honeycombs are obviously improved. Under low or moderate velocity crushing,the specimens exhibit the obvious"neck shrinkage"phenomenon of auxetic materials,and show the unique plateau stress enhancement effect. Based on the energy absorption efficiency method and the one-dimensional shockwave theory,the empirical formulae of densification strain and dynamic plateau stress were given to predict the dynamic load-bearing capacity of the honeycombs with NPR. Our study can serve as a guidance for the multi-objective optimal dynamic design of auxetic cellular materials.
In this work,for the traditional square honeycombs,we obtained a joint-based hierarchical honeycomb model with the negative Poisson's ratio( NPR) by replacing the structural nodes of the original honeycombs having smaller inner concave structures. We numerically investigated the dynamic responses and energy absorption characteristics of these honeycombs with NPR under in-plane crushing using the explicit dynamic finite element analysis( DFEA),revealing that,apart from the impact velocity and the relative density,the inplane dynamic properties of the honeycombs also depend upon the cell micro-structure. Compared with those of the square honeycombs,the dynamic strengths and energy absorption abilities of these honeycombs are obviously improved. Under low or moderate velocity crushing,the specimens exhibit the obvious"neck shrinkage"phenomenon of auxetic materials,and show the unique plateau stress enhancement effect. Based on the energy absorption efficiency method and the one-dimensional shockwave theory,the empirical formulae of densification strain and dynamic plateau stress were given to predict the dynamic load-bearing capacity of the honeycombs with NPR. Our study can serve as a guidance for the multi-objective optimal dynamic design of auxetic cellular materials.
引文
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[5]张新春,祝晓燕,李娜.六韧带手性蜂窝结构的动力学响应特性研究[J].振动与冲击,2016,35(8):1-7.DOI:10.13465/j.cnki.jvs.2016.08.001.ZHANG Xinchun,ZHU Xiaoyan,LI Na.A study of the dynamic response characteristics of hexagonal chiral honeycombs[J].Journal of Vibration and Shock,2016,35(8):1-7.DOI:10.13465/j.cnki.jvs.2016.08.001.
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[7]张伟,侯文彬,胡平.新型负泊松比多孔吸能盒平台区力学性能[J].复合材料学报,2015,32(2):534-541.DOI:10.13801/j.cnki.fhclxb.20140616.003.ZHANG Wei,HOU Wenbin,HU Ping.Mechanical properties of new negative Poisson's ratio crush box with cellular structure in plateau stage[J].Acta Materiae Compositae Sinica,2015,32(2):534-541.DOI:10.13801/j.cnki.fhclxb.20140616.003.
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[9]ZHANG X C,AN L Q,DING H M,et al.The influence of cell micro-structure on the in-plane dynamic crushing of honeycombs with negative Poisson's ratio[J].Journal of Sandwich Structures and Materials,2015,17(1):26-55.DOI:10.1177/1099636214554180.
[10]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.DOI:10.1016/S0734-743X(02)00056-8.
[11]LIU Y,ZHANG X C.The influence of cell micro-topology on the in-plane dynamic crushing of honeycombs[J].International Journal of Impact Engineering,2009,36(1):98-109.DOI:10.1016/j.ijimpeng.2008.03.001.
[12]QIU X M,ZHANG J,YU T X.Collapse of periodic planar lattices under uniaxial compression,PartⅡ:Dynamic crushing based on finite element simulation[J].International Journal of Impact Engineering,2009,36(10):1231-1241.DOI:10.1016/j.ijimpeng.2009.05.010.
[13]ZHANG X C,AN L Q,DING H M.Dynamic crushing behavior and energy absorption of honeycombs with density gradient[J].Journal of Sandwich Structures and Materials,2014,16(2):125-147.DOI:10.1177/1099636213509099.
[14]SUN D,ZHANG W,ZHAO Y,et al.In-plane crushing and energy absorption performance of multi-layer regularly arranged circular honeycombs[J].Composite Structures,2013,96(2):726-735.DOI:10.1016/j.compstruct.2012.10.008.
[15]ZHOU G,MA Z D,GU J,et al.Design optimization of a NPR structure based on HAM optimization method[J].Structural and Multidisciplinary Optimization,2016,53(3):635-643.DOI:10.1007/s00158-015-1341-x.
[16]胡玲玲,蒋玲.胞孔构型对金属蜂窝动态力学性能的影响机理[J].爆炸与冲击,2014,34(1):41-46.DOI:10.3969/j.issn.1001-1455.2014.01.008.HU Lingling,JIANG Ling.Mechanism of cell configuration affecting dynamic mechanical properties of metal honeycombs[J].Explosion and Shock Waves,2014,34(1):41-46.DOI:10.3969/j.issn.1001-1455.2014.01.008.
[2]余同希,邱信明.冲击动力学[M].北京:清华大学出版社,2011:197-220.
[3]GIBSON L J,ASHBY M F.Cellular solids:Structure and properties[M].Cambridge:Cambridge University Press,1997:1-13.
[4]PRALL D,LAKES R S.Properties of a chiral honeycomb with a Poisson's ratio of-1[J].International Journal of Mechanical Sciences,1997,39(3):305-314.DOI:10.1016/S0020-7403(96)00025-2.
[5]张新春,祝晓燕,李娜.六韧带手性蜂窝结构的动力学响应特性研究[J].振动与冲击,2016,35(8):1-7.DOI:10.13465/j.cnki.jvs.2016.08.001.ZHANG Xinchun,ZHU Xiaoyan,LI Na.A study of the dynamic response characteristics of hexagonal chiral honeycombs[J].Journal of Vibration and Shock,2016,35(8):1-7.DOI:10.13465/j.cnki.jvs.2016.08.001.
[6]SCARPA F,SMITH C W,RUZZENE M,et al.Mechanical properties of auxetic tubular truss-like structures[J].Physica Status Solid,2008,245(3):584-590.DOI:10.1002/pssb.200777715.
[7]张伟,侯文彬,胡平.新型负泊松比多孔吸能盒平台区力学性能[J].复合材料学报,2015,32(2):534-541.DOI:10.13801/j.cnki.fhclxb.20140616.003.ZHANG Wei,HOU Wenbin,HU Ping.Mechanical properties of new negative Poisson's ratio crush box with cellular structure in plateau stage[J].Acta Materiae Compositae Sinica,2015,32(2):534-541.DOI:10.13801/j.cnki.fhclxb.20140616.003.
[8]QIAO J X,CHEN C Q.Impact resistance of uniform and functionally graded auxetic double arrowhead honeycombs[J].International Journal of Impact Engineering,2015,83(9):47-58.DOI:10.1016/j.ijimpeng.2015.04.005.
[9]ZHANG X C,AN L Q,DING H M,et al.The influence of cell micro-structure on the in-plane dynamic crushing of honeycombs with negative Poisson's ratio[J].Journal of Sandwich Structures and Materials,2015,17(1):26-55.DOI:10.1177/1099636214554180.
[10]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.DOI:10.1016/S0734-743X(02)00056-8.
[11]LIU Y,ZHANG X C.The influence of cell micro-topology on the in-plane dynamic crushing of honeycombs[J].International Journal of Impact Engineering,2009,36(1):98-109.DOI:10.1016/j.ijimpeng.2008.03.001.
[12]QIU X M,ZHANG J,YU T X.Collapse of periodic planar lattices under uniaxial compression,PartⅡ:Dynamic crushing based on finite element simulation[J].International Journal of Impact Engineering,2009,36(10):1231-1241.DOI:10.1016/j.ijimpeng.2009.05.010.
[13]ZHANG X C,AN L Q,DING H M.Dynamic crushing behavior and energy absorption of honeycombs with density gradient[J].Journal of Sandwich Structures and Materials,2014,16(2):125-147.DOI:10.1177/1099636213509099.
[14]SUN D,ZHANG W,ZHAO Y,et al.In-plane crushing and energy absorption performance of multi-layer regularly arranged circular honeycombs[J].Composite Structures,2013,96(2):726-735.DOI:10.1016/j.compstruct.2012.10.008.
[15]ZHOU G,MA Z D,GU J,et al.Design optimization of a NPR structure based on HAM optimization method[J].Structural and Multidisciplinary Optimization,2016,53(3):635-643.DOI:10.1007/s00158-015-1341-x.
[16]胡玲玲,蒋玲.胞孔构型对金属蜂窝动态力学性能的影响机理[J].爆炸与冲击,2014,34(1):41-46.DOI:10.3969/j.issn.1001-1455.2014.01.008.HU Lingling,JIANG Ling.Mechanism of cell configuration affecting dynamic mechanical properties of metal honeycombs[J].Explosion and Shock Waves,2014,34(1):41-46.DOI:10.3969/j.issn.1001-1455.2014.01.008.