一种有负泊松比效应的二维多胞材料力学模型

卢子兴; 赵亚斌

一种有负泊松比效应的二维多胞材料力学模型

北京航空航天大学航空科学与工程学院, 北京 100083

基金项目: NSAF联合基金资助项目(10276004);北京市教育委员会共建项目建设计划资助项目(XK100060522)

详细信息

作者简介:
卢子兴(1960-),男,河北枣强人,教授, luzixing@263.net.

中图分类号: TB 383; O 341
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- 被引次数: 0
出版历程
- 收稿日期: 2005-05-12
- 网络出版日期: 2006-05-31

Mechanical model of two-dimensional cellular materials with negative Poisson’s ratio

School of Aeronautic Science and Technology, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

摘要

摘要: 负泊松比多胞材料具有独特的力学性能,有着良好的应用前景.基于旋转机制,提出了一种具有负泊松比效应的、由部分内凹以及部分规则六边形组成的二维多胞材料力学模型;预测了模型的泊松比及刚度系数随角度的变化关系,计算了该模型的剪应变,并通过能量法给出了其弹性本构方程.结果表明:该力学模型不但能产生负的泊松比,而且还可导致大于1的正泊松比及呈现"负刚度"特征;通过调整模型胞壁长度的比值和特征角的大小可以改变模型的刚度系数.这些结果对二维多胞材料的微结构设计具有一定的工程参考价值.
- 多胞材料 /
- 泡沫 /
- 负泊松比 /
- 刚度 /
- 本构关系
Abstract: Cellular materials with negative Poisson’s ratio have unique mechanical performance and a promising prospect of applications. A mechanical model of two-dimensional cellular materials with negative Poisson’s ratio, composed of partly re-entrant and partly regular hexagons, was proposed based on rotation mechanism. The relationships of both Poisson’s ratio and sitiffness coefficients with the angles were predicted. The shear strain of the model was obtained. Energy method was used to develop the elastic constitutive equations. Results show that the mechanical model gave rise to not only a negative Poisson’s ratio, but also a positive one greater than 1 and performed a characteristic of negative stiffness. The stiffness coefficients of the model could be altered by adjusting the ratio of the cell ribs length and the characteristic angle. The results are useful for designing the microstructures of two-dimensional cellular materials.
- cellular materials /
- foam /
- negative Poisson’s ratio /
- stiffness /
- constitutive relationship

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参考文献(1)

[1] Friis E A, Lakes R S, Park J B. Negative Poisson's ratio polymeric and metallic foams[J]. Journal of Materials Science,1988,23(12):4406-4414 [2] Lakes R S. Deformation mechanisms in negative Poisson’s ratio materials:structural aspects[J]. Journal of Materials Science,1991,26(9):2287-2292 [3] Almgren R F. An isotropic three-dimensional structure with Poisson’s ratio=-1[J]. Journal of Elasticity,1985,15(4):427-430 [4] Warren T L. Negative Poisson’s ratio in transversely isotropic foam structure [J]. Journal of Applied Physics,1990,67(12):7591-7594 [5] Masters I G, Evans K E. Models for the elastic deformation of honeycombs[J]. Composite Structures, 1996, 35(4):403-422 [6] Lim T C. Material structure for attaining pure Poisson-shearing[J]. Journal of Materials Science Letters, 2002, 21(20):1595-1597 [7] Lim T C. Constitutive relationship of a material with unconventional Poisson’s ratio[J]. Journal of Materials Science Letters, 2003, 22(24):1783-1786 [8] Wan Hui, Ohtaki H, Kotosaka S, et al. A study of negative Poisson’s ratios in auxetic honeycombs based on a large deflection model[J]. European Journal of Mechanics A/Solids, 2004, 23(1):95-106 [9] Smith C W, Grima J N, Evans K E. A novel mechanism for auxetic behavior in reticulated foams:missing rib foam model[J]. Acta Materialia, 2000, 48(17):4349-4356 [10] Alderson A, Evans K E. Microstructural modelling of auxetic microporous polymers[J]. Journal of Materials Science, 1995, 30(13):3319-3332 [11] Prall D, Lakes R S. Properties of a chiral honeycomb with a Poisson's ratio of-1[J]. Int J Mech Sci, 1997, 39(3):305-314 [12] Nye J F. Physical properties of crystals[M]. Oxford:Oxford University Press, 1985 [13] Lee T, Lakes R S. Anisotropic polyurethane foam with Poisson’s ratio greater than 1[J]. Journal of Materials Science, 1997, 32(9):2397-2401 [14] Chan N, Evans K E. Microscopic examination of the microstructure and deformation of conventional and auxetic foams[J]. Journal of Materials Science, 1997, 32(21):5725-5736 [15] Brandel B, Lakes R S. Negative Poisson’s ratio polyethylene foams[J]. Journal of Materials Science, 2001, 36(24):5885-5893

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