一种有负泊松比效应的二维多胞材料力学模型

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

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.

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.