理想线弹性体的泊松比

Poisson’s Ratio of Ideal Linear Elastomer

摘要: 小变形下，基于体积不变假设，材料的泊松比上限为0.5，在大变形下材料泊松比的取值鲜有讨论。通过建立理想线弹性体的弹簧模型，认为体积比和泊松比均为拉伸比的独立变量，和应力模式无关。在大形变过程中，体积是变化的，变化趋势取决于初始泊松比的大小。泊松比的取值范围是(0, ∞)。当初始泊松比小于0.5时，拉伸时体积先增加后减小，压缩时体积减小；当初始泊松比大于0.5时，拉伸时体积减小，压缩时体积先增大后减小；当初始泊松比等于0.5时，拉伸或压缩时体积均减小。因此理论上应存在压缩体胀和拉伸体缩的超材料。

Abstract: Under small deformation, based on the assumption of constant volume, the upper limit of Poisson’s ratio is 0.5. Under large deformation, the value of Poisson’s ratio is rarely discussed. By establishing the spring model of ideal linear elastomer, it is considered that the volume ratio and Poisson’s ratio are independent variables of tensile ratio and independent of stress mode. In the process of large deformation, the volume changes, and the change trend depends on the initial Poisson’s ratio. The range of Poisson’s ratio is (0, ∞). When the initial Poisson’s ratio is less than 0.5, the volume in-creases first and then decreases in tension and decreases in compression; When the initial Poisson’s ratio is greater than 0.5, the volume decreases in tension and increases first and then decreases in compression; When the initial Poisson’s ratio is equal to 0.5, the volume decreases in tension or compression. Therefore, in theory, there should be metamaterials with compressive volume expan-sion and tensile volume contraction.