理想弹性体体积模量二维与三维不一致原因分析

Analysis of the inconsistency between two and three-dimensional expressions for bulk modulus of idealized elastomer

体积模量是理想弹性体固有的材料属性,本不应随线弹性体所处的应力空间而变化,但体积模量的表达出现了二维与三维的不一致,且在二维中,它还出现了平面应力状态和平面应变状态各不相同的现象。从线弹性本构理论出发,找出了体积模量随应力空间维数变化的原因,系体积模量在不同维应力空间存在截然不同的定义所致,从而提出了使其在各维应力空间保持一致的解决办法。

Bulk modulus is an inherent material property of idealized elastomer which should maintain the same expression in stress space of all dimension. However, there is an obvious difference for the expression of bulk modulus between 2 D and 3 D, moreover, the expression of the bulk modulus in plane stress is also different from it in plane strain. Based on the linear elastic constitutive theory, the ultimate cause of the difference is found out that the different definitions of bulk modulus are adopted in 2 D and 3 D. Then a method is suggested to keep bulk modulus consistent in stress space of all dimension.