含孔橡胶矩形板的单向压缩

Uniaxial compression of a rectangular rubber plate with a single void

在船舶和海洋工程领域,以橡胶材料为代表的超弹性材料应用越来越广泛,故研究橡胶材料的损伤和破坏的力学机理是一个非常现实的重大课题.该文力求通过研究橡胶材料的空穴萌生和增长来了解超弹性材料的损伤和破坏的力学机理.利用高玉臣给出的一类应变能函数分析了含单个微孔橡胶矩形板在受单向压缩作用下生长的有限变形问题.利用不可压缩条件确定了矩形板的变形模式,此变形模式含有2个物理意义完全不一样的参数,其中一个参数可由远场的变形状态确定,另一个参数可用最小势能原理导出变分近似解.进而给出了反映微孔变形的参数与外载间的关系,以及孔边应力分布的解析解.结果显示,高玉臣给出的应变能函数能较好地描述橡胶材料的有限变形特性,含有单个圆柱微孔的三维橡胶矩形板受压与受拉时的力学特性相差较大.

The use of hyperelastic materials, of which rubber materials are representative, is widespread in the field of naval architecture and ocean engineering. This makes it important to study the mechanical process of damage and failure of rubber materials. We studied this issue by analyzing the advent and growth of voids in rubber materials. With the help of a class of strain energy functions proposed by Y. C. Gao, the finite deformation of a rectangular rubber plate with a single void subjected to uniaxial compression was examined. Using the assumption that it is incompressible, the deformation mode of the rubber rectangular plate was determined. There are two parameters with completely different physical meanings in this mode, one parameter can be determined by the state of deformation in the remote field, and the other can obtain an approximate solution using the minimum potential energy principle. Furthermore, the relationship between the parameters related to the deformation of the void and the exterior load was analyzed, and an analytic solution of the stress distribution around the edge of the void was also obtained. The resuits indicated that the strain energy function proposed by Y. C. Gao can appropriately describe the finite deformation behavior of rubber materials, and that a rectangular rubber plate displays distinct mechanical properties in uniaxial compression and in uniaxial extension.