多孔Mooney-Rivlin材料矩形板的单向拉伸

本文利用不同可压超弹性材料大变形的Mooney-Rivlin应变能函数研究了含有多个微孔的矩形板在单向拉伸作用下的有限变形和受力分析。首先利用不可压条件得到了文中所给的含有某种对称性分布的多个微孔的矩形板的变形模式函数，其中所含的一个参数可由远离微孔的无穷远处的变形状态确定，另一个参可用最小势能原理导出变分近似解。文中详细分析了板中微孔（一个，三个和五个）随载荷作用的增长情况和微孔边缘应力的分布情况，并进行了比较。讨论了微孔的个数和排列方式，微孔的孔间距离等因素对微孔增长和应力分布的影响。

Mooney-Rivlin Material Rectangular Plate with Voids under Uniaxial Extension

In this paper, the finite deformation and stress analyses for a rectangular plate with voids under uniaxial extension were studied, which is made of the hyper-elastic material with Mooney-Rivlin strain energy function. At first, the deformation mode functions of the rectangular plate with voids that are symmetrically distributed in a certain manner were given by use of the condition of incompressibility. One parameter in the functions may be determined by the state of deformation in the field far from the voids and the other parameter may by approximately obtained from the minimum potential energy principle. The growth of voids in the plates with one, three or five voids during loading and the stress distibution along the edges of voids were analyzed and compared in details. The influences of the number, the distribution manner, the size and the distance of the voids on the deformation and the stress distribution are discussed.