一类可压缩超弹性圆柱体轴线上的空穴现象

对于由一类均匀各向同性可压缩的广义Varga材料组成的实心圆柱体,研究其在给定的外表面拉伸和轴向拉伸或压缩共同作用下的轴对称变形问题.利用能量变分原理得到了问题的控制方程和边界条件,并求得了描述柱体径向对称变形的参数型解析解和描述圆柱体轴线上空穴生成和增长的空穴分岔解.给出了与泊松比和轴向伸长相关的径向临界伸长的表达式和空穴生成后的应力表达式;并通过数值算例讨论了这些参数对圆柱体轴线上空穴生成和增长、圆柱体的径向位移以及应力的集中和突变的影响,同时给出了相应的数值模拟.

CAVITATION AT THE AXIAL LINE OF A CLASS OF COMPRESSIBLE HYPERELASTIC CYLINDER

The problem of axially symmetric deformation is examined for a solid cylinder composed of a class of homogeneous isotropic compressible hyperelastic generalized Varga materials,where the cylinder is subjected to the actions of a surface tension and an axial tension or compression simultaneously.The governing equation and the boundary conditions of the problem is obtained by using the energy principle,moreover,the parametric solution that describes the radially symmetric deformation of the cylinder and the c...