不可压缩超弹性球形结构的径向有限变形

摘要

In this paper, the radial finite deformation problems are examined for spherical struc- tures composed of isotropic incompressible hyperelastic material under tensile loads on their outer -surfaces. First of all, an exact relation between tensile load and inner radius of spherical structure is obtained by the incompressibility condition and the boundary conditions. Secondly, qualitative analyses are performed for solutions describing the finite deformation of the four spherical structures （i. e. , solid sphere, sphere with an initial micro-void, spherical shell, spherical membrane）. Finally, the effects of material parameters and structure parameters on ra- dial deformation of spherical structures are discussed in detail by utilizing numerical examples.%研究了在表面拉伸载荷的作用下,各向同性不可压缩超弹性材料组成的球形结构的有限变形问题。首先利用不可压缩性条件及边界条件求得了拉伸载荷和球形结构内半径之间的关系,进而分别给出了4种球形结构（实心球体、预存微孔、球壳和球形薄膜）有限变形解的定性分析,最后结合数值算例详细讨论了材料参数和结构参数对球形结构径向变形的影响。