Cavitation in soft solids has been intensively studied in the past. In previous works, soft solids are often assumed to be incompressible in the modeling. However, in practice, many soft solids are compressible. In this article, we try to find analytical solutions of cavity expansion in a slightly compressible hyperelastic solid. In the formulation, we adopt one commonly used compressible neo-Hookean hyperelastic model for the material. To obtain the analytical solutions, we regard the bulk modulus much larger than the shear modulus of the solid, define the ratio between the shear modulus and the Lame’s first parameter as a small dimensionless parameter, and then apply the regular perturbation method. Using the analytical solutions, we also elaborate on the effects of the material compressibility on the cavitation. The analytical solutions obtained in the article have further been compared with the exact numerical solutions.

过去已经对软固体中的空化进行了深入研究。在以前的工作中，通常在模型中假定软固体是不可压缩的。但是，实际上，许多软固体都是可压缩的。在本文中，我们试图找到可压缩的超弹性固体中空腔膨胀的解析解。在配方中，我们采用一种常用的可压缩新霍克超弹性模型作为材料。为了获得解析解，我们认为体积模量比固体的剪切模量大得多，将剪切模量和Lame的第一个参数之间的比率定义为小的无量纲参数，然后应用常规的摄动方法。使用分析解决方案，我们还详细说明了材料可压缩性对空化的影响。