Analytical stress solution in hyperelastic thick-walled sphere under external pressure using different strain energy functions

Abstract

Due to their large deformation, rubber-like materials are used in many industrial applications. However, few studies are available in the literature on the classification of rubber-like materials, their mechanical properties and the behavior of this material due to their hyperelastic and nonlinear behavior. In this work, an incompressible isotropic nonlinear elastic thick-walled spherical structure subjected to external pressure is studied using analytical formulation. The study aims to analyze the behavior and the stress field of such materials which are characterized by high deformability. Five different type strain energy functions are applied to a pressurized thick-walled hollow sphere to model the material behavior. A closed-form analytical solution is obtained and the results predicted from classic strain energy models (Neo-Hookean and Mooney Rivlin) and those obtained by Isihara, Biderman and Gent-Thomas models are compared in the prescribed case. The solution obtained, for different models, was used to determine the stress field (radial and hoop stresses) across thickness of the sphere. Finally, the influence of some parameters such as the radial pre-stretched sphere on stress components was examined. Comparisons are done to investigate the accuracy and evaluating the effectiveness of some existing constitutive models in the analysis of spherical vessel under external pressure.