On the Hyperelastic Pressurized Thick-Walled Spherical Shells and Cylindrical Tubes Using the Analytical Closed-Form Solutions

Abstract

This paper focuses on thick-walled spherical shells and cylindrical tubes made of the soft tissues and the rubber-like materials. These materials are characterized by high deformability in which their stress–stretch curves are arranged in the range of S-shaped to J-shaped forms. From the continuum viewpoint, a strain energy density function is postulated for modeling the behavior of these materials. In order to fulfill the main aims of this paper, among all existing energy functions including polynomial, power law, logarithmic and exponential functions, or a linear combination of them, we deduced to evaluate the performance of an Ogden-type model with only integer powers for the mechanical behavior modeling of the S-shaped to J-shaped materials. Most of all, this strain energy function because of its mathematical form can play a constructive role in presentation of the analytical closed-form solutions for the boundary value problems in the field of the finite deformation elasticity. This constitutive model due to the high performance in constitutive modeling and the simplicity of its mathematical form is applied to pressurized thick-walled spherical shells and cylindrical tubes in order to find a closed-form analytical solution for their analysis. Using these analytical solutions, a comprehensive study is done on vanishing circumstance of the snap-through instability that occurs in the inflation of internally pressurized spherical shells and cylindrical tubes. It was observed that the parameters such as shell thickness, the elastic material properties specially the materials with J-shaped mechanical behaviors and the absence and presence of axial forces in cylindrical tubes have significant influence on vanishing of the snap-through instability in the thick-walled pressurized spherical shells and cylindrical tubes.