Inflation and Stability Analysis of Hyperelastic Thin Shell

Abstract

The elastic instability in internally pressurized hyperelastic thin shells composed of an newlineincompressible isotropic hyperelastic material is analyzed under large and homogeneous newlinedeformation. A mathematical model for the inflation of thin shells is established by an newlineamended new strain energy density function. The polyconvexity principle and the fundamental newlineprinciples of the strain energy density function ensure that this energy density newlinefunction exists in its lowest possible potential state. To analyze the stability of a hyperelastic newlinethin shell, the characteristics curve of the inflation pressure against volume newlineexpansion ratio with variations in the material parameters is employed. Several material newlinemodels in the family of limited elastic materials demonstrate strain-stiffening phenomena newlineduring their deformation. However, they are unable to anticipate severe strain-stiffening newlinephenomena in each range of deformations in the stress-strain relations. Only three material newlineparameters constitute an amended new energy density function, which exhibits far newlinebetter strain stiffening characteristics than the existing limited elastic material models. newlineIn comparison to prevailing models, the mathematical model derived from the amended newlinenew energy density function demonstrates significantly more strain-stiffening at moderate newlineand large stretch levels. It also exhibits better agreement with experimental data. newlineA localized type of instability occurs while inflating the hyperelastic cylindrical thin newlineshell. The localization forms a sudden expansion along the length of the thin shell. As its newlinediameter grows to a specific diameter, it starts to expand axially. This can happen at a newlinewell-defined pressure value that is significantly lower than the pressure needed to initiate newlinethe inflation of a thin shell. The current study models such a phenomenon, predicting newlinethe impact of axial load on the value of instability pressure. The model is being developed newlineby combining existing experimental and proposed analytical efforts to determine the newlineconditions that