Inflation and eversion of spherical shells of a special compressible material (Q1260609)

A study is made of the qualitative features of the inflation of a shell of the so-called material of type II. This material has a strain energy function which is linear in \(i_ 1\), \(i_ 3\) and arbitrary in \(i_ 2\), where \(i_ 1\), \(i_ 2\), and \(i_ 3\) are the three principal invariants of the stretch tensors. For a specific form of the arbitrary function, a closed-form solution to the equations of equilibrium describing spherical eversion can also be found. By using this solution, a comparison can be made between the qualitative features of the regular and everted shells under internal pressure.