Large Deformation Analysis of Hyperelastic Membranes Containing a Hole or Inclusion

Abstract

A large deformation analysis has been given by using a modified Gao’s second constitutive relation. In certain circumstances, the new constitutive relation may be simplified to the Mooney-Rivlin and Neo-Hookean models. With regard to incompressible materials, when the influence of the second strain invariant is neglected, the modified model brings a unified form of Gao’s two constitutive models. The new constitutive relation has been utilized to resolve a problem of a hyperelastic membrane containing a hole or rigid inclusion. The basic governing equations of incompressible materials have been obtained and numerical solutions of equations illustrate how constitutive parameters affect the result of membranes’ deformation. These conclusions may provide helps to practical problems.