ABSTRACT
There are many proposed strain energy density expressions in the literature which are used to model the constitutive behaviour of rubber under large deformations. These models can be grouped into those dealing with incompressible materials and those extended to deal with compressibility. The right Cauchy-Green deformation tensor is symmetric, positive definite and invertible. This chapter summarises the derivations in Attard and Attard & Hunt providing the finite strain constitutive relationships for a hyperelastic material. The equi-biaxial tension problem of Treloar is studied for various levels of compressibility. The chapter presents constitutive relationship for the second Piola Kirchhoff and Eulerian stress tensors, as well as the associated constitutive relationships for the principal Lagrangian and Eulerian physical stresses. It argues that the assumption of incompressibility results in inconsistent results for the calculation of the hydrostatic pressure while assuming an "almost" incompressible material gives numerically consistent results.
