Hyperelastic constitutive modeling under finite strain

A strain energy density function for isotropic higher order elasticity is developed. The strain energy density is decomposed into a compressibility component being a generalization of the Simo and Pister [Comput. Methods Appl. Mech. Eng. 46, 201–215] proposal for neo-Hookean elasticity, and an incompressibility component being the generalized Mooney expression. A general constitutive relationship for the second Piola Kirchhoff and Eulerian stress tensor for higher order elasticity is then derived from the proposed strain energy density. Constitutive relationships for the principal Lagrangian and Eulerian physical stresses in terms of the principal stretches are also developed. Predictions based on the proposed strain energy density are compared with experimental results including incompressible rubber-like materials under homogeneous strain, compressible materials under high hydrostatic compression, and measured volume changes in rubber and foam under large deformation uniaxial tension.