An Invariant-Based Ogden-Type Model for Incompressible Isotropic Hyperelastic Materials

Abstract

The Ogden model for an incompressible isotropic hyperelastic material is versatile enough to match complicated data for rubber-like materials at large deformations. However, the tensorial expression for the Cauchy stress in the Ogden model requires determination of the eigenvalues and eigenvectors of the left Cauchy-Green deformation tensor $\mathbf{B}$. The objective of this paper is to propose an invariant-based Ogden-type model for isotropic incompressible hyperelastic materials. The strain energy function in this new model depends on classical invariants of $\mathbf{B}$ and the Cauchy stress tensor can be expressed directly in terms of the tensor $\mathbf{B}$ without need for its spectral form. Examples show that this new Ogden-type model retains the versatility of the original Ogden model in characterizing material response.