Theory Manual Version 3.4
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Subsection 5.3.3: Veronda-Westmann Hyperelasticity Up Section 5.3: Nearly-Incompressible Materials Subsection 5.3.5: Transversely Isotropic Hyperelastic

### 5.3.4 Arruda-Boyce Hyperelasticity

Arruda and Boyce proposed a model for the deformation of rubber materials [3]. Their main motivation was to develop a model that accurately captures the behavior of rubbers in different loading scenarios and that can be described with a limited number of physically motivated parameters. Their model is based on the Langevin chain statistics, which models a rubber chain segment between chemical crosslinks as a number of rigid links of equal length . The parameter is related to the locking stretch , the stretch at which the chains reach their full extended state, .
Their proposed strain-energy is a truncated Taylor series of the inverse Langevin function. A formulation that retains the first five terms of this function takes on the following form: where is a shear-modulus like parameter and the coefficients are The Cauchy stress is given by where,
Subsection 5.3.3: Veronda-Westmann Hyperelasticity Up Section 5.3: Nearly-Incompressible Materials Subsection 5.3.5: Transversely Isotropic Hyperelastic