Development of a constitutive relation for elastomers exhibiting self-reinforcement

A constitutive relation was developed to describe the mechanical behavior of elastomers that exhibit self-reinforcement, or elastic strain-hardening behavior, such as most polyurethane elastomers and some hydrogels. A number of constitutive relations based on both molecular network theory and phenomenological behavior were evaluated. Generally, molecularly based constitutive relationships work well for small deformations, but demonstrate gross deviations from actual behavior at large deformations. Phenomenological relations often predict behavior well but employ mathematical functions based on strain invariants that may cause difficulty in identifying and consistently predicting material properties. The constitutive relation developed here has an exponential functional form. The argument of the exponential is a general fourth order tensor reduced to the isotropic case. The tensor coefficients used in the exponential function are sensitive to variations in molecular weight and can be related to the shear modulus. This exponential constitutive relation is relatively simple to implement, and the two material parameters can be predicted from the maximum extension ratio, the molecular weight between crosslinks, and the experimentally determined shear modulus in the high strain region.