Arruda–Boyce model

In continuum mechanics, an Arruda–Boyce model is a hyperelastic constitutive model used to describe the mechanical behavior of rubber and other polymeric substances. This model is based on the statistical mechanics of a material with a cubic representative volume element containing eight chains along the diagonal directions. The material is assumed to be incompressible.

The strain energy density function for the incompressible Arruda–Boyce model is given by

where ${\displaystyle n}$ is the number of chain segments, ${\displaystyle k_{B}}$ is the Boltzmann constant, ${\displaystyle \theta }$ is the temperature in kelvins, ${\displaystyle N}$ is the number of chains in the network of a cross-linked polymer,

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