 Therefore,
The left Cauchy–Green deformation tensor can then be expressed as
If the directions of the principal stretches are oriented with the coordinate basis vectors, we have
The engineering strain is formula_43.The engineering stress is

The deformation gradient for a simple shear deformation has the form
where formula_66 are reference orthonormal basis vectors in the plane of deformation and the shear deformation is given by
In matrix form, the deformation gradient and the left Cauchy–Green deformation tensor may then be expressed as
Therefore,
and the Cauchy stress is given by

The Arruda–Boyce model is based on the statistical mechanics of polymer chains.In this approach, each macromolecule is described as a chain of formula_5 segments, each of length formula_72.