Nonlinearity parameters for pulse propagation in isotropic elastomers

The propagation of one-dimensional shear waves in isotropic hyperelastic materials is examined. Both compressible and incompressible materials subject to arbitrarily large shear prestrains are considered. The nonlinear evolution equation governing small disturbances on prestrained undisturbed states is derived. The prestrain is seen to change the nonlinearity from the cubic form found in the unstrained case to the stronger quadratic form governed by the conventional Burgers' equation. Additional results include explicit and general expressions for the quadratic and cubic nonlinearity parameters. Numerical estimates are also provided for natural rubber and foamed polyurethane. It is demonstrated that the quadratic nonlinearity parameter does not increase monotonically with prestrain and may actually vanish at nonzero values of the prestrain.