Nonlinear waves in approximately constrained materials

We give a general treatment of the propagation of nonlinear acceleration waves in approximately constrained elastic materials. By means of a suitable perturbative scheme, namely a Laurent expansion for the constitutive functions, we can derive the characteristic of acceleration waves, speeds and amplitudes, for elastic bodies with first and second-order poles. The theory is applied to St. Venant-Kirchhoff materials, which can be used to approximate rigid or incompressible bodies, to isotropic, anisotropic materials and to a model for unidirectionally fiber-reinforced composites.