Finite amplitude waves in nonlinear elastodynamics and related theories: A personal overview?

Abstract

This Chapter presents a personal survey of some basic results about finite amplitude waves in nonlinear elasticity and related theories. For isotropic materials, general classes of solutions for the basic equations of wave propagation are obtained by reducing the equations of motion to a system of ordinary differential equations. When dispersive or dissipative effects are taken into account, solitary wave solutions are possible. The effects of a general homogeneous prestress on finite amplitude wave propagation are investigated for a large family of materials.