PLANE WAVES IN AN INHOMOGENEOUS HYPERELASTIC SOLID

Abstract

This paper is concerned with finite amplitude longitudinal plane waves in hyperelastic solids whose densities and/or elastic properties vary continuously in the direction of propagation. The relations along the characteristics of the strictly hyperbolic system of governing equations are put in finite difference form and used in a numerical scheme for the determination of shock free solutions. A second-order Godunov-type finite difference scheme is also used to obtain solutions, including those which involve shocks. Numerical results are shown graphically for sudden application of loading and unloading of a string in simple tension.