One-dimensional pulse propagation in a nonlinear elastic media

This paper considers the problem of wave propagation in a nonlinear elastic medium with a quadratic stress-strain relationship. The paper is limited to one-dimensional wave propagation. Under these conditions, the initial value problem is formulated into a hyperbolic system of conservation laws. The Riemann problem due to an initial step function excitation is considered first. Analytical solutions to the Riemann problem are obtained by solving the corresponding eigenvalue problem. In addition, a computer program is developed based on the high-resolution central scheme of Kurganov and Tadmor. The accuracy of this numerical procedure is verified by comparing the numerical results with the exact solutions. The second part of the paper considers several different types of initial excitations in order to determine special characteristics of the wave propagation due to material nonlinearity.