Uniform asymptotic analysis for transient waves in a pre-stressed compressible hyperelastic rod (Q1570861)

The authors investigate the wave propagation in a pre-stressed circular rod composed of a general compressible hyperelastic material. The behaviour of such a system (for small axial-radial deformations superimposed on the pre-stess) is described by two coupled equations which include four parameters. It is shown that only one of the parameters is really important. The system under consideration is shown to exhibit two wave velocities whose magnitudes are controlled by the main parameter. Then, the initial value problem is solved by the use of Fourier transform, and the solution is represented as a sum of integrals. By the use of the method of stationary phase, the authors derive asymptotic expansions for the solutions. Numerical examples are presented for Mooney-Rivlin material.