Two-dimensional wave propagation in a nonlinear elastic half-space

Finite amplitude wave propagation in an elastic, isotropic half-space is investigated. A numerical scheme that was previously developed and shown to yield satisfactory accurate results whenever smooth solutions occur is modified here for the cases in which steep solutions are obtained. The stability analysis of the proposed numerical procedure is carried out, and the stability criteria are given in terms of the spectral radii of the matrices involved in the equations of motion. The hyperbolicity conditions of the equations of motion are derived and shown to impose restrictions on the possible values of displacement gradients so that the range of variation of the strength of the applied load is limited. As a first chek of the accuracy of the numerical results, a propagating shock wave is produced numerically and compared with the analytical solution. In a second check, propagating circularly polarized waves are numerically simulated and compared with the corresponding analytical solution. In each case good agreement is obtained. For the "quadratic material" adopted in this paper, it is shown that a compressive normal line force yields propagating pulses having larger amplitudes, broader widths and larger arrival times, as compared with those caused by a tensile one. The linear response is also shown for comparison.