Finite-difference time-domain scheme for nonlinear acoustic waves in solids

A general finite-difference time-domain (FDTD) method for numerical simulation of the nonlinear acoustic wave in conservative (nondissipative) solids is presented. We apply the spatial derivatives of displacements instead of stress and particle velocity as the bases to discretize the governing partial differential equations. The mathematical model is completely compatible with its linear counterpart. The model solution keeps stable even very near to the formation of a shock wave. As numerical examples, the FDTD scheme is used to investigate the longitudinal and transverse plane waves in infinite isotropic material. In the case of longitudinal wave, a sinusoidal wave transforms into a wave with a sawtooth profile eventually. The distance for the formation of a discontinuity can be obtained directly. The primary and the high order harmonic waves vary with the travelling distance in a very complex way. In the case of transverse wave, high order transverse waves are neglectable and high order longitudinal waves are generated instead. This method dose not need linearization of the governing equations. It can also be used to deal with nonlinear acoustic wave in anisotropic solids without modification. (C) 2018 Elsevier Ltd. All rights reserved.