A hyperbolic framework for shear sound beams in nonlinear solids
Abstract
In soft elastic solids, directional shear waves are in general governed by coupled nonlinear KZK-type equations for the two transverse velocity components, when both quadratic nonlinearity and cubic nonlinearity are taken into account. Here we consider spatially two-dimensional wave fields. We propose a change of variables to transform the equations into a quasi-linear first-order system of partial differential equations. Its numerical resolution is then tackled by using a path-conservative MUSCL-Osher finite volume scheme, which is well-suited to the computation of shock waves. We validate the method against analytical solutions (Green's function, plane waves). The results highlight the generation of odd harmonics and of second-order harmonics in a Gaussian shear-wave beam.
Cite
@article{arxiv.2012.02742,
title = {A hyperbolic framework for shear sound beams in nonlinear solids},
author = {Harold Berjamin and Michel Destrade},
journal= {arXiv preprint arXiv:2012.02742},
year = {2021}
}