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arXiv · 2012.02742

A hyperbolic framework for shear sound beams in nonlinear solids

Harold Berjamin·Michel Destrade
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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.

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Harold Berjamin, Michel Destrade. 2020-12-04. A hyperbolic framework for shear sound beams in nonlinear solids. https://doi.org/10.1016/j.cnsns.2021.106036

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