A hyperbolic framework for shear sound beams in nonlinear solids

H. Berjamin, M. Destrade (2021). "A hyperbolic framework for shear sound beams in nonlinear solids", Communications in Nonlinear Science and Numerical Simulation 103, 106036. https://doi.org/10.1016/j.cnsns.2021.106036

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.

Nonlinear acoustics, Soft elastic solids, KZK-type equations, Finite volume method