A hyperbolic framework for shear sound beams in nonlinear solids
arXiv:2012.02742 · doi:10.1016/j.cnsns.2021.106036
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.
References in corpus (9)
- ExaHyPE: An Engine for Parallel Dynamically Adaptive Simulations of Wave Problems
- Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis
- Onset of Non-Linearity in the Elastic Bending of Blocks
- Shear shock waves are observed in the brain
- A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation
- Generalization of the Zabolotskaya equation to all incompressible isotropic elastic solids
- Time-domain numerical modeling of brass instruments including nonlinear wave propagation, viscothermal losses, and lips vibration
- Plane-strain waves in nonlinear elastic solids with softening
- Analytical solution to the Riemann problem of 1D elastodynamics with general constitutive laws