Magnetoelastic waves in a soft electrically conducting solid in a strong magnetic field

Shear wave motion of a soft, electrically conducting solid in the presence of a strong magnetic field excites eddy currents in the solid. These, in turn, give rise to Lorentz forces that resist the wave motion. We derive a mathematical model for linear elastic wave propagation in a soft electrically conducting solid in the presence of a strong magnetic field. The model reduces to an effective anisotropic dissipation term resembling an anisotropic viscous foundation. We consider the application to magnetic resonance elastography, which uses strong magnetic fields to measure shear wave speed in soft tissues for diagnostic purposes. We find that for typical values of magnetic field, mass density, and electrical conductivity of soft tissues, eddy current dissipation is negligible. For materials with higher conductivity (e.g., metals), the effect can be stronger.