Friday, January 26, 2018
4:00 pm in ETC 4.150
John M. Cormack
Applied Research Laboratories
The University of Texas at Austin
Soft materials such as rubbers, polymers, and tissue exhibit low shear-wave speeds, facilitating the generation of shear waves with large acoustic Mach numbers that propagate very slowly, on the order of meters per second, exhibiting waveform distortion and even shock formation within a few centimeters from the source. In addition to finite-amplitude effects that result from cubic nonlinearity, plane shear wave propagation in these materials is subject to frequency-dependent attenuation and dispersion that result from viscoelastic effects. Stress relaxation is a simple model for viscoelasticity that has been observed in measurements of soft rubbers and biomaterials in the frequency range of interest. A model is presented that describes plane shear waves in a relaxing material, accounting for cubic nonlinearity as well as the attenuation and dispersion associated with relaxation. For both progressive and standing waves, analytical solutions of the model equations are derived and supplemented with numerical simulations in order to investigate the interaction of, and competition between, nonlinear and viscoelastic effects in shear wave motion.
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