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Updated: Oct 15, 2025
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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
Published on: April 25, 2019
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Plane nonlinear shear wave propagation in transversely isotropic soft solids.
1Center for Ultrasound Molecular Imaging and Therapeutics, Department of Medicine, University of Pittsburgh Medical Center, Pittsburgh, Pennsylvania 15261-1909, USA.
The Journal of the Acoustical Society of America
|October 31, 2021
Summary
Elastic anisotropy in soft solids introduces quadratic nonlinear effects for shear waves. This study derives nonlinear wave equations and analyzes harmonic generation, revealing low efficiency between wave modes due to speed disparities.
Area of Science:
- Solid Mechanics
- Nonlinear Acoustics
- Materials Science
Background:
- Nonlinear wave propagation in soft solids is crucial for understanding material behavior.
- Isotropic soft solids exhibit cubic nonlinearity, while anisotropy introduces quadratic effects.
Purpose of the Study:
- To derive nonlinear wave equations for plane shear waves in transversely isotropic soft solids.
- To investigate the nature and efficiency of nonlinear interactions and harmonic generation.
Main Methods:
- General expansion of strain energy density up to fourth order.
- Derivation of coupled nonlinear wave equations for two shear wave modes.
- Approximation for linearly polarized waves and derivation of evolution equations.
Main Results:
- Elastic anisotropy introduces quadratic nonlinear effects, including mode interaction.
- Second harmonic generation in elliptically polarized waves shows low efficiency due to speed differences.
- Explicit expressions for leading order nonlinearity coefficients and third harmonic generation are provided.
Conclusions:
- Transversely isotropic soft solids exhibit unique nonlinear wave phenomena at quadratic order.
- Mode interaction efficiency is limited by propagation speed disparities.
- The derived equations provide a framework for analyzing nonlinear wave propagation and harmonic generation in anisotropic materials.
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