Shear waves in a nonlinear relaxing media: A three-dimensional perspective.

Area of Science:

• Continuum Mechanics
• Rheology
• Wave Propagation

Background:

• A one-dimensional rheological model for linearly polarized shear waves was previously proposed by Cormack and Hamilton.
• Existing models lack a comprehensive three-dimensional framework.

Purpose of the Study:

• To embed the existing one-dimensional model within a broader three-dimensional continuum mechanics framework.
• To derive governing equations for circularly polarized shear waves.
• To analyze the influence of objective time derivatives on wave propagation models.

Main Methods:

• Utilizing rigorous continuum mechanics principles.
• Developing general three-dimensional rheological models.
• Deriving equations for circularly polarized shear wave propagation.

Main Results:

• Successfully embedded the one-dimensional model into a three-dimensional framework.
• Derived straightforward equations for circularly polarized shear waves.
• Confirmed that the derived equations reduce to the linearly polarized case when the wave phase is constant.
• Demonstrated the independence of results from the choice of objective time derivative under asymptotic assumptions.

Conclusions:

• The study provides a more comprehensive theoretical framework for understanding shear wave propagation.
• The derived equations offer a simplified approach to analyzing circularly polarized shear waves.
• The findings highlight the robustness of the model across different objective time derivatives.