What is Shear Wave

TL;DR

This paper challenges the traditional definition of shear waves, showing it violates shear stress reciprocity and proposing a modified approach based on local rigid body rotation that aligns with continuum mechanics.

Contribution

It introduces a new perspective on shear wave definition, modifies constitutive relations, and derives a consistent motion equation considering local rigid body rotation.

Findings

Traditional shear wave definition breaks shear stress reciprocity.

Displacement field relates to local rigid body rotation.

Modified elastic tensor aligns shear wave with continuum mechanics.

Abstract

This study shows that the traditional definition of shear wave breaks the shear stress reciprocity. By analyzing the displacement field for shear wave and the motion equation of material element, it is found that the displacement field is related to local rigid body rotation, and the local rigid body rotation cannot be balanced by the stress state assumed in classical continuum mechanics. It is also found that the displacement field caused by shear deformation, which is neither divergence nor rotation, is replaced with that caused by local rigid body rotation during the derivation of wave equation. This indicates that the definition of shear wave is beyond the basic assumption of continuum mechanics. The study modified the constitutive relation and elastic tensor based on that the traditionally defined shear wave is objective. The motion equation corresponding to shear wave is also derived. It is concluded from the definition of traditional shear wave that the local rigid body rotation should contribute stress and the shear stress reciprocity is not prerequisite for nonpolar continuum.