Surface waves in deformed Bell materials

TL;DR

This paper investigates surface wave propagation on a predeformed Bell constrained material, deriving a unique secular equation for wave speed that differs from incompressible materials, highlighting the effects of Bell constraints.

Contribution

It derives a new secular equation for surface waves in Bell constrained materials under finite predeformation, distinguishing it from the incompressible case.

Findings

Surface waves propagate in principal strain directions with orthogonal attenuation.

The secular equation for wave speed is different from that of incompressible materials.

Bell constraints influence wave behavior distinctly from incompressibility.

Abstract

Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semi-infinite body made of Bell constrained material. The predeformation corresponds to a finite static pure homogeneous strain. The surface wave propagates in a principal direction of strain and is attenuated in another principal direction, orthogonal to the free surface. For these waves, the secular equation giving the speed of propagation is established by the method of first integrals. This equation is not the same as the secular equation for incompressible half-spaces, even though the Bell constraint and the incompressibility constraint coincide in the isotropic infinitesimal limit.