On the Rectilinear Shear of Compressible and Incompressible Elastic Slabs

TL;DR

This paper extends pseudo-planar deformation solutions from incompressible to compressible elastic slabs, incorporating gravity effects, and explores their implications for understanding complex nonlinear elasticity equations.

Contribution

It introduces new approximate solutions for compressible elastic slabs and discusses their relevance to nonlinear elasticity theory, expanding on previous incompressible models.

Findings

Extended pseudo-planar deformations to compressible materials

Incorporated gravity effects into elasticity models

Proposed new approximate solutions for complex field equations

Abstract

We review some pseudo-planar deformations for the equations of incompressible isotropic nonlinear elasticity first introduced in 1985 by Rajagopal and Wineman. We extend this class of deformations to compressible isotropic and transverse isotropic materials, and also consider the influence of gravity. We consider some new approximate solutions and we discuss the possible relevance of such solutions to the understanding of the complex structure of the fields equations of nonlinear elasticity, using weakly nonlinear theories.