Asymptotic bifurcation solutions for compressions of a clamped nonlinearly elastic rectangle: transition region and barrelling to a corner-like profile

TL;DR

This paper investigates the buckling and barrelling instabilities of a nonlinearly elastic rectangle under clamped conditions, providing asymptotic solutions for transition regions and profile changes, addressing practical friction issues.

Contribution

It introduces asymptotic bifurcation solutions for elastic rectangle compressions under realistic clamped boundary conditions, extending prior work beyond idealized lubricated ends.

Findings

Derived asymptotic solutions for transition regions.

Analyzed the change from barrelling to corner-like profiles.

Provided insights into practical boundary condition effects.

Abstract

Buckling and barrelling instabilities in the uniaxial compressions of an elastic rectangle have been studied by many authors under lubricated end conditions. However, in practice it is very difficult to realize such conditions due to friction. Here, we study the compressions of a two-dimensional nonlinearly elastic rectangle under clamped end conditions.