Confinement induced instability of thin elastic film

TL;DR

This paper investigates how thin elastic films become unstable and develop undulations under confinement and adhesive stresses, revealing a critical thickness and curvature where instability occurs, with implications for material adhesion and stability.

Contribution

It introduces a perturbation analysis demonstrating the conditions under which confined elastic films become unstable and form undulations, highlighting the role of film thickness and curvature.

Findings

Undulations have a wavelength proportional to film thickness.

Instability occurs below a critical film thickness or curvature.

Total energy minima correspond to finite amplitude undulations.

Abstract

A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical peel geometry, undulations appear along the contact line below a critical film thickness or below a critical curvature of the plate. Perturbation analysis of the stress equilibrium equations shows that for a critically confined film the total excess energy indeed attains a minima for a finite amplitude of the perturbations which grow with further increase in the confinement.