The delamination of a growing elastic sheet with adhesion

TL;DR

This paper analyzes the conditions under which a growing elastic sheet adhered to a substrate develops delamination blisters, providing an analytic expression for the critical deformation triggering this instability.

Contribution

It introduces a new analytical model linking the critical delamination threshold to geometric, mechanical, and adhesive parameters.

Findings

Critical deformation scales with a single dimensionless parameter.

Analytic expression for the onset of delamination.

Residual stresses induce buckling leading to delamination.

Abstract

We study the onset of delamination blisters in a growing elastic sheet adhered to a flat stiff substrate. When the ends of the sheet are kept fixed, its growth arouses residual stresses that lead to delamination. This instability can be viewed as a discontinuous buckling between the complete adhered solution and the buckled solution. We provide an analytic expression for the critical deformation at which the instability occurs. We show that the critical threshold scales with a single dimensionless parameter that comprises information from the geometry of the sheet, the mechanical parameters of material and the adhesive features of the substrate.