A refined model for the buckling of film/substrate bilayers

TL;DR

This paper introduces a refined model for film/substrate bilayers that accurately captures the response by incorporating exact theory, improving upon the classical Winkler foundation assumption for predicting buckling behavior.

Contribution

The authors develop a refined model expressing tractions in terms of displacements and using exact half-space theory, enhancing the classical buckling model for bilayers.

Findings

Refined model matches the critical strain expansion from exact theory.

Model applies to both compressible and incompressible cases.

Improves accuracy over classical Winkler foundation assumption.

Abstract

The classical reduced model for a film/substrate bilayer is one in which the film is governed by the Euler-Bernoulli beam equation and the substrate is replaced by an array of springs (the so-called Winkler foundation assumption). We derive a refined model in which the normal and shear tractions at the bottom of the film are expressed in terms of the corresponding horizontal and vertical displacements, and the response of the half-space is described by the exact theory. The self-consistency of the refined model is confirmed by showing that it yields a four-term (in the incompressible case) or six-term (in the compressible case) expansion for the critical strain that agrees with the expansion given by the exact theory.