Analytical and numerical results for the elasticity and adhesion of elastic films with arbitrary Poisson’s ratio and confinement

Abstract

We present an approximate, analytical treatment for the linearly elastic response of a film with arbitrary Poisson's ratio (Formula presented.), which is indented by a flat cylindrical punch while resting on a rigid foundation. Our approach is based on a simple scaling argument allowing the vast changes of the elastomer’s effective modulus (Formula presented.) with the ratio of film height (Formula presented.) and indenter radius (Formula presented.) to be described with a compact, analytical expression. This yields exact asymptotics for large and small reduced film heights (Formula presented.), whereby it also reproduces the observation that (Formula presented.) has a pronounced minimum for (Formula presented.) at (Formula presented.). Using Green’s function molecular dynamics (GFMD), we demonstrate that the predictions for (Formula presented.) are reasonably correct and generate accurate reference data for effective modulus and pull-off force. GFMD also reveals that the nature of surface instabilities occurring during stable crack growth as well as the crack initiation itself depend sensitively on the way how continuum mechanics is terminated at small scales, that is, on parameters beyond the two dimensionless numbers (Formula presented.) and (Formula presented.) defining the continuum problem.