Stability of a thin elastic film close to a rigid plate

Yi Chao Chen, Eliot Fried, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review


We introduce and study a variational model for the formation of patterns induced by bringing the surface of a rigid plate into contact proximity with the surface of a polymeric film strongly bonded to a substrate. We treat the film as a homogeneous, isotropic, hyperelastic solid and account for both attractive and repulsive van der Waals interactions between the film surface and the proximate contractor. Aside from confirming the intuitive expectation that the presence of a repulsive contribution to the van der Waals potential should stabilize patterns that form on the film surface, we elucidate the role of repulsive interactions at the onset of instability. For a recently proposed van der Waals potential involving two parameters, the Hamaker constant A and the equilibrium spacing de, our results include estimates for the critical gap dc at which undulations appear on the film surface, the corresponding wavenumber kc of the undulations, and a lower bound fm for the attractive force needed to induce the undulations. To leading order, dc∼(Ah/μ) 1/4, kc∼1/h, and fm∼( μ3A/ h3) 1/4, where h and μ denote the thickness and infinitesimal shear modulus of the film. Correction terms due to repulsive interactions indicate that, while kc may be influenced by μ and A, dc may also be influenced by de. Granted knowledge of μ and A, our results also suggest a simple experimental protocol for determining de.

Original languageEnglish (US)
Pages (from-to)904-920
Number of pages17
JournalJournal of the Mechanics and Physics of Solids
Issue number5
StatePublished - May 2012


  • Attractive and repulsive van der Waals interactions
  • Bifurcation
  • Energy minimization
  • Instability
  • Pattern formation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Stability of a thin elastic film close to a rigid plate'. Together they form a unique fingerprint.

Cite this