Folding patterns in partially delaminated thin films

TL;DR

This paper reviews recent mathematical progress on folding patterns in partially delaminated thin films, emphasizing the complex phase diagrams and various geometries studied since the 1990s.

Contribution

It provides a comprehensive overview of advances in understanding the calculus of variations applied to thin film delamination and folding patterns with different boundary conditions.

Findings

Rich phase diagrams of partially debonded films

Analysis of various geometries including anisotropic compression

Progress in mathematical modeling of folding patterns

Abstract

Michael Ortiz and Gustavo Gioia showed in the 90s that the complex patterns arising in compressed elastic films can be analyzed within the context of the calculus of variations. Their initial work focused on films partially debonded from the substrate, subject to isotropic compression arising from the difference in thermal expansion coefficients between film and substrate. In the following two decades different geometries have been studied, as for example anisotropic compression. We review recent mathematical progress in this area, focusing on the rich phase diagram of partially debonded films with a lateral boundary condition.