Morphologies of expansion ridges of elastic thin films onto a substrate

TL;DR

This paper models the formation of various expansion ridge morphologies in elastic thin films on substrates, revealing patterns like spots, stripes, and rings, with implications for understanding delamination and epitaxial growth.

Contribution

It introduces a numerical study of non-linear elastic behavior leading to diverse ridge morphologies, connecting these patterns to real-world phenomena.

Findings

Ridge morphologies include spots, stripes, and rings.

Patterns resemble those in delamination and bi-phase growth.

Numerical results match observed film behaviors.

Abstract

We consider a model of a thin film elastically attached to a rigid substrate. In the case in which the film expands relative to the substrate and assuming certain non-linear elastic behavior of the film, expansion ridges may appear, in which the material has collapsed, and the density is higher. By studying numerically this process, the possible morphologies of these collapsed regions are presented. They range from circular spots and straight stripes, to wiggle polygonal patterns and ring-shaped domains. The similarity of some of these results with patterns observed in delamination of thin films and bi-phase epitaxial growth is emphasized.