Department of Physics Papers

Document Type

Journal Article

Date of this Version

8-12-2009

Comments

Suggested Citation:
Matsumoto, E.A. and R.D. Kamien. (2009). "Elastic-instability triggered pattern formation." Physical Review E. 80, 021604.

© 2009 The American Physical Society
http://dx.doi.org/10.1103/PhysRevE.80.021604

Abstract

Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple model for determining the orientational order of such patterns using only linear elasticity theory which correctly predicts the outcomes of several experiments. Each element of the pattern is modeled by a “dislocation dipole” located at a point on a lattice, which then interacts elastically with all other dipoles in the system. We explicitly consider a membrane with a square lattice of circular holes under uniform compression and examine the changes in morphology as it is allowed to relax in a specified direction.

Date Posted: 06 January 2011

This document has been peer reviewed.