Elastic Instability Triggered Pattern Formation

Details Elastic Instability Triggered Pattern Formation Elastic Instability Triggered Pattern Formation

2009-02-20

arxiv.org/abs/0902.3627v1

Phys. Rev. E 80 (2009) 021604

Physics

Condensed Matter

Soft Condensed Matter

15 pages, 7 figures, the full catastrophe

Scientific paper

10.1103/PhysRevE.80.021604

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.

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