Journal
PHYSICAL REVIEW E
Volume 80, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.80.021604
Keywords
dislocation dipoles; elasticity; lattice theory; membranes; pattern formation
Categories
Funding
- NSF [CMMI09-00468]
- NSF MRSEC [DMR05-20020]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [0900468] Funding Source: National Science Foundation
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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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