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Curvature-induced symmetry breaking determines elastic surface patterns.
Norbert Stoop1, Romain Lagrange1, Denis Terwagne2
1Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue Cambridge, Massachusetts 02139-4307, USA.
Nature Materials
|February 3, 2015
Summary
Researchers developed a new theory to predict wrinkling patterns in curved elastic materials, overcoming limitations of previous models. This breakthrough accurately describes pattern selection in systems from biological tissues to thin films.
Area of Science:
- Materials Science
- Theoretical Physics
- Applied Mathematics
Background:
- Buckling and folding of curved multilayered surfaces are observed in diverse natural and engineered systems, including embryogenesis and thin film formation.
- Existing theoretical models struggle to predict these symmetry-breaking transitions due to the nonlinear stretching and bending forces involved.
- Experimental characterization of these phenomena is extensive, but theoretical prediction remains a significant challenge.
Purpose of the Study:
- To develop a generalized theoretical framework for predicting wrinkling morphology and pattern selection in curved elastic bilayer materials.
- To provide a reliable theoretical model that overcomes the limitations of current nonlinear approaches.
- To establish a universally applicable theory for diverse macroscopic and microscopic systems.
Main Methods:
- Developed a generalized Swift-Hohenberg theory tailored for curved elastic bilayer materials.
- Validated the theory through experimental testing on spherically shaped surfaces.
- Utilized general differential-geometry principles as the foundation for the theoretical approach.
Main Results:
- The generalized Swift-Hohenberg theory accurately describes wrinkling morphology and pattern selection.
- Experimental results on spherical surfaces showed quantitative agreement with analytical predictions for phase transition curves (labyrinth, hybrid, hexagonal).
- The theory demonstrates universal applicability, consistent with previous experimental findings across different scales.
Conclusions:
- The developed theory provides a robust and accurate method for predicting wrinkling phenomena in curved elastic materials.
- This approach bridges the gap between experimental observations and theoretical predictions for complex surface deformations.
- The differential-geometry-based framework is extensible to arbitrarily shaped surfaces, offering broad applicability.
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