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Universal Wrinkling of Supported Elastic Rings
Benjamin Foster1, Nicolás Verschueren1,2, Edgar Knobloch1
1Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA.
Physical Review Letters
|October 28, 2022
Summary
Researchers identified exactly solvable models for wrinkling in compressed, inextensible elastic rings on substrates. The universal wrinkle shapes, derived from analytical expressions, match numerical results, offering insights into elastic material behavior.
Area of Science:
- Solid Mechanics
- Materials Science
- Applied Mathematics
Background:
- Wrinkling in elastic structures is a common phenomenon, particularly in thin films and shells under compression.
- Understanding the mechanics of compressed elastic rings is crucial for various engineering applications, from microdevices to large-scale structures.
- Previous models often lacked exact solvability or comprehensive analytical descriptions of wrinkle formation.
Purpose of the Study:
- To identify and analyze an exactly solvable family of models for the wrinkling of substrate-supported inextensible elastic rings under compression.
- To derive universal wrinkle profiles and their relationship to the mechanical properties of the rings.
- To provide closed-form analytical expressions for these universal shapes and the conditions under which they emerge.
Main Methods:
- Development of an exactly solvable theoretical model for elastic ring wrinkling.
- Derivation of closed-form analytical expressions for wrinkle profiles and phase transitions.
- Comparison of analytical predictions with results obtained from numerical continuation methods.
Main Results:
- Identification of a family of exactly solvable models for wrinkling in compressed, substrate-supported, inextensible elastic rings.
- Demonstration that the resulting wrinkle profiles are universal, linked to the buckling of unsupported rings.
- Provision of analytical expressions for universal shapes and the precise pressure-tension relationships governing their emergence.
Conclusions:
- The study successfully provides an analytically tractable framework for understanding elastic ring wrinkling.
- The universality of the wrinkle profiles simplifies predictions and offers broad applicability.
- Excellent agreement between analytical predictions and numerical results validates the proposed models across a wide parameter range.
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