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Singularities, structures, and scaling in deformed m-dimensional elastic manifolds
B A DiDonna1, T A Witten, S C Venkataramani
1Department of Physics, University of Chicago, Chicago, Illinois 60637, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
Summary
Elastic energy condenses into ridges and vertices when materials are compressed. This study numerically explores how embedding dimension affects this energy condensation in 2D and 3D elastic sheets, revealing distinct scaling behaviors.
Area of Science:
- Physics
- Materials Science
- Applied Mathematics
Background:
- Elastic energy condensation is a phenomenon observed in the crumpling of thin sheets.
- This process involves the formation of ridges and vertices where elastic energy concentrates.
- The principle is expected to apply to elastic objects in any dimension greater than one under compressive strain.
Purpose of the Study:
- To numerically investigate elastic energy condensation in 2D and 3D elastic sheets.
- To determine the influence of the embedding spatial dimension on energy condensation patterns.
- To identify and characterize different scaling behaviors of local energy density.
Main Methods:
- Representing elastic sheets as lattices of nodes with defined stretching and bending rigidity.
- Employing numerical simulations to find minimum energy configurations under various boundary conditions.
- Analyzing the local energy density falloff from singular points.
Main Results:
- Observed two distinct energy density falloff behaviors: cone scaling and ridge scaling.
- Demonstrated that the form of energy condensation is dependent on the embedding dimension.
- Identified significant differences in energy condensation between sheets embedded in different spatial dimensions.
Conclusions:
- Elastic energy condensation exhibits dimension-dependent characteristics.
- The study provides insights into the fundamental mechanics of elastic material deformation.
- Understanding these scaling laws is crucial for predicting material behavior under stress.
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