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Published on: October 1, 2019
Numerical investigation of isolated crescent singularity.
1The James Franck Institute and the Department of Physics, The University of Chicago, 929 East 57th Street, Chicago, Illinois 60637, USA.
Summary
This study numerically investigates an isolated crescent singularity in elastic sheets. Researchers found two distinct scaling laws for the crescent’s width and radius of curvature, offering insights into complex singularity behavior.
Area of Science:
- Solid Mechanics
- Materials Science
- Applied Mathematics
Background:
- Crescent singularities in elastic sheets are complex phenomena.
- Previous studies on developable cones observed specific scaling behaviors.
- Understanding these singularities is crucial for predicting material properties.
Purpose of the Study:
- To numerically examine the properties of an isolated crescent singularity.
- To identify and analyze the scaling properties of the crescent region.
- To investigate the relationship between length scales and physical parameters like thickness and potential separation.
Main Methods:
- Numerical examination of an isolated crescent singularity in an elastic sheet.
- Controlled application of six potential forces to create the crescent region.
- Analysis of two distinct length scales within the crescent.
Main Results:
- Identified two types of length scales for the crescent singularity.
- Demonstrated that the crescent's width scales with thickness and separation to the 1/2 power.
- Revealed that the crescent's radius of curvature scales with thickness to the 1/3 power and separation to the 2/3 power.
Conclusions:
- The study successfully characterized the scaling properties of an isolated crescent singularity.
- The findings align with previous observations for developable cones, confirming distinct scaling behaviors.
- These results are expected to aid in understanding the complex scaling of crescent singularities.
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