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Positive disclination in a thin elastic sheet with boundary.
Animesh Pandey1, Manish Singh1, Anurag Gupta1
1Department of Mechanical Engineering, Indian Institute of Technology Kanpur, 208016, India.
Physical Review. E
|January 15, 2022
Summary
A wedge disclination deforms elastic sheets into cones. Finite extensibility causes deviations from perfect cones, with negative Gaussian curvature and no stress singularity, unlike ideal inextensible sheets.
Area of Science:
- Solid Mechanics
- Materials Science
- Applied Mathematics
Background:
- Wedge disclinations create conical shapes in ideal elastic sheets.
- Perfect cone formation assumes infinite extent and elastic inextensibility.
Purpose of the Study:
- Investigate deviations from perfect cones in bounded, finitely extensible elastic sheets.
- Analyze the impact of elastic extensibility on deformation and stress fields.
- Examine the role of boundary conditions and material properties.
Main Methods:
- Rigorous analytical solutions.
- Numerical simulations.
- Föppl-von Kármán plate theory.
Main Results:
- Elastic extensibility prevents Dirac singularities in Gaussian curvature and stress fields.
- Gaussian curvature becomes negative in regions away from the defect.
- Increasing Young's modulus promotes singularity development, but inextensibility is not fully achieved.
- Boundary conditions influence Gaussian curvature and buckling transitions.
Conclusions:
- Real elastic sheets deviate from perfect cones due to finite extensibility.
- The model captures complex behaviors like negative Gaussian curvature and stress field modifications.
- Understanding these deviations is crucial for predicting material behavior under stress.
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