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Deformation of a sheet with coupling between elasticity and concentration
Constantine Khripin1, Tian Tang, Anand Jagota
1Department of Chemical Engineering, Lehigh University, 111 Research Drive, Bethlehem, Pennsylvania 18015, USA.
The Journal of Physical Chemistry. B
|December 19, 2007
Summary
This study models how sheets deform with changing material concentration. Sheets can smoothly adapt to small distortions but may develop complex, nonsmooth solutions for larger deformations.
Area of Science:
- Materials Science
- Solid Mechanics
- Physical Chemistry
Background:
- Deformation of sheets is often influenced by the concentration of mobile species.
- Applications include quasi-2D carbon nanotube arrays where material concentration affects sheet properties.
Purpose of the Study:
- To develop and analyze a simple model for equilibrium deformation of sheets with concentration-dependent elasticity.
- To understand the system's response to imposed distortions based on material concentration.
Main Methods:
- Utilized a free energy functional incorporating concentration-dependent potential energies and free energy of mixing.
- Employed phase plane analysis and numerical simulations to study system behavior.
- Investigated the conditions for smooth versus nonsmooth solutions.
Main Results:
- The model demonstrates that sheets rearrange constituents in response to distortion.
- Smooth and stable deformation is achievable only for sufficiently small imposed distortions.
- Larger distortions can lead to nonsmooth solutions to meet boundary conditions.
Conclusions:
- The model provides insights into the mechanics of concentration-modulated sheet deformation.
- Understanding the transition to nonsmooth solutions is crucial for predicting material behavior under significant stress.
- This work has implications for designing and analyzing materials like carbon nanotube sheets.
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