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Contrasting bending energies from bulk elastic theories
1Department of Biomedical Engineering and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA. wood2316@vt.edu.
Soft Matter
|February 20, 2019
Summary
Choosing the right elastic energy for thin plates and shells significantly impacts soft matter modeling. Our study reveals four elastic theories yield different bending predictions, with some not supporting an isometric ground state.
Area of Science:
- Continuum Mechanics
- Soft Matter Physics
- Material Science
Background:
- The selection of elastic energy functions for thin plates and shells is critical for accurate soft matter modeling.
- Discrepancies exist in current models, leading to varied predictions for material behavior.
Purpose of the Study:
- To investigate the impact of different elastic energy formulations on the bending behavior of thin bodies.
- To determine if existing theories predict an isometric ground state at finite thickness.
Main Methods:
- Analysis of simple deformations in thin bodies within a 2D plane.
- Comparison of predictions from four distinct bulk isotropic quadratic elastic theories.
- Examination of kinematic measures from rod mechanics for defining stretching and bending.
Main Results:
- Four elastic theories exhibit fundamentally different bending behaviors for thin plates and shells.
- These differences persist near the limit of mid-surface isometry for finite thickness bodies.
- Not all considered theories predict an isometric ground state.
Conclusions:
- The choice of elastic energy significantly influences the predicted bending response in thin structures.
- Adopting kinematic measures for stretching and bending can lead to more coherent theoretical frameworks.
- A covariant theory based on stretches, rather than metrics, is proposed for improved modeling.
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