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Strain tensor selection and the elastic theory of incompatible thin sheets
1Raymond & Beverly Sackler School of Physics & Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel.
Physical Review. E
|June 17, 2017
Summary
This study introduces a new theory for incompatible elastic sheets, defining strain using distance deviations. This alternative formulation offers simpler equations and aligns with existing theories in specific cases.
Area of Science:
- Solid Mechanics
- Materials Science
- Continuum Mechanics
Background:
- Existing theory of incompatible elastic sheets defines strain via metric deviations.
- This framework is crucial for understanding non-Euclidean material behavior.
Purpose of the Study:
- To examine an alternative formulation for incompatible elastic sheets.
- To define strain based on deviations of distances from rest values.
Main Methods:
- Analysis of simple axisymmetric problems.
- Comparison of a novel strain definition with the existing metric-based approach.
- Investigation of limiting cases: small slopes and incompressible sheets.
Main Results:
- The alternative formulation is not always equivalent to the existing theory.
- It yields linear, solvable equilibrium equations for planar deformations.
- It aligns with extensible elastica theory for uniaxial deformations, predicting unstrained cylindrical configurations.
- A criterion for mechanical equilibrium of isometric immersions is proposed.
Conclusions:
- The alternative formulation provides new insights and advantages over existing theories.
- It simplifies analysis for specific deformation modes.
- It offers a clear condition for equilibrium in immersed incompatible sheets.
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