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Energetic rigidity. I. A unifying theory of mechanical stability
Ojan Khatib Damavandi1, Varda F Hagh2, Christian D Santangelo1
1Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA.
Physical Review. E
|March 16, 2022
Summary
Energetic rigidity, where deformations increase energy, is a more practical measure than constraint counting or second-order rigidity. This new concept unifies mechanical stability and aids material design.
Area of Science:
- Physics
- Materials Science
- Mechanics
Background:
- Rigidity is crucial for system integrity and function.
- Existing rigidity tests include Maxwell-Calladine constraint counting (first-order rigidity) and second-order rigidity.
Purpose of the Study:
- Propose "energetic rigidity" as a more useful practical measure.
- Compare energetic rigidity with existing first- and second-order rigidity tests.
Main Methods:
- Investigate the relationship between constraint counting, second-order rigidity, and energetic rigidity.
- Analyze systems with and without states of self-stress.
Main Results:
- Constraint counting predicts energetic rigidity only in systems without self-stress.
- Second-order rigidity can imply energetic rigidity in systems not deemed rigid by constraint counting.
- Neither first- nor second-order rigidity always imply energetic rigidity.
Conclusions:
- Energetic rigidity offers a unified understanding of mechanical stability.
- The formalism of energetic rigidity opens new pathways for material design.
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