TY - JOUR
T1 - Energetic rigidity. I. A unifying theory of mechanical stability
AU - Damavandi, Ojan Khatib
AU - Hagh, Varda F.
AU - Santangelo, Christian D.
AU - Manning, M. Lisa
N1 - Funding Information:
We are grateful to Z. Rocklin for an inspiring initial conversation pointing out the connection between rigidity and origami, and to M. Holmes-Cerfon for substantial comments on the manuscript. This work is partially supported by grants from the Simons Foundation, Grants No. 348126 to S. Nagel (V.F.H.), No. 454947 to M.L.M. (O.K.D. and M.L.M.), and No. 446222 (M.L.M.). C.D.S. acknowledges funding from the NSF through Grant No. DMR-1822638, and M.L.M. acknowledges support from NSF through Grant No. DMR-1951921.
Publisher Copyright:
© 2022 American Physical Society.
PY - 2022/2/1
Y1 - 2022/2/1
N2 - Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that "energetic rigidity,"in which all nontrivial deformations raise the energy of a structure, is a more useful notion of rigidity in practice than two more commonly used rigidity tests: Maxwell-Calladine constraint counting (first-order rigidity) and second-order rigidity. We find that constraint counting robustly predicts energetic rigidity only when the system has no states of self-stress. When the system has states of self-stress, we show that second-order rigidity can imply energetic rigidity in systems that are not considered rigid based on constraint counting, and is even more reliable than shear modulus. We also show that there may be systems for which neither first- nor second-order rigidity imply energetic rigidity. The formalism of energetic rigidity unifies our understanding of mechanical stability and also suggests new avenues for material design.
AB - Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that "energetic rigidity,"in which all nontrivial deformations raise the energy of a structure, is a more useful notion of rigidity in practice than two more commonly used rigidity tests: Maxwell-Calladine constraint counting (first-order rigidity) and second-order rigidity. We find that constraint counting robustly predicts energetic rigidity only when the system has no states of self-stress. When the system has states of self-stress, we show that second-order rigidity can imply energetic rigidity in systems that are not considered rigid based on constraint counting, and is even more reliable than shear modulus. We also show that there may be systems for which neither first- nor second-order rigidity imply energetic rigidity. The formalism of energetic rigidity unifies our understanding of mechanical stability and also suggests new avenues for material design.
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U2 - 10.1103/PhysRevE.105.025003
DO - 10.1103/PhysRevE.105.025003
M3 - Article
C2 - 35291185
AN - SCOPUS:85125594761
VL - 105
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
SN - 1063-651X
IS - 2
M1 - 025003
ER -