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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 3, Pages 336–352
DOI: https://doi.org/10.4213/tmf6354 (Mi tmf6354) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Existence of energy minimums for thin elastic rods in static helical configurations

M. Argeria, V. Baroneb, S. De Lilloc, G. Lupoc, M. Sommacalc

a Università degli Studi di Napoli Federico II
b Scuola Normale Superiore in Pisa
c Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia
Full-text PDF (625 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf6354
Abstract: We characterize families of solutions of the static Kirchhoff model of a thin elastic rod physically. These families, which are proved to exist, depend on the behavior of the so-called register and also on the radius and pitch. We describe the energy densities for each of the solutions in terms of the elastic properties and geometric shape of the unstrained rod, which allows determining the selection mechanism for thepreferred helical configurations. This analysis promises to be a fundamental tool for understanding the close connection between the study of elastic deformations in thin rods and coarse-grained models with widespread applications in the natural sciences.
Keywords: thin elastic rod, Kirchhoff equation, inverse problem, integrability, helix.
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 3, Pages 698–711
DOI: https://doi.org/10.1007/s11232-009-0058-7
Bibliographic databases:
Language: Russian
Citation: M. Argeri, V. Barone, S. De Lillo, G. Lupo, M. Sommacal, “Existence of energy minimums for thin elastic rods in static helical configurations”, TMF, 159:3 (2009), 336–352; Theoret. and Math. Phys., 159:3 (2009), 698–711
Citation in format AMSBIB
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\paper Existence of energy minimums for thin elastic rods in static helical configurations
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  • https://www.mathnet.ru/eng/tmf6354
  • https://doi.org/10.4213/tmf6354
  • https://www.mathnet.ru/eng/tmf/v159/i3/p336
    • This publication is cited in the following 3 articles:
    1. Ablowitz M.J., Barone V., De Lillo S., Sommacal M., “Traveling Waves in Elastic Rods with Arbitrary Curvature and Torsion”, J. Nonlinear Sci., 22:6 (2012), 1013–1040  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Matthews J.F., Bergenstrahle M., Beckham G.T., Himmel M.E., Nimlos M.R., Brady J.W., Crowley M.F., “High-temperature behavior of cellulose I”, J. Phys. Chem. B, 115:10 (2011), 2155–2166  crossref  isi  elib  scopus
    3. De Lillo S., Lupo G., Sommacal M., “Helical configurations of elastic rods in the presence of a long-range interaction potential”, J. Phys. A, 43:8 (2010), 085214, 19 pp.  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:388
    Full-text PDF :191
    References:55
    First page:4
     
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