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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 152, Number 1, Pages 177–190
DOI: https://doi.org/10.4213/tmf6079
(Mi tmf6079)
 

This article is cited in 9 scientific papers (total in 9 papers)

A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory

C. Rogersab, W. K. Schiefcb, K. W. Chowd

a University of New South Wales
b Australian Research Council, Centre of Excellence for Mathematics and Statistics of Complex Systems
c Institut für Mathematik, Technische Universität Berlin
d University of Hong Kong, Department of Mechanical Engineering
Full-text PDF (413 kB) Citations (9)
References:
Abstract: Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress–strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel–titanium.
Keywords: nonlinearity, elasticity, Loewner theory.
English version:
Theoretical and Mathematical Physics, 2007, Volume 152, Issue 1, Pages 1030–1042
DOI: https://doi.org/10.1007/s11232-007-0087-z
Bibliographic databases:
Language: Russian
Citation: C. Rogers, W. K. Schief, K. W. Chow, “A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory”, TMF, 152:1 (2007), 177–190; Theoret. and Math. Phys., 152:1 (2007), 1030–1042
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6079
  • https://doi.org/10.4213/tmf6079
  • https://www.mathnet.ru/eng/tmf/v152/i1/p177
  • This publication is cited in the following 9 articles:
    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:381
    Full-text PDF :216
    References:61
    First page:4
     
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