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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
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.
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
Linking options:
https://www.mathnet.ru/eng/tmf6079https://doi.org/10.4213/tmf6079 https://www.mathnet.ru/eng/tmf/v152/i1/p177
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Abstract page: | 384 | Full-text PDF : | 216 | References: | 61 | First page: | 4 |
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