Geodesic
A~novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 177-190

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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. 
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     author = {C. Rogers and W. K. Schief and K. W. Chow},
     title = {A~novel class of model constitutive laws in nonlinear elasticity: {Construction} via {Loewner} theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {152},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a13/}
}
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C. Rogers; W. K. Schief; K. W. Chow. A~novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 177-190. http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a13/