Geodesic
Application of the nonlinear theory of elasticity and similarity method for assessment of the metallic jersey deformation properties
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 49 (2017), pp. 105-113 Cet article a éte moissonné depuis la source Math-Net.Ru

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Earlier, a two-dimensional deformation of the square knitwear samples made of the microwires have been experimentally investigated under condition of the equal forces acting in the two mutually perpendicular directions. It has been found that the contact points between the structural elements in these samples stay almost immovable along the microwire. We have developed a computer program for calculating the two-dimensional deformation of such samples. It is based on the nonlinear theory of elasticity taking into account the current observation. The theoretical calculations obtained for several structures have been shown to be in a good agreement with experimental data. The program code has been analyzed in order to determine the influence of structure parameters on the deformation properties of the samples. It has been shown that if the two structures are similar, the samples are of the same size, but the size of the elements in the second structure is $n_1$ times smaller and the microwire rigidity on the bend is $n_2$ times larger than that in the first one. Therefore, to obtain the same sizes of the sample after deformation, the force acting on the second sample should be $n_1^3\cdot n_2$ times greater than that acting on the first sample. It has been found that the simultaneous decrease in dimensions of the structure elements and in the wavelength by an equal number of times does not lead to the significant changes in reflection coefficient.
Keywords: metallic jersey, reflective surface, reflection coefficient of electromagnetic waves, similarity method, nonlinear theory of elasticity. 
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     author = {V. I. Khalimanovich and L. A. Kudryavin and O. F. Belyaev and V. A. Zavaruev},
     title = {Application of the nonlinear theory of elasticity and similarity method for assessment of the metallic jersey deformation properties},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {105--113},
     year = {2017},
     number = {49},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2017_49_a9/}
}
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V. I. Khalimanovich; L. A. Kudryavin; O. F. Belyaev; V. A. Zavaruev. Application of the nonlinear theory of elasticity and similarity method for assessment of the metallic jersey deformation properties. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 49 (2017), pp. 105-113. http://geodesic.mathdoc.fr/item/VTGU_2017_49_a9/

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