Geodesic
Incompressible layered composites with finite deformations on the basis of the asymptotic averaging method
Matematičeskoe modelirovanie i čislennye metody, no. 13 (2017), pp. 32-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article considers the modeling results of incompressible layered composites with finite strains deformation according to the individual layers characteristics. The article proposes an asymptotic averaging method version for layered nonlinearly elastic incompressible composites with finite deformations and periodic structure. We are using a universal representation of the defining relations for incompressible composite layers, proposed by Yu.I. Dimitrienko, which allows us to simulate simultaneously for a complex of various nonlinear elastic media models characterizedby the choice of a pair of energy tensors. We proved that if all composite layers are incompressible, the composite as a whole is also an incompressible, but anisotropic, medium. The article considers the problem of laminated plate uniaxial stretching from incompressible layers with finite deformations. Using the developed method, we calculated the effective deformation diagrams connecting the averaged Piola — Kirchhoff stress tensors components and the strain gradient, as well as the stress distribution in the composite layers. The developed method for calculating effective deformation diagrams and stresses in composite layers can be used in the design of elastomeric composites with specified properties.
Keywords: layered composites, finite deformations, asymptotic averaging method, Piola — Kirchhoff stress tensor, universal models of determining relations, deformation diagrams.
Mots-clés : incompressible media, strain gradient 
@article{MMCM_2017_13_a2,
     author = {Yu. I. Dimitrienko and E. A. Gubareva and D. Yu. Kolzhanova and S. B. Karimov},
     title = {Incompressible layered composites with finite deformations on the basis of the asymptotic averaging method},
     journal = {Matemati\v{c}eskoe modelirovanie i \v{c}islennye metody},
     pages = {32--54},
     year = {2017},
     number = {13},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMCM_2017_13_a2/}
}
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Yu. I. Dimitrienko; E. A. Gubareva; D. Yu. Kolzhanova; S. B. Karimov. Incompressible layered composites with finite deformations on the basis of the asymptotic averaging method. Matematičeskoe modelirovanie i čislennye metody, no. 13 (2017), pp. 32-54. http://geodesic.mathdoc.fr/item/MMCM_2017_13_a2/

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