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Tr. Mat. Inst. Steklova, 2016, Volume 295, Pages 229–240 (Mi tm3763)  

This article is cited in 7 scientific papers (total in 7 papers)

Homogenization of the equations of state for a heterogeneous layered medium consisting of two creep materials

A. S. Shamaev, V. V. Shumilova

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: A mathematical model that describes the joint motion of periodically alternating layers of two isotropic creep materials is considered. It is assumed that all layers are parallel to one of the coordinate planes and the thickness of any two adjacent layers is $\varepsilon$. For this model, the corresponding homogenized model for $\varepsilon\to0$ is constructed, which describes the behavior of a homogeneous creep material.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 295, 213–224

Bibliographic databases:

UDC: 517.958
Received: June 22, 2016

Citation: A. S. Shamaev, V. V. Shumilova, “Homogenization of the equations of state for a heterogeneous layered medium consisting of two creep materials”, Modern problems of mechanics, Collected papers, Tr. Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 229–240; Proc. Steklov Inst. Math., 295 (2016), 213–224

Citation in format AMSBIB
\by A.~S.~Shamaev, V.~V.~Shumilova
\paper Homogenization of the equations of state for a~heterogeneous layered medium consisting of two creep materials
\inbook Modern problems of mechanics
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2016
\vol 295
\pages 229--240
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 295
\pages 213--224

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    This publication is cited in the following articles:
    1. T. N. Bobyleva, “Method of calculation of stresses in the layered elastic-creeping arrays”, 5th International Scientific Conference Integration, Partnership and Innovation in Construction Science and Education, MATEC Web Conf., 86, ed. V. Andreev, EDP Sciences, 2016, UNSP 01024  crossref  isi  scopus
    2. T. N. Bobyleva, A. S. Shamaev, “An efficient algorithm for calculating rheological parameters of layered soil media composed from elastic-creeping materials”, Soil Mech. Found. Eng., 54:4 (2017), 224–230  crossref  isi  scopus
    3. T. Bobyleva, A. Shamaev, “Stress distribution in layered elastic creeping array with a vertical cylindrical shaft”, RSP 2017 (XXVI R-S-P Seminar 2017 Theoretical Foundation of Civil Engineering), MATEC Web Conf., 117, eds. S. Jemiolo, A. Zbiciak, M. MitewCzajewska, M. Krzeminski, M. Gajewski, EDP Sciences, 2017, UNSP 00020  crossref  isi  scopus
    4. T. N. Bobyleva, A. S. Shamaev, “Method of approximate calculation of the stress tensor in layered elastic-creeping environments”, IFAC-PapersOnLine, 51:2 (2018), 138–143  crossref  isi  scopus
    5. A. A. Gavrikov, D. Knyazkov, A. M. Melnikov, A. S. Shamaev, V. V. Vedeneev, “On limits of applicability of the homogenization method to modeling of layered creep media”, IFAC-PapersOnLine, 51:2 (2018), 144–149  crossref  isi  scopus
    6. A. A. Gavrikov, A. S. Shamaev, “On the modeling of creep layered structures with nonlinear constitutive relations”, IFAC-PapersOnLine, 51:2 (2018), 150–155  crossref  isi  scopus
    7. T. Bobyleva, A. Shamaev, “The averaged model of layered elastic-creeping composite materials”, XXI International Scientific Conference on Advanced in Civil Engineering Construction - the Formation of Living Environment, IOP Conference Series-Materials Science and Engineering, 365, eds. A. Askadskiy, A. Pustovgar, T. Matseevich, A. Adamtsevich, IOP Publishing Ltd, 2018, 042078  crossref  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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