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 ε. For this model, the corresponding homogenized model for ε→0 is constructed, which describes the behavior of a homogeneous creep material.
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, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 229–240; Proc. Steklov Inst. Math., 295 (2016), 213–224
\Bibitem{ShaShu16}
\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 Trudy Mat. Inst. Steklova
\yr 2016
\vol 295
\pages 229--240
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968516040142}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 295
\pages 213--224
\crossref{https://doi.org/10.1134/S0081543816080149}
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Linking options:
https://www.mathnet.ru/eng/tm3763
https://doi.org/10.1134/S0371968516040142
https://www.mathnet.ru/eng/tm/v295/p229
This publication is cited in the following 17 articles:
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Tatyana Bobyleva, Alexey Shamaev, Lecture Notes in Civil Engineering, 282, Proceedings of FORM 2022, 2023, 211
Jing Zhang, Jingyu Zhang, Haoyu Wang, Changbing Tang, Pan Yuan, Chunyu Yin, Shurong Ding, Yuanming Li, “Modeling of Mesoscale Creep Behaviors and Macroscale Creep Responses of Composite Fuels Under Irradiation Conditions”, Acta Mech. Solida Sin., 35:6 (2022), 1040
T. Bobyleva, A. Shamaev, Lecture Notes in Civil Engineering, 189, XXX Russian-Polish-Slovak Seminar Theoretical Foundation of Civil Engineering (RSP 2021), 2022, 20
V. V. Shumilova, “Homogenization of the System of Acoustic Equations for Layered Viscoelastic Media”, J Math Sci, 261:3 (2022), 488
Choo J., Semnani Sh.J., White J.A., “An Anisotropic Viscoplasticity Model For Shale Based on Layered Microstructure Homogenization”, Int. J. Numer. Anal. Methods Geomech., 45:4 (2021), 502–520
A. S. Shamaev, V. V. Shumilova, “Asymptotics of the spectra of one-dimensional natural vibrations in media consisting of solid and fluid layers”, Dokl. Phys., 65:4 (2020), 153–156
T N Bobyleva, A S Shamaev, “Effective modules of a layered elastic creep medium with power creep kernels”, IOP Conf. Ser.: Mater. Sci. Eng., 913:3 (2020), 032059
Tatyana Bobyleva, Tat'yana Bobyleva, “AVERAGED MODEL OF LAYERED ELASTIC-CREEPING COMPOSITE MATERI-ALS”, Bulletin of Belgorod State Technological University named after. V. G. Shukhov, 4:1 (2019), 45
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
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
A. A. Gavrikov, A. S. Shamaev, “On the modeling of creep layered structures with nonlinear constitutive relations”, IFAC-PapersOnLine, 51:2 (2018), 150–155
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
Tatiana Bobyleva, Alexei Shamaev, A. Volkov, A. Pustovgar, A. Adamtsevich, “Effective characteristics of a layered tube consisting of elastic-creeping materials”, MATEC Web Conf., 251 (2018), 04039
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
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
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
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