Two-way estimates of porous solid body elasticity moduli
Authors: Zarubin V.S., Saveleva I.Yu., Sergeeva E.S.
Published in issue: #12(72)/2017
DOI: 10.18698/2308-6033-2017-12-1709
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
The dual variational formulation of the problem of linear elasticity of the porous non-homogeneous solid body consisting of the chaotically directed isotropic fragments with different elastic characteristics is used for constructing the two-way estimates of the effective elastic behaviour of such body. We have conducted the quantitative analysis of these estimates and compared them with the known previously published results. The presented calculated ratios can be applied for forecasting the effective values of elasticity moduli of the porous composite material reinforced with isotropic inclusions as well as the materials obtained by means of powder metallurgical techniques and self-propagating high-temperature synthesis.
References
[1] Komkov M.A., Tarasov V.A. Nauka i obrazovanie: Nauchnoe izdanie - Science and Education: Scientific Publication, 2014, no. 12. DOI: 10.7463/1214.0745284
[2] Nazarenko L.V. Thermoelastic Properties of Ortotropic Porous Materials. International Applied Mechanics, 1997, vol. 33, no. 2, pp. 114-122.
[3] Fedosova N.A., Koltsova E.M., Popova N.A., Zharikov E.V. Novye ogneupory - Refractories and Industrial Ceramics, 2015, no. 12, pp. 13-17.
[4] Pogozhev Yu.S., Potanin A.Yu., Levashov E.A., Kovalev D.Yu. Izvestiya vuzov. Poroshkovaya metallurgiya i funktsionalnye pokrytiya - Russian Journal of Non-Ferrous Metals, 2014, no. 4, pp. 19-29.
[5] Amosov A.P., Samboruk A.R., Samboruk A.A., Ermoshkin A.A., Zakamov D.V., Krivolutskiy K.S. Izvestiya vuzov. Poroshkovaya metallurgiya i funktsionalnye pokrytiya - Russian Journal of Non-Ferrous Metals, 2013, no. 4, pp. 31-38.
[6] Zarubin V.S. Modelirovanie [Modeling]. Moscow, Akademiya Publ., 2013, 336 p.
[7] Zarubin V.S., Kuvyrkin G.N. Matematicheskie modeli mekhaniki i elektrodinamiki sploshnoy sredy [Mathematical models of mechanics and electrodynamics of continuous media]. Moscow, BMSTU Publ., 2008, 512 p.
[8] Shermergor T.D. Teoriya uprugosti mikroneodnorodnykh sred [Inhomogeneous media elasticity theory]. Moscow, Nauka Publ., 1977, 400 p.
[9] Golovin N.N., Zarubin V.S., Kuvyrkin G.N. VestnikMGTU im. N.E. Baumana. Seriya: Estestvennye nauki - Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2009, no. 3, pp. 36-49.
[10] Bruno G., Efremov A.M., Levandovskyi A.N., Clausen B. Connecting the macro- and microstrain responses in technical porous ceramics: modeling and experimental validations. Journal of Materials Science, 2011, vol. 46, pp. 161-173.
[11] Roberts A., Garboczi E. Elastic properties of model porous ceramics. Journal of the American Ceramic Society, 2000, vol. 83, no. 12, pp. 3041-3048. DOI: 10.1111/j.1151-2916.2000.tb01680.x
[12] Torquato S. Random Heterogeneous Media: Microstructure and Improved Bounds on Elastic Properties. Applied Mechanics Reviews, 1991, vol. 44, pp. 37-76.
[13] Smolin I.Yu., Eremin M.O., Makarov P.V., Buyakova S.P., Kulkov S.N., Evtushenko E.P. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika - Tomsk State University Journal of Mathematics and Mechanics, 2013, no. 5 (25), pp. 78-90.
[14] Zarubin V.S. Prikladnye zadachi termoprochnosti elementov konstruktsiy [Applied problems of constructional elements thermostability]. Moscow, Mashinostroenie Publ., 1985, 296 p.
[15] Christensen R.M. Mechanics of Composite Materials. John Wiley & Sons, Inc., 1979 [In Russ.: Christensen R. Vvedenie v mekhaniku kompozitov (Introduction to composite mechanics). Moscow, Mir Publ., 1982, 336 p.].
[16] Zarubin V.S., Kuvyrkin G.N., Saveleva I.Yu. VestnikMGTU im. N.E. Baumana. Seriya: Mashinostroenie - Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, 2014, no. 5 (98), pp. 53-69.
[17] Attetkov A.V., Zarubin V.S., Kanatnikov A.N. Vvedenie v metody optimizatsii [Introduction to optimization methods]. Moscow, NITs INFRA-M Publ., 2008, 272 p.
[18] Attetkov A.V., Zarubin V.S., Kanatnikov A.N. Metody optimizatsii [Optimization methods]. Moscow, RIOR Publ., 2012, 270 p.
[19] Butarovich D.O., Smirnov A.A., Ryabov D.M. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie - Proceedings of Higher Educational Institutions. МаМne Building, 2011, no. 7, pp. 53-58.