Выходит 4 номеров в год
ISSN Печать: 2152-2057
ISSN Онлайн: 2152-2073
Indexed in
HEAT TRANSFER IN A COMPOSITE MATERIAL WITH STRUCTURAL HIERARCHY
Краткое описание
An asymptotic homogenization is used to study heat transfer in a heterogeneous material with multiscale periodic structure. We suppose the existence of a hierarchy of spatial scales and a contrast of physical properties of the components of the composite. The proposed multiscale approach allows one to replace real heterogeneous material with homogeneous medium with effective characteristics. As a result, we have got an analytical approximation for the distribution of temperature in composite with structural hierarchy and studied how effective characteristics can be influenced by the details of the geometry and the properties of the material on different spatial scales.
-
Allaire, G. and Habibi, Z., Homogenization of a Conductive, Convective, and Radiative Heat Transfer Problem in a Heterogeneous Domain, SIAM J. Math. Anal, vol. 45, pp. 1136-1178, 2013.
-
Allaire, G., Homogenization and Two-Scale Convergence, SIAM J. Math. Anal., vol. 23, pp. 1482-1518, 1992.
-
Auriault, J.L., Effective Macroscopic Description for Heat Conduction in Periodic Composites, Int. J. Heat Mass Transf, vol. 26, no. 6, pp. 861-869, 1985.
-
Bakhvalov, N.S. and Panasenko, G.P., Homogenization: Averaging Processes in Periodic Media. Mathematical Problems in the Mechanics of Composite Material, Dordrecht, Netherlands: Kluwer Academic, 1989.
-
Geng, Q., Zhu, S., and Chong, K.P., Issues in Design of One-Dimensional Metamaterials for Seismic Protection, Soil Dyn. Earthquake Eng., vol. 107, pp. 264-278, 2018.
-
Incropera, F. and De Witt, D., Fundamentals of Heat and Mass Transfer, Introduction to Heat Transfer, 6th ed., New York: John Wiley and Sons, 2007.
-
Lakes, R., Materials with Structural Hierarchy, Nature, vol. 361, pp. 511-515, 1993.
-
Mei, Ch.C. and Vernescu, B., Homogenization Methods for Multiscale Mechanics, World Scientific, 2010.
-
Sanchez-Palencia, E., Nonhomogeneous Media and Vibration Theory, Lecture Notes in Physics, New York: Springer-Verlag, 1980.
-
Savatorova, V.L., Talonov, A.V., and Vlasov, A.N., Homogenization of Thermoelasticity Processes in Composite Materials with Periodic Structure of Heterogeneities, Z. Angew. Math. Mech. (ZAMM), vol. 93, no. 8, pp. 575-596, 2012a. DOI: 10.1002/zamm.201200032.
-
Savatorova, V.L., Talonov, A.V., Vlasov, A.N., and Volkov-Bogorodsky, D.B., Multiscale Modeling of Thermoelastic Properties of Composites with Periodic Structure of Heterogeneities, Mater. Phys. Mech., vol. 13, pp. 130-142, 2012b.
-
Telega, J.J., Tokarzewski, S., and Galka, A., Effective Conductivity of Nonlinear Two-Phase Media: Homogenization and Two-Point Pade Approximants, Acta Appl. Math., vol. 61, pp. 295-315, 2000.
-
White, J., Analysis of Heat Conduction in a Heterogeneous Material by Multiple-Scale Averaging Method, ASME J. Heat Transf., vol. 137, no. 7, article ID 071301, 2015.
-
Yang, Z., Hao, Z., Sun, Y., Liu, Y., and Dong, H., Thermo-Mechanical Analysis of Nonlinear Heterogeneous Materials by Second-Order Reduced Asymptotic Expansion Approach, Int. J. Solids Struct., vols. 178-179, pp. 91-107, 2019.
-
Zhang, H.W., Zhang, S., Bi, J.Y., and Schrefler, B.A., Thermo-Mechanical Analysis of Periodic Multiphase Materials by a Multiscale Asymptotic Homogenization Approach, Int. J. Numer. Methods Eng., vol. 69, pp. 87-113, 2007.