×

Thermo-mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach. (English) Zbl 1129.74018

Summary: We study a spatial and temporal multiscale asymptotic homogenization method to simulate thermo-dynamic wave propagation in periodic multiphase materials. A general field governing equation of thermo-dynamic wave propagation is expressed in a unified form with both inertia and velocity terms. Amplified spatial and reduced temporal scales are, respectively, introduced to account for spatial and temporal fluctuations and for non-local effects in the homogenized solution due to material heterogeneity and diverse time scales. The model is derived from higher-order homogenization theory with multiple spatial and temporal scales. It is also shown that the modified higher-order terms bring in a non-local dispersion effect of the microstructure of multiphase materials. One-dimensional non-Fourier heat conduction and dynamic problems under thermal shock are computed to demonstrate the efficiency and validity of the developed procedure. The results indicate the disadvantages of classical spatial homogenization.

MSC:

74F05 Thermal effects in solid mechanics
74Q10 Homogenization and oscillations in dynamical problems of solid mechanics
80M40 Homogenization for problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Andrianov, Applied Mechanics Reviews 56 pp 87– (2003)
[2] . Homogenization: Averaging Processes in Periodic Media. Kluwer: Dordrecht, The Netherlands, 1989.
[3] , . Asymptotic Analysis for Periodic Structures. North-Holland: Amsterdam, 1978.
[4] Non-homogeneous Media and Vibration Theory. Springer: Berlin, 1980. · Zbl 0432.70002
[5] Chung, International Journal for Numerical Methods in Engineering 59 pp 825– (2004)
[6] Boutin, International Journal of Solids and Structures 33 pp 1023– (1996)
[7] Schrefler, Mechanics of Composite Materials and Structures 4 pp 159– (1997)
[8] Gambin, Physica Status Solidi 51 pp 513– (1989)
[9] Boutin, International Journal of Engineering Science 31 pp 1669– (1993)
[10] Chen, Journal of Applied Mechanics 68 pp 153– (2001)
[11] Fish, International Journal for Numerical Methods in Engineering 54 pp 331– (2002)
[12] Raghavan, Computer Modeling in Engineering and Sciences 5 pp 151– (2004)
[13] Fish, International Journal for Multiscale Computational Engineering 1 pp 43– (2003)
[14] Zhang, Computational Mechanics 24 pp 217– (1999)
[15] Zhang, Mechanics of Composite Materials and Structures 7 pp 355– (2000)
[16] Özisik, Journal of Heat Transfer 116 pp 526– (1994)
[17] Kaminski, Journal of Heat Transfer 112 pp 555– (1990)
[18] Roetzel, International Journal of Thermal Sciences 42 pp 541– (2003)
[19] Tsai, International Journal of Heat and Mass Transfer 46 pp 5137– (2003)
[20] Chen, Composites Engineering 5 pp 1135– (1995)
[21] Feldman, Composite Structures 47 pp 619– (1999)
[22] Makhecha, Composite Structures 51 pp 221– (2001)
[23] Lefik, Archives of Mechanics 52 pp 203– (2000)
[24] Boutin, International Journal of Heat and Mass Transfer 38 pp 3181– (1995)
[25] Aboudi, Journal of Heat Transfer 68 pp 697– (2001)
[26] Yu, International Journal of Solids and Structures 39 pp 6429– (2002)
[27] Zhang, International Journal of Solids and Structures 42 pp 877– (2005)
[28] Hassani, Computers and Structures 69 pp 707– (1998)
[29] Cattaneo, Compte Rendus 247 pp 431– (1958)
[30] Vernotte, Compte Rendus 252 pp 2190– (1961)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.