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Variational bounds for thermal fields in media with heterogeneous microstructure. (English) Zbl 1362.74029

Summary: This work develops a rigorous variational upper bound for the difference between thermal fields generated in uniform media and thermal fields generated in heterogeneous media, for the same external loading. The bound can be calculated in a simple manner, with knowledge only of the heterogeneous material properties and a relatively easy-to-compute thermal field associated with a uniform medium. In order to evaluate the bound, the difficult-to-compute thermal field, associated with the heterogeneous material, does not need to be calculated. Three-dimensional numerical examples are provided to illustrate the results.

MSC:

74Q20 Bounds on effective properties in solid mechanics
74E05 Inhomogeneity in solid mechanics
74F05 Thermal effects in solid mechanics
74M25 Micromechanics of solids
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References:

[1] Maxwell JC, Philos Trans Soc London 157 pp 49– (1867)
[2] Maxwell JC, A treatise on electricity and magnetism, 3. ed. (1873)
[3] Rayleigh JW, Phil Mag 32 pp 481– (1892)
[4] DOI: 10.1007/978-1-4757-6355-3
[5] DOI: 10.1007/978-3-642-84659-5
[6] Hashin Z, ASME J Appl Mech 50 pp 481– (1983) · Zbl 0542.73092
[7] Mura T, Micromechanics of defects in solids, 2. ed. (1993)
[8] Nemat-Nasser S, Micromechanics: Overall properties of heterogeneous solids, 2. ed. (1999)
[9] Huet C, Mech Res Commun 9 (3) pp 165– (1982) · Zbl 0519.73011
[10] Huet C, Mech Res Commun 11 (3) pp 195– (1984)
[11] Ghosh S, Micromechanical analysis and multi-scale modeling using the Voronoi cell finite element method (2011) · Zbl 1236.74002
[12] Ghosh S, Computational methods for microstructure-property relations (2011)
[13] Zohdi TI, Introduction to computational micromechanics (2008)
[14] Zohdi TI, Electromagnetic properties of multiphase dielectrics: A primer on modeling, theory and computation (2012) · Zbl 1314.78002
[15] Zohdi TI, Z Angew Math Phys 56 (3) pp 497– (2005) · Zbl 1065.74055
[16] Zohdi TI, Comput Meth Appl Mech Eng 138 pp 273– (1996) · Zbl 0921.73080
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