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Article

Keywords:
stationary heat conduction problem; $Y$-periodicity; homogenized coefficients; bounds; laminate structures.
Summary:
In this paper we study bounds for the off-diagonal elements of the homogenized tensor for the stationary heat conduction problem. We also state that these bounds are sharp by proving a formula for the homogenized tensor in the case of laminate structures.
References:
[1] A. Bensoussan, J. L. Lions, G. Papanicolaou: Asymptotic analysis for periodic structures. North-Holland, Amsterdam, 1978. MR 0503330
[2] L. V. Gibiansky: Bounds on effective moduli of composite materials. Lecture notes, School on Homogenization, ICTP, Trieste, 1993.
[3] Z. Hashin, S. Shtrikman: A variational approach to the theory of effective magnetic permeability of multi phase materials. J. Appl. Phys. 33 (1962), 3125–3131. DOI 10.1063/1.1728579
[4] C. Johnson: Numerical solution of partial differential equations by the finite element method. Studentlitteratur, Lund, 1987. MR 0911477 | Zbl 0628.65098
[5] D. Lukkassen: Upper and lower bounds for homogenized coefficients. Uspekhi Mat. Nauk 49 (1994), no. 4, 115.
[6] D. Lukkassen, L. E. Persson, P. Wall: On some sharp bounds for the effective conductivity. Proceedings from the first International Conference on Composites Engineering (ICCE/1), New Orleans, 1994, pp. 855–856.
[7] G. W. Milton: On characterizing the set of possible effective tensors of composites: The Variational Method and the Translation Method. Comm. on Pure and Appl. Math. XLIII (1990), 63–125. MR 1024190 | Zbl 0751.73041
[8] L. E. Persson, L. Persson, N. Svanstedt, J. Wyller: The homogenization method: An introduction. Studentlitteratur, Lund, 1993. MR 1250833
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