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A variational approach to the overall sink strength of a nonlinear lossy composite medium. (English) Zbl 0604.76078

Based on the Hashin-Shtrikman variational structure the authors treat the problem of homogenization of the semilinear steady-state diffusion equation where the convex energy function W is assumed to vary randomly with the position. A suitably defined overall function \(\tilde W\) describes the homogeneized medium. Classical energy bounds as well as tighter bounds (due to the H.-S. structure) are derived for a n-phase medium. Especially a two-phase composite medium is investigated explicitely. Sample results demonstrate both the sensitivity of the system to the details of the microstructure and the potential use of the new variational formulation. Paper is a generalization of a recent study of the authors to the case of nonlinear sinks [Mech. Mater. 3, 171-181; 183-191 (1984)].
Reviewer: H.Bufler

MSC:

76R99 Diffusion and convection
35A15 Variational methods applied to PDEs
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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