Bounds and estimates for the properties of nonlinear heterogeneous systems. (English) Zbl 0776.73062

The author reviews his variational principle which allows to estimate the effective properties of nonlinear heterogeneous systems, and applies it to establish bounds and exact estimates for the effective properties of arbitrarily nonlinear heterogeneous dielectrics. The relations between his bounds and the Hashin-Shtrikman and Beran bounds for linear dielectrics are discussed. Its sharpness and optimality are examined. For special microgeometries of the composite the effective nonlinear properties can be computed exactly; the new variational principle plays a central role. The author asserts that, although the nonlinear bounds given in this paper may not be optimal in general, they are probably not too far from the optimal bounds.
Reviewer: S.Minagawa (Tokyo)


74F15 Electromagnetic effects in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74E30 Composite and mixture properties
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