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A new variational principle and its application to nonlinear heterogeneous systems. (English) Zbl 0759.73064

A new variational principle is proposed for estimating the effective properties of nonlinear heterogeneous systems. The variational principle expresses the effective energy-density function of a given nonlinear heterogeneous dielectric in terms on an infinite-dimensional optimization problem involving the effective energy-density functions of the class of linear heterogeneous comparison materials with variable dielectric coefficients. The application of the procedure is illustrated by computing an exact estimate for the effective energy-density function of a nonlinear laminated dielectric material (which has overall anisotropic effective behavior). It is also demonstrated that the Talbot-Willis nonlinear extension [D. R. S. Talbot, IMA J. Appl. Math. 35, 39-54 (1985; Zbl 0588.73025)] of the Hashin-Shtrikman variational principle can be generated from the new variational principle by estimating the effective energy of the linear comparison material.

MSC:

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

Citations:

Zbl 0588.73025
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