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.


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


Zbl 0588.73025
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