Abstract
The aim of the present contribution is to perform nonlinear homogenization of piezoelectric composites with periodic or random microstructure. As it was argued by Tiersten [10], for stronger electric fields one has to take into account higher order terms in the electric field E. The form of the electric enthalpy H (e, E) proposed by this author, being of the third order in E, cannot be concave in E; here e denotes the strain tensor. It should be remembered that H (e, E) is here understood as a partial concave conjugate of the internal energy function U (e, D) with respect to D, D being the electric displacement vector. By using the Г-convergence theory we obtain general form of the macroscopic potential (the effective internal energy function). The homogenization process smears out the microscopic inhomogeneities, cf. [1,2,5,7,8,11,12]. To perform this procedure the duality argument will play an essential role. The dual approach is also useful in finding bounds on effective properties. The homogenized potential U h and its dual U h * are also formulated for a statistically homogeneous ergodic medium.
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Telega, J.J., Gambin, B., Galka, A. (1999). Nonlinear Piezoelectric Composites: Deterministic and Stochastic Homogenization. In: Holnicki-Szulc, J., Rodellar, J. (eds) Smart Structures. NATO Science Series, vol 65. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4611-1_40
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DOI: https://doi.org/10.1007/978-94-011-4611-1_40
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