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Asymptotic Homogenization Applied to Flexoelectric Rods
David Guinovart-Sanjuán1, Jose Merodio2, Juan Carlos López-Realpozo3
1Department of Mathematics, University of Central Florida, 4393 Andromeda Loop N, Orlando, FL 32816, USA. Guinovart@ucf.edu.
Abstract:
In this manuscript, the equilibrium problem for a flexoelectric one-dimensional composite material is studied. The two-scales asymptotic homogenization method is used to derive the homogenized formulation of this problem. The manuscript offers a step-by-step methodology to derive effective coefficients and to solve local problems. As an illustrative example, results reported in the literature for piezoelectric composites are obtained as a particular case of the formulation derived here. Finally, three flexoelectric/piezoelectric composites are studied to illustrate the influence of the flexoelectric property on the effective coefficients and the global behavior of the structure.
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