Extended mean-field homogenization of unidirectional piezoelectric nanocomposites with generalized Gurtin-Murdoch interfaces

Abstract

This paper presents for the first time an extended Mori-Tanaka approach aimed at identifying the little-explored piezoelectric response of unidirectional nanoporous composites with energetic surfaces. The interface is simulated using the generalized Gurtin-Murdoch coherent interface model considering nonvanishing in-plane surface stress and surface electric displacement. The analytical solutions for Eshelby’s inhomogeneity problems are obtained by solving four systems of equations, generated from the known macroscopic electromechanical loading conditions. The dilute concentration tensors for the fiber and energetic surface are evaluated exactly for coupled electromechanical fields, which are then utilized in the extended multiphysics Mori-Tanaka homogenization scheme. The reliability and accuracy of the extended theory are demonstrated through an extensive comparison with the predictions of the composite cylinder assemblage (CCA), the generalized self-consistent method (GSCM), as well as the finite-element (FE) homogenization technique. New results generated in this work demonstrate that, except for the transverse shear modulus, the extended Mori-Tanaka, CCA, and FE provide indistinguishable results under axisymmetric, axial shear, and electric loading, even at high volume fractions and small pore sizes where the surface piezoelectric effects are significant.