Micromechanical modeling of magnetoelectroelastic composite materials with multicoated inclusions and functionally graded interphases

Abstract

In this article, micromechanical modeling of magnetoelectroelastic composites with multicoated inclusions and functionally graded interphases are elaborated. The integral equation taking into account the continuously varying interphase properties as well as the multifunctional coating effects is introduced based on Green’s tensors and interfacial operators. Magnetoelectroelastic composites with functionally graded interphases are analyzed, and the effective properties are derived. Based on the Mori–Tanaka, Self-Consistent, and Incremental Self-Consistent models, the numerically predicted effective properties of magnetoelectroelastic composites are presented with respect to the volume fractions, shapes of the multicoated inclusions, and the thickness of the coatings. The multicoating and functionally graded interphase concepts can be used to optimize the effective properties of multifunctional composites. This can be used to design new multifunctional composite materials with higher coupling coefficients.

Viscomagnetoelectroelastic effective properties’ modeling for multi-phase and multi-coated magnetoelectroelastic composites

“…Using the condensed notation (Bakkali et al, 2011(Bakkali et al, , 2012(Bakkali et al, , 2013a(Bakkali et al, , 2013b, one can write the time constitutive model in the following form…”

“…The concept of periodic structure was improved by Tang and Yu (2008) via a variational asymptotic homogenization scheme for composites including piezoelectric and piezomagnetic phases embedded in an epoxy matrix. The effective behavior of N-phase and multi-coated magnetoelectroelastic composites was predicted based on different micromechanical models by Bakkali et al (2011Bakkali et al ( , 2012Bakkali et al ( , 2013aBakkali et al ( , 2013b. The focus was on the incremental self-consistent model which was developed to circumvent the limitation of the self-consistent model.…”

Analytical and semi-analytical modeling of effective moduli bounds: Application to transversely isotropic piezoelectric materials

“…Different micromechanical models are used to predict effective moduli of heterogeneous piezoelectric materials. Although these models give direct estimates of effective moduli in terms of composite microstructures, they do not give similar predictions in the most cases and particularly for large volume fractions of inclusions or large contrast of heterogeneities (see for instance Bakkali et al, 2011, 2013; Dunn and Taya, 1993b; El Ouafi et al, 2015; Fakri et al, 2003). It is well known that variational bounds provide good estimations for effective moduli of heterogeneous materials and present a rigorous approach for micromechanical approximations.…”

“…Micromechanical models represent an efficient tool to evaluate the overall properties of heterogeneous bodies. Several methods, mostly based on the fundamental solution of Eshelby (1957) of the problem of an ellipsoidal inclusion in an infinite isotropic medium, have been proposed to compute estimation or bounds of the effective elastic or electroelastic properties of composite materials when the volume fractions or the actual geometry of the constituent phases is known (Bakkali et al, 2013; Dunn and Taya, 1993a-1993b, El Ouafi et al, 2015; Fakri and Azrar, 2010; Fakri et al, 2003; Mura, 1982). Viscoelectroelastic properties for multi-coated piezoelectric composites are investigated by Azrar et al (2014).…”

An analytical method for predicting the anti-plane effective magnetoelectroelastic coefficients of composites containing doubly periodic multicoated fibers

“…Different models are employed to predict the effective properties of magnetoelectroelastic composites with the interphase (coating). For random (disordered) magnetoelectroelastic composites, some micromechanical models, such as the dilute model, self-consistent model, generalized self-consistent model, Mori-Tanaka model, multi-inclusion model and so on, are often applied [13][14][15][16], these models treat the inclusion interactions either approximately or in a statistically sense. To account for the interaction effect more accurately, periodic microstructures are considered using the concept of repeating unit cells.…”