Effective properties of periodic fibrous electro-elastic composites with mechanic imperfect contact condition

Abstract

International audienceIn this work, two-phase parallel fiber-reinforced periodic piezoelectric composites are considered wherein the constituents exhibit transverse isotropy and the cells have different configurations. Mechanical imperfect contact at the interface of the composites is studied via linear spring model. The statement of the problem for two phase piezoelectric composites with mechanical imperfect contact is given. The local problems are formulated by means of the asymptotic homogenization method (AHM) and their solutions are found using complex variable theory. Analytical formulae are obtained for the effective properties of the composites with spring imperfect type of contact and different parallelogram cells. Some numerical examples and comparisons with other theoretical results illustrate that the model is efficient for the analysis of composites with presence of parallelogram cells and the aforementioned imperfect contact

An approach for modeling three‐phase piezoelectric composites

“…This analysis leads to monoclinic behavior of periodic piezoelectric composites with the parallelepiped cell. The present work generalizes other relative investigations, like the aforementioned references by the previous authors of this contribution, and new ones, such as Rodríguez-Ramos et al, [5], in which effective elastic properties using three different approaches for composite materials under imperfect contact adherence are calculated. Kari et al, [24] used numerical homogenization techniques based on FEM to calculate the effective properties for different three-phase types of composites.…”

“…The multiple-scale method is well adapted to the periodic framework in which we are focused in this work. Even the first approximation of the solutions in problem (1)-(2) yields an error of order "=L, where L is a macroscopic substantial characteristic of the heterogeneous body, in comparison with the solutions of the problem (5). This value is within thousandths of the one percent for many composites with a fine scale ."…”

“…Different micromechanical models of piezoelectric composite materials have been applied for understanding the coupling behavior between the electric and mechanic field and to predict the electroelastic effective properties (for example, Benveniste [1], Zhang et al, [2], Jiang et al, [3], Dinzart and Sabar [4], Rodríguez-Ramos et al, [5], Xu et al, [6] and Eynbeygi and Aghdam [7]). An appropriate description of the coupling phenomena produced for piezoelectric-reinforced materials is often of interest, including non-well bonded reinforcement (Wang and Pan [8], Gu et al, [9]) or coated inclusions (Shen et al, [10]; Shiah et al, [11]; Xiao et al, [12]) added in the matrix.…”

Anti-plane time-harmonic Green’s functions for a coated circular inhomogeneity in a piezoelectric medium with spring- or membrane-type imperfect interfaces

“…In the same manner, the unknown coefficients can be determined by introducing equations (24) to (27) into equations (18) to (23) to give …”

Characterization of piezoelectric composites with mechanical and electrical imperfect contacts

“…24 A detailed description of the local-value problems solution set up in (8)- (9), (11)- (12) using complex variable methods, the properties of doubly periodic elliptic and related functions with periods w 1 and w 2 applied to such problems has not been reported until now. The local-value problems solution under mechanical imperfect and electrical perfect conditions is reported in Rodriguez-Ramos et al 17 Taking into account that the rate of debonding depends on material property and interphase thickness, the following relations are usedK n ¼ C Since the electrical imperfection is related only with the antiplane problem we focus our aim in the out-ofplane problems where the mechanical and electrical imperfect conditions are coupled. For convenience we use in all subsequent derivations dimensionless imperfection parameters K s and K which are related toK s andK by K s ¼K s t=C ðIÞ 44 and K ¼K t= I ð Þ…”