An analytical method for piezoelectric composites containing doubly periodic piezoelectric fibers with ring-shaped cross-section under antiplane shear and its application

An approach for modeling three‐phase piezoelectric composites

“…The obtained model is applied to the situation presented in Figure 3 for a composite with imperfect contact between the matrix and fiber and modeled by a thin interphase (Figure 3(a)). A composite with ring-shaped fiber considered in Xu et al [6] (Figure 3(b)) and a three-phase composite with a thick mesophase (Figure 3(c)) are studied in detail. Some numerical results derived from the present model are given in order to illustrate the effect of the mesophase and their validation with other approaches.…”

“…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.…”

“…(3) In Xu et al, [6] is an analytical method using the generalized eigenstrain concept integrated with the theory of doubly quasi-periodic Riemann boundary value problem is presented. The piezoelectric composites containing the doubly periodic piezoelectric fibers with a ring-shaped cross-section under antiplane shear coupled with in-plane electric load are investigated (Figure 3(b)).…”

“…The piezoelectric composites containing the doubly periodic piezoelectric fibers with a ring-shaped cross-section under antiplane shear coupled with in-plane electric load are investigated (Figure 3(b)). In this work, motivated by the study of ring-shaped cross-section piezoelectric composites, a comparison between the out-of-plane effective electro-elastic coefficients by a three-phase model and those reported in Xu et al, [6] is given in In Table VI, we consider the same piezoelectric composite reported in Table V, (21) and (22)-(34) denoted by AHM and FEM, respectively, reported in Section 3. The results have shown good concordance.…”

“…The results have shown good concordance. In Figure 6, we consider two types of piezoelectric composites, that is, composites with ring-shaped cross-section (Figure 3(b)) and circular cross-section piezoelectric fibers as in Xu et al, [6]. The fiber is PZT-7A, and the matrix is Epoxy 1.…”