Analysis of mechanical and electrical imperfect contacts in piezoelectric composites

Asymptotic Homogenization Applied to Flexoelectric Rods

“…A variational formulation of the local problem is proposed and the system is solved using the classical finite element method (FEM). As an important benchmark, the model reproduces the solution of the local problems reported in Reference [30] for a one-dimensional piezoelectric structure. Finally, in Section 4, the theoretical results derived in the previous sections are used to study some numerical cases.…”

“…To validate the model, our goal is to reproduce the results of the one-dimensional piezoelectric composite analyzed in Reference [30]. The constituents of this one-dimensional piezoelectric structure are lead zirconate titanate (PZT) C-91 and P-82.…”

“…The constituents of this one-dimensional piezoelectric structure are lead zirconate titanate (PZT) C-91 and P-82. The materials properties are given in Table 1 of Reference [30]. For this particular case, the flexoelectric coefficient μ associated with the components of the structure is considered zero.…”

“…For this particular case, the flexoelectric coefficient μ associated with the components of the structure is considered zero. Therefore, the equilibrium problems (5)–(8) take the expression (1) and (2) of Reference [30]. Using the asymptotic expansion (9) and (10) and following the methodology described in the previous section, the non-vanishing local problems are (13), (15), (18), and (20), which corresponds with Equations (23) and (24) in Reference [30].…”

“…Finally, in Section 4, the theoretical results derived in the previous sections are used to study some numerical cases. The effective coefficients reported in References [19,30] for a two-material piezoelectric structure made of lead zirconate titanate (PZT) C91 and P-82 are derived using the model developed here, which makes use of the solution of the local problem variational formulation (FEM). In order to extend the study for the case of randomly distribute one-dimensional flexoelectric composites, a two-constituents structure sans-serifΩN is considered for which the materials properties are randomly distributed along the rod with a binomial probability.…”