Piezoelectric composites: Imperfect interface models, weak formulations and benchmark problems

This work is concerned with piezoelectric composites with imperfect interfaces. The general piezoelectric imperfect interface model derived from the replacement of a piezoelectric interphase of small uniform thickness between two bulk piezoelectric phases by an imperfect interface through an asymptotic analysis is reformulated so as to obtain simpler compact characteristic expressions. Further, it is exploited to deduce two particular piezoelectric imperfect interface models which include as special cases the widely used Kapitza model, highly conducting model, elastic spring-layer model and membrane-type (or Gurtin–Murdoch) model. The weak formulations for the mixed boundary value problems of a piezoelectric composite with the interfaces described by the derived particular piezoelectric imperfect interface models are provided and serve as the basis for their numerical treatment by the extended finite element method (XFEM). The analytical solutions for benchmark problems are found and can be used for carrying out the accuracy and convergence analyzes of numerical methods such as XFEM.