The numerical manifold method for piezoelectric materials with hole flaws under electro-mechanical loadings

Piezoelectric intelligent materials are pivotal in a multitude of fields. In this work, the numerical manifold method (NMM) is developed to model piezoelectric solids with arbitrarily shaped cavities. The superiority of this method roots in its dual-cover systems, namely, the mathematical and physical covers, which enable the NMM to straightforwardly discretize physical domain with non-conforming mathematical covers. The governing equations and boundary conditions are introduced, upon which the NMM global discrete equations are formulated via the weighted residual method and the NMM physical field approximations. Several numerical examples with increasing complexity are conducted to verify the proposed approach. Furthermore, the impacts of hole configurations, polarization directions and loading conditions on the electro-mechanical behavior of perforated piezoelectric materials are also investigated.