Asymptotical construction of a fully coupled, Reissner–Mindlin model for piezoelectric and piezomagnetic laminates

The variational asymptotic method is used to construct a fully coupled Reissner–Mindlin model for piezoelectric and piezomagnetic laminates with some surfaces parallel to the reference surface coated with electrodes and magnetism. Taking advantage of the smallness of the plate thickness, we asymptotically split the original 3D electromagneto-mechanical problem into a 1D through-the-thickness analysis and a 2D plate analysis, and both are fully-coupled multiphysics analyses. The through-the-thickness analysis serves as a link between the original 3D analysis and the plate analysis by providing a constitutive model for the plate analysis and recovering the 3D field variables in terms of global responses calculated by the plate analysis. The present theory is implemented into the computer program VAPAS (Variational Asymptotic Plate and Shell Analysis). A numerical example of three-layer sandwich plate has been used to validate the present model.

► A fully coupled Reissner–Mindlin model for a PE-PM laminate is developed using VAM. ► The 3D problem is decoupled into a 1D through-the-thickness analysis and a 2D plate analysis. ► The model is derived without any ad hoc assumptions for any multiphysics field. ► The multiphysics behavior of smart structures can be captured by the present model.