A multiscale approach to visco-electro-elastic complex materials: Asymptotic homogenization versus high-frequency continualization schemes

This work deals with the study of the viscous effects on the electro-mechanical behavior of periodic materials paving the way for remarkable applications in many scientific fields. In a three-dimensional context, the constitutive equations that describe a visco-electro-elastic periodic material are recast into the complex frequency space via the two-sided Laplace transform yielding a Stroh-like formulation. Then, the governing equations are manipulated by means of the Floquet–Bloch transform to study the wave propagation and the characteristic equation, which is generalized for a periodic visco-electro-elastic laminate, is obtained and solved to achieve its frequency complex spectra. Thereafter, an asymptotic homogenization method and a continualization scheme, which is based on the kernel developed as a Padé approximant, are detailed to identify equivalent non-local visco-electro-elastic continua. Finally, the homogenized frequency band structures are compared with the heterogeneous one to validate the proposed models.