Wave propagation analysis in non-local flexoelectric composite materials

The effective flexoelectric properties of heterogeneous piezoelectric materials are computed in the context of periodic homogenization, whereby a variational formulation is developed, articulated with the extended Hill macro-homogeneity condition. This framework accounts for higher gradient effects that may be induced by a strong contrast of properties of the composite constituents. The obtained homogenized properties are employed for the determination of the wave propagation attributes of piezoelectric composites. The dynamic equilibrium equations, accounting for higher gradient effects, are formulated to deal with wave propagation in flexoelectric media, considering the Classical Flexoelectric Theory (CFE) and the Non-Local Flexoelectric Theory (NLFE). The obtained dispersion relations show that flexoelectric medium are dispersive medium. Furthermore, it can be observed that the flexoelectric medium becomes more anisotropic when increasing the wavenumber unlike the piezoelectric medium. The analysis of the influence of the nonlocality reveals that the frequency of propagating waves is decreasing when increasing the non-local parameter.