Flexoelectricity and surface effects on coupled electromechanical responses of graphene reinforced functionally graded nanocomposites: A unified size-dependent semi-analytical framework

[Display omitted] •Coupled electromechanical behavior of graphene reinforced functionally graded piezoelectric material (FGPM) nanoplates is investigated using Modified Couple Stress Theory.•The surface and flexoelectricity effects concerning static and dynamic responses are analyzed computationally.•A unified semi-analytical ‘single-term extended Kantorovich method (EKM)’ and ‘Ritz method’ based powerful framework is developed.•The study unravels the notion of on-demand property modulation and active control based on quantitative electromechanical understanding.•The mechanical behavior (softer/stiffer) is found to be greatly dependent on the sign and magnitude of residual surface stress. Owing to inhomogeneous strain and high surface-to-volume ratio in nanostructures, it is imperative to account for the flexoelectricity as well as surface effect while analyzing the size-dependent electromechanical responses of nano-scale piezoelectric materials. In this article, a semi-analytical ‘single-term extended Kantorovich method (EKM)’ and ‘Ritz method’ based powerful framework is developed for investigating the static and dynamic electromechanical responses of graphene reinforced piezoelectric functionally graded (FG) nanocomposite plates, respectively. The residual surface stresses, elastic and piezoelectric surface modulus, and direct flexoelectric effects are taken into account while developing the unified governing equations and boundary conditions. The modified Halpin Tsai model and rules of mixture are implemented to predict the effective bulk properties. Our results reveal that the static deflection and resonance frequency of the proposed FG nanoplates are significantly influenced due to the consideration of flexoelectricity and surface effects. While such outcomes emphasize the fact that such effects cannot be ignored, these also open up the notion of on-demand property modulation and active control. The effects are more apparent for nanoplates of lesser thickness, but they diminish as plate thickness increases, leading to the realization and quantification of a size-dependent behavior. Based on the developed unified formulation, a comprehensive numerical investigation is further carried out to characterize the electromechanical responses of nanoplates considering different critical parameters such as plate thicknesses, aspect ratios, flexoelectric coefficients, piezoelectric multiples, distribution, and weight fraction of graphene platelets along with di