Formulation of non-local space-fractional plate model and validation for composite micro-plates

Abstract

It is challenging to design nano/micro-devices because of their small size and tight engineering tolerances. Computer-aided design uses mathematical models of device parts, but contemporary models are not precise enough to capture all characteristics of the materials at the nano/micro-scale. In this work, we propose a novel mathematical model for composite nano/micro-plates in bending in the framework of a space-fractional continuum mechanics approach. This model yields closer mapping of experimental results compared to existing formulations. The developed theory is named the space-Fractional Kirchhoff–Love Plate (s-FKLP). We investigate how the parameters of the s-FKLP model, responsible for the scale effect description, affect the bending behavior of the micro-plates, considering different support conditions. In addition, we compare the results predicted by s-FKLP with the previously developed simpler (one-dimensional) space-Fractional Euler–Bernoulli Beam (s-FEBB) model to show that the choice of structural analysis strategy can influence design decisions. Despite its greater complexity, the s-FKLP is a more versatile approach to modeling micro-sized structures than the s-FEBB. The proposed s-FKLP model is empirically validated using real sandwich micro-plates. We conclude model alignment with the experimental data indicating that the model is suitable for representing sandwich micro-plates. We also find that the model’s length scale parameter corresponds to the microstructure’s grain size. The findings of this research may have implications for future work in the design and optimization of micro-sized devices.