Boundary Value Problems in a Theory of Bending of Thin Micropolar Plates with Surface Elasticity

Abstract

We generalize a recent theory of bending of thin micropolar plates by incorporating surface effects through the modeling of plate surfaces as adjacent two-dimensional micropolar elastic bodies. By incorporating both elastic surface effects and the micropolar elastic behavior of the plate, the proposed model is capable of taking into account the contribution of high surface-to-volume ratios as well as the influence of microstructural mechanics at micro/nano scales. We determine the fundamental solution of the resulting system of equations and establish uniqueness results for the corresponding Dirichlet and Neumann boundary value problems. Moreover, we provide a numerical example to demonstrate the efficiency of the model in representing the size-dependence arising from various factors that incorporate characteristic lengths. Furthermore, we showcase the sensitivity of the results to different types of characteristic lengths present in the model.