Surface element design of nanomaterials considering surface curvature dependence

Nanomaterials have garnered recognition for their notable surface effects and demonstration of superior mechanical properties. Previous studies on the surface effects of nanomaterials, employing the finite element method, often relied on simplified two-dimensional models due to theoretical complexities. Consequently, these simplified models inadequately represent the mechanical properties of nanomaterials and fail to capture the substantial impact of surface effects, particularly the curvature dependence of nanosurfaces. This study applies the principle of minimum energy and leverages the Steigmann-Ogden surface theory of nanomaterials to formulate a novel finite element surface element that comprehensively accounts for surface effects. We conducted an analysis of the stress distribution and deformation characteristics of four typical 2D and 3D nanomaterial models. The accuracy of the developed surface element and finite element calculation method was verified through comparison with established references. The resulting finite element model provides a robust and compelling scientific approach for accurately predicting the mechanical performance of nanomaterials.