Elastic properties of honeycombs with spline curve cell walls

Abstract

In the ideal models, cell walls of honeycomb structures are perfect flat sheets or straight lines (viewed from out-of-plane projection), whereas most of the real honeycomb products contain curved cell walls due to the widely employed manufacturing processes. Moreover, some honeycomb products are made intentionally to have corrugated cell walls for an enhanced out-of-plane stability or an increase of structural stiffness. In the presented study, a relative new modeling method for the nonlinear cell walls of honeycomb structures is used. The method makes use of Bezier spline functions to describe the curved cell walls. Energy method and Castigliano's theorem are used to formulate the force-displacement relationship of a single cell wall, and the homogenized stiffness matrix is derived based on the proper boundary conditions of the cell walls. Analytical and experimental verification shows that the proposed model is very accurate and versatile in predicting the mechanical responses of different honeycomb geometries. Parametric studies are conducted, analytically and numerically, to examine the influence of the spline cell wall geometries on the honeycomb's effective in-plane properties and the out-of-plane stability. The study leads to the recommendation of a cell wall design strategy for maximizing the out-of-plane buckling resistance of honeycomb structures.