Effective Young’s modulus of Bézier-based honeycombs: Semi-analytical modeling and the role of design parameters and curvature

Abstract

Metamaterials and lightweight structures are widely used in various engineering applications and additive manufacturing technologies have enhanced their potential. Curved elements have been increasingly used in the design of planar mechanical metamaterials or honeycombs. A honeycomb cellular structure topology with cell walls parametrized using cubic Bézier curves is proposed and analyzed here. The effective Young’s modulus of the Bézier-based honeycomb is characterized semi-analytically using Castigliano’s second theorem. Semi-analytical estimations of the effective Young’s modulus were contrasted to those obtained with numerical finite element models and measured on additively manufactured samples. By considering the relative influence of bending, axial, and shear loads, the deformation mechanism of the honeycomb can be predicted and explained in terms of the load orientation, which depends on the definition of the Bézier curve. A large region achievable by tailoring the design parameters of the curve is presented in the so-called Ashby maps and compared to other existing topologies. The methodology presented here enables designers to propose topologies with a customized effective stiffness, expanding the design space for honeycombs in various engineering applications.