Bézier-based metamaterials: Synthesis, mechanics and additive manufacturing

Abstract

The design of mechanical metamaterials often uses lattice arrangements being benefited from the increase in Additive Manufacturing technologies available. Such design freedom allows the fabrication of lattice arrangements with complex curved geometries. Here we propose a whole family of novel lattice matematerials parametrized using cubic Bézier curves. The methodology presented permits the generation of unit cells with different degrees of curvature based on the location of the Bézier control points along a spiral. The apparent stiffness of these structures was characterized using finite element analysis and compression tests on additively manufactured samples using stereolithography. The mechanical properties of spiral based cubic Bézier metamaterials were related to the location of the control points, curvature, etc. It was found that the apparent stiffness decreases proportionally to the cubic root of the distance between the control point and the predefined origin of the coordinate system. Due to symmetry conditions, the slope continuity in the curves conforming the unit cells is fulfilled and the origin of the coordinate system used coincides with the center of the unit cells. The procedure presented for the synthesis of metamaterials enables the generation of structures with customized mechanical properties by adjusting the geometry of the unit cells.

Keywords

• Metamaterials
• Apparent mechanical properties
• Structure-property relationship
• Cubic Bézier curves
• Lattice
• Additive manufacturing