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Bézier-based metamaterials: synthesis, mechanics and additive manufacturing
Luis Gerardo Trápaga Martínez
Acceso Abierto
Apparent mechanical properties
Structure-property relationship
Cubic Bézier curves
Additive manufacturing
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 com-plex 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 charac-terized 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 thecontrol points,curvature,etc.Itwasfoundthatthe 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 con-ditions, 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. © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (
High lights: 1. A novel method for the synthesis of spiral-based cubic Bézier metamaterials is presented. 2. Apparent stiffness was characterized via additively manufactured samples and computational simulations. 3. Apparent Young’s modulus is related to the mathematical parametrization of the curves conforming the structures. 4. The synthesis method allows the control of the form of the stress-strain curves of the metamaterials. 5. Apparent stiffness decreases proportion-ally to the cubic root of the distance from the control point to the unit cell center.
Primer autor: Alberto Álvarez Trejo (ITESM).
Elsevier B.V.
Materials & Design, v. 199, no. 1 (february), no. 109412
Público en general
Álvarez-Trejo, A., Cuan-Urquizo, E., Roman-Flores, A., Trapaga-Martinez, L. G., & Alvarado-Orozco, J. M. (2021). Bézier-based metamaterials: Synthesis, mechanics and additive manufacturing. Materials & Design, 199, 109412.
Versión publicada
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