Novel parametrization approaches with curved and non-planar Bézier elements for the design of metamaterials, towards tailoring their energy absorption capabilities

Abstract

The design of mechanical metamaterials can be enhanced when using parametric curved elements, providing the possibility of tuning their mechanical properties, such as stiffness, strength, and energy absorption. The design of these novel metamaterials can benefit from the recent progress in additive manufacturing and parametric design. In this work, cubic Bézier curves are used as building blocks in the design of both two-dimensional and three-dimensional metamaterials. Two-dimensional topologies are designed from the tessellation of cubic Bézier curves in the plane. A semi-analytical model is derived to predict their effective Young’s modulus and compared with both experiments and finite element simulations, accurately modeling the effective stiffness and providing a way of quantifying the relative contribution of bending, axial, and shear loadings. Three-dimensional topologies based on the gyroid minimal surface were also synthesized, replacing the gyroid level curve with a cubic Bézier curve and generating Coons patches defined by boundary curves. These topologies were additively manufactured, tested and simulated via numerical homogenization. Results showed the possibility of generating surface-based toopologies with up to 40% more flexibility relative to the quasi-gyroid. Energy absorption of surface-based topologies under compression can also be tailored. Topology design and selection guidelines are provided, along with the design region achievable with these novel 2D and 3D topologies.