Design and analysis of smooth geometry‐conforming lattices via Generalized Bézier patches

Abstract

Abstract We propose a novel methodology to model globally G 1 geometry‐conforming metamaterials using Generalized Bézier‐based (GB) patches. Since every canonical tile is inscribed in a unit cube, we exploit its natural decomposition in octants and design multi‐sided patches for each octant. The orthogonality constraints in each octant's GB surface ensure global G 1 continuity in the entire parametric domain and, under the assumption of a global smooth mapping that fills a desired free‐form volume by deformed cubes, results in globally G 1 metamaterial in physical space. The presented tiles can be graded in both shape and thickness using only a few shape parameters preserving their continuity properties, thus enabling optimization of novel metamaterials in various applications. Using isogeometric analysis tools we show that a G 1 metamaterial results in a smoother stress field than a typical G 0 tile used in state‐of‐the‐art parametric approaches. We further show that our tile, given the continuity constraints, is lighter in terms of necessary control points than state‐of‐the‐art parametric tiles and can approximate popular implicit tiles with sufficient accuracy. Finally, our pipeline is demonstrated in several design/analysis examples.