A Robust "Shrink-and-wrap" Piecewise Construction Transforms 3-Dimensional Mesh Structures into Mechanical Metamaterials

Abstract

Mechanical metamaterials are materials that, by virtue of their microstructural architectures, exhibit mechanical properties not often found in nature: for example, auxetic mechanical metamaterials are materials that possess a negative Poisson's ratio in response to deforming forces. However, outside of relatively simple crystalline, lattice-based, or repeating-pattern architectures composed of mostly identical unit cells, mechanical metamaterials like auxetics are notoriously difficult to design, particularly across all three dimensions. Here we show that, for any structure that can be decomposed into triangular or tetrahedral meshes, those structures can be subjected to a simple transformation that that creates conditions within those triangular or tetrahedral simplexes that, regardless of their individual geometries, introduces a counter-rotating polygon/polyhedron mechanism that both guarantees a negative Poisson ratio and allows locally programmable mechanical properties. We apply this "shrink-and-wrap" construction to generate mechanical metamaterials from increasingly complex 3D structures, first from simple (convex) polyhedrons; then, to designs with arbitrarily large numbers of vertices and designed using constructive solid geometry (CSG) and 3D scanning; and, ultimately to 3D objects generated from videos captured by mobile phone camera -- making potentially any object or geometric structure designed or found in the real world transformable into a mechanical metamaterial. We show that these monolithic auxetic constructions remain readily 3D-printable via additive manufacturing techniques. We expect this piecewise approach to designing arbitrarily complex mechanical metamaterial structures can enable numerous potential applications where programmable internal reconfigurations and/or force redirection are required across and throughout their 3D geometries.