A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials

TL;DR

This paper reveals how a tunable characteristic lengthscale in mechanical metamaterials causes anomalous size effects and boundary programmability, impacting their mechanical properties in large or heterogeneous systems.

Contribution

It uncovers the role of a characteristic lengthscale in governing size-dependent anomalies and boundary effects in a broad class of mechanical metamaterials.

Findings

Non-monotonic stiffness variation with system size

Boundary textures can drastically alter mechanical properties

A tunable lengthscale controls these phenomena

Abstract

The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework successfully captures the physics of small systems under idealized conditions, large systems or heterogeneous driving conditions remain essentially unexplored. Here we uncover strong anomalies in the mechanics of a broad class of metamaterials, such as auxetics, shape-changers or topological insulators: a non-monotonic variation of their stiffness with system size, and the ability of textured boundaries to completely alter their properties. These striking features stem from the competition between rotation-based deformations---relevant for small systems---and ordinary elasticity, and are controlled by a characteristic length scale which is entirely tunable by the architectural details. Our study provides new vistas for designing, controlling and programming the mechanics of metamaterials in the thermodynamic limit.