Conformal Elasticity of Mechanism-Based Metamaterials

TL;DR

This paper introduces conformal elasticity as a new theoretical framework for understanding low energy deformations in mechanism-based metamaterials, validated through experiments and simulations, enabling precise deformation control.

Contribution

It presents a novel conformal elasticity theory for mechanism-based metamaterials, linking nonlinear deformations to conformal maps and establishing a holographic principle for deformation prediction.

Findings

Deformations follow conformal maps under certain conditions

Experimental and simulation validation of the theory

Holographic bulk-boundary principle enables deformation control

Abstract

Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate symmetry due to the presence of a designer soft strain pathway. Here we show that low energy deformations of designer dilational metamaterials will be governed by a novel field theory, conformal elasticity, in which the nonuniform, nonlinear deformations observed under generic loads correspond with the well-studied conformal maps. We validate this approach using experiments and finite element simulations and further show that such systems obey a holographic bulk-boundary principle, which enables an unprecedented analytic method to predict and control nonuniform, nonlinear deformations. This work both presents a novel method of precise deformation control and demonstrates a general principle in which mechanisms can generate special classes of soft deformations.