Breaking Mechanical Holography in Combinatorial Metamaterials

TL;DR

This paper explores the design principles of combinatorial mechanical metamaterials, revealing how holographic order influences boundary deformation control and scaling properties of compatible structures.

Contribution

It introduces a classification of block types based on holographic order and demonstrates how this affects the design and scaling of compatible metamaterials.

Findings

Holographic blocks enable boundary-only deformation control.

Non-holographic blocks allow full boundary deformation.

Number of compatible structures scales exponentially with boundary or bulk depending on holographic order.

Abstract

Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system's response strongly depends on the mutual orientations of the blocks within the lattice. We study a family of possible block types for the square, honeycomb, and cubic lattices. Blocks that are centrally symmetric induce holographic order, such that mechanical compatibility (meaning that blocks do not impede each other's motion) implies bulk-boundary coupling. With them, one can design a compatible metamaterial that will deform in any desired texture only on part of its boundary. With blocks that break holographic order, we demonstrate how to design the deformation texture on the entire boundary. Correspondingly, the number of compatible holographic metamaterials scales exponentially with the boundary, while in non-holographic cases we show that it scales exponentially with the bulk.