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Emergent nonlocal combinatorial design rules for multimodal metamaterials.

Ryan van Mastrigt^1,2, Corentin Coulais¹, Martin van Hecke^2,3

¹Institute of Physics, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.

Physical Review. E

|January 20, 2024

Summary

Designing multimodal mechanical metamaterials requires complex local and nonlocal rules, unlike simpler single-mode designs. This research introduces a framework for creating multiple soft modes in these advanced materials.

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Area of Science:

Materials Science
Mechanical Engineering
Physics

Background:

Combinatorial mechanical metamaterials exhibit unique properties due to spatially textured soft modes.
Designing single soft modes often follows simple tiling rules for building blocks.
Realizing multiple soft modes in metamaterials presents a significant design challenge.

Purpose of the Study:

To develop a framework for designing multiple soft modes in combinatorial metamaterials.
To derive specific design rules for multimodal metamaterial configurations.
To explore the complexity of achieving advanced, selectable mechanical functionalities.

Main Methods:

Introduction of a transfer matrix-like framework for designing multiple soft modes.
Application of the framework to aperiodic tilings of building blocks.
Derivation of real-space configuration rules and constraints for multimodal designs.

Main Results:

Identified that multimodal designs necessitate a high number of degeneracies between constraints.
Established precise rules for real-space configurations that enable these degeneracies.
Characterized multimodal design rules as a combination of local (pairs of building blocks) and nonlocal (global tile constraints) rules.

Conclusions:

Multimodal mechanical metamaterials require significantly more complex design rules than single-mode counterparts.
A novel framework facilitates the systematic design of multimodal metamaterials with spatially textured soft modes.
The findings represent a foundational step towards advanced, on-demand mechanical functionalities in metamaterials.