Assur graphs, marginally jammed packings, and reconfigurable metamaterials

TL;DR

This paper explores the role of Assur graphs in understanding marginally jammed packings and introduces their application as a design principle for reconfigurable mechanical metamaterials that maintain rigidity while allowing controlled motion.

Contribution

It generalizes Assur graphs to torus structures and demonstrates their relevance in physical systems and metamaterial design.

Findings

Contact networks of jammed packings approach torus Assur graphs in large systems.

Assur graphs enable reconfigurable pathways for motion and stress in metamaterials.

Rigidity is preserved while allowing reconfigurable motion through Assur graph principles.

Abstract

Isostatic frames are mechanical networks that are simultaneously rigid and free of self-stress states, and is a powerful concept in understanding phase transitions in soft matter and designing of mechanical metamaterials. Here we analyze substructures of isostatic frames, by generalizing ``Assur graphs'' to the torus and examine them in physical systems. We show that the contact network of marginally jammed packings approach torus Assur graphs in the thermodynamic limit, and demostrate how Assur graphs offer a new design principle for mechanical metamaterials in which motion and stress can propagate in reconfigurable pathways, while rigidity of the entire structure is maintained.