Geometric control and memory in networks of hysteretic elements

TL;DR

This paper explores how networks of hysteretic elements can be modeled and controlled through geometric configurations, revealing both their potential for designing advanced metamaterials and their fundamental modeling limitations.

Contribution

It provides explicit mappings from physical networks to abstract hysteron models and uncovers geometric nonlinearities that affect hysteron interactions and modeling accuracy.

Findings

Mappings from physical networks to hysteron models

Geometric nonlinearities can break hysteron assumptions

Design principles for metamaterials with controlled interactions

Abstract

The response of driven frustrated media stems from interacting hysteretic elements. We derive explicit mappings from networks of hysteretic springs to their abstract representation as interacting hysterons. These maps reveal how the physical network controls the signs, magnitudes, symmetries, and pair-wise nature of the hysteron interactions. In addition, strong geometric nonlinearities can produce pathways that require excess hysterons or even break hysteron models. Our results pave the way for metamaterials with geometrically controlled interactions, pathways, and functionalities, and highlight fundamental limitations of abstract hysterons in modeling disordered systems.