Response evolution of mechanical metamaterials under architectural transformations

TL;DR

This paper presents a framework for understanding how the linear mechanical response of complex network-based metamaterials evolves through architectural transformations involving elastic element modifications, emphasizing the role of self stress states.

Contribution

It introduces a general approach to analyze the response evolution of metamaterials under structural changes, highlighting the significance of self stress states and localized representations.

Findings

Self stress states determine response differences between architectures.

Localized representation captures response evolution effectively.

Topological defects influence stress-steering behavior.

Abstract

Architectural transformations play a key role in the evolution of complex systems, from design algorithms for metamaterials to flow and plasticity of disordered media. Here, we develop a general framework for the evolution of the linear mechanical response of network structures under discrete architectural transformations via sequential removal and addition of elastic elements. We focus on a class of spatially complex metamaterials, consisting of triangular building blocks. Rotations of these building blocks, corresponding to removing and adding elastic elements, introduce (topological) architectural defects. We show that the metamaterials' states of self stress play a crucial role, and that the mutually exclusive self stress states between two different network architectures span the difference in their mechanical response. For our class of metamaterials, we identify a localized representation of these states of self stress, which allows us to capture the evolving response. We use our insights to understand the unusual stress-steering behaviour of topological defects.