Toughness and damage tolerance of fractal hierarchical metamaterials

TL;DR

This paper develops a theory for hierarchical fractal metamaterials, revealing that while absolute toughness decreases with more scales, the toughness per unit density increases, and tensile strength remains constant.

Contribution

It introduces a theoretical framework for understanding toughness and damage tolerance in hierarchical fractal metamaterials, highlighting the benefits of multiple scales.

Findings

Specific toughness increases with hierarchical scales.

Tensile strength remains constant regardless of hierarchy.

Absolute toughness decreases as hierarchy increases.

Abstract

We present a theory for the toughness, damage tolerance, and tensile strength of a class of hierarchical, fractal, metamaterials. We show that the even though the absolute toughness and damage tolerance decrease with increasing number of hierarchical scales, the specific toughness (toughness per-unit density) grows with increasing number of hierarchical scales in the material, while the specific tensile strength and damage tolerance remain constant.