Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization

TL;DR

This paper develops a computational method using asymptotic homogenization to determine parameters of metamaterials with substructures, especially in additive manufacturing, demonstrated on honeycomb structures with variable infill ratios.

Contribution

It introduces a novel computational scheme combining multiple scales to identify metamaterials parameters, applicable to various substructures and leveraging open-source tools.

Findings

Successfully applied to honeycomb substructure

Enables parameter identification from substructure details

Supports optimization of infill ratio in additive manufacturing

Abstract

Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These parameters are linked to internal length scales. Describing on a macroscopic level a material possessing a substructure at a microscopic length scale calls for introducing additional constitutive parameters. Therefore, in principle, an asymptotic homogenization is feasible to determine these parameters given an accurate knowledge on the substructure. Especially in additive manufacturing, known under the infill ratio, topology optimization introduces a substructure leading to higher order terms in mechanical response. Hence, weight reduction creates a metamaterial with an accurately known substructure. Herein, we develop a computational scheme using both scales for numerically identifying metamaterials parameters. As a specific example we apply it on a honeycomb substructure and discuss the infill ratio. Such a computational approach is applicable to a wide class substructures and makes use of open-source codes; we make it publicly available for a transparent scientific exchange.