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

**Authors:** Bilen Emek Abali, Emilio Barchiesi  
**arXiv:** [2009.12589](https://arxiv.org/abs/2009.12589)  
**Date:** 2020-09-26  
**Summary page:** https://www.summarizepaper.com/en/paper/2009.12589v1/

## Key points

- Metamaterials deviate from conventional elasticity and exhibit unique behavior
- Generalized elasticity introduces additional parameters linked to internal length scales
- Asymptotic homogenization approach is used to introduce constitutive parameters for materials with substructures on a macroscopic scale
- Topology optimization in additive manufacturing can create metamaterials with accurately known substructures, reducing weight strategically
- Computational scheme utilizing multiple scales developed by authors Bilen Emek Abali and Emilio Barchiesi for numerically identifying metamaterial parameters
- Approach applied to analyze implications of infill ratio on honeycomb substructure
- Methodology can be applied across various material classes and provides insights into introducing complex substructures through additive manufacturing techniques
- Authors promote transparency in scientific exchange and utilize open-source codes to advance understanding of metamaterials and their potential applications

## Summary

Metamaterials are materials that exhibit unique behavior due to their deviation from conventional elasticity. This is captured through generalized elasticity, which introduces additional parameters linked to internal length scales. When describing a material with a substructure on a macroscopic scale, additional constitutive parameters must be introduced using an asymptotic homogenization approach. By strategically reducing weight through topology optimization in additive manufacturing, metamaterials with accurately known substructures can be created. In this study by authors Bilen Emek Abali and Emilio Barchiesi, a computational scheme utilizing multiple scales is developed for numerically identifying metamaterial parameters. The researchers specifically apply this approach to analyze the implications of infill ratio on a honeycomb substructure. This methodology can be applied across various classes of materials and provides valuable insights into how additive manufacturing techniques can introduce complex substructures within materials. By promoting transparency in scientific exchange and utilizing open-source codes, the authors contribute to advancing our understanding of metamaterials and their potential applications in various industries.