Verification of asymptotic homogenization method developed for periodic architected materials in strain gradient continuum

TL;DR

This paper develops and verifies an asymptotic homogenization method to accurately identify constitutive parameters for strain gradient theories in periodic architected materials, enabling better modeling of size effects.

Contribution

It introduces a computational approach using open-source FEniCS codes to determine high-rank tensor parameters for strain gradient models in various composite materials.

Findings

Effective parameter identification demonstrated on composites and foams.

Volume fraction and unit cell size significantly influence parameters.

Open-source computational tool facilitates broad application and transparency.

Abstract

Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determined with the demonstrated computational approach. Examples for epoxy carbon fiber composite, metal matrix composite, and aluminum foam illustrate the effectiveness and versatility of the proposed method. The influences of volume fraction of matrix, the stack of RVEs, and the varying unit cell lengths on the identified parameters are investigated. The homogenization computational tool is applicable to a wide class materials and makes use of open-source codes in FEniCS. We make all of the codes publicly available in order to encourage a transparent scientific exchange.