Mapping of Elastic Properties of Twisting Metamaterials onto Micropolar Continuum using Static Calculations

TL;DR

This paper investigates the mechanical properties of a new twisting cubic metamaterial by comparing finite element, analytical, and micropolar continuum models, demonstrating their qualitative and quantitative agreement through dispersion relation analysis.

Contribution

It introduces a systematic method to map the elastic properties of twisting metamaterials onto micropolar continuum models using static calculations.

Findings

Models show good qualitative and quantitative agreement.

Dispersion relations confirm the accurate mapping.

Microstructure size influences the metamaterial's behavior.

Abstract

Recent developments in the engineering of metamaterials have brought forth a myriad of mesmerizing mechanical properties that do not exist in ordinary solids. Among these, twisting metamaterials, acoustical chirality, or Willis coupling are sample-size dependent. The purpose of this work is, first, to examine the mechanical performance of a new twisting cubic metamaterial. Then, we perform a comparative investigation of its twisting behavior using the finite element method on microstructure elements computation, an analytical model, and we compare them to Eringen micropolar continuum. Notably, the results of the three models are in good qualitative and quantitative agreements. Finally, a systematic comparison of dispersion relations was made for the continuum and for the microstructures with different sizes in unit cells as final proof of perfect mapping.