Finite element modeling of micropolar-based phononic crystals

TL;DR

This paper investigates the use of finite element modeling to analyze dispersive media represented by micropolar (Cosserat) solids, focusing on band structures and boundary conditions relevant to phononic crystals.

Contribution

It introduces a finite element approach for modeling micropolar phononic crystals with detailed boundary conditions and analyzes their band structures for various parameters.

Findings

Band structures vary with material parameters

Finite element method effectively models dispersive media

Boundary conditions are crucial for accurate simulations

Abstract

The performance of a Cosserat/micropolar solid as a numerical vehicle to represent dispersive media is explored. The study is conducted using the finite element method with emphasis on Hermiticity, positive definiteness, principle of virtual work and Bloch-Floquet boundary conditions. The periodic boundary conditions are given for both translational and rotational degrees of freedom and for the associated force- and couple-traction vectors. Results in terms of band structures for different material cells and mechanical parameters are provided.