Optimal design of auxetic hexachiral metamaterials with local resonators

TL;DR

This paper presents an optimal design method for auxetic hexachiral metamaterials with local resonators to maximize low-frequency band gaps, using a parametric model and advanced optimization techniques.

Contribution

It introduces a parametric beam lattice model and an optimization framework for designing auxetic metamaterials with tailored wave propagation properties.

Findings

Maximized low-frequency band gaps in the designed metamaterials.

Effective use of global optimization methods for material design.

Demonstrated control over wave propagation through geometric parameters.

Abstract

A parametric beam lattice model is formulated to analyse the propagation properties of elastic in-plane waves in an auxetic material based on a hexachiral topology of the periodic cell, equipped with inertial local resonators. The Floquet-Bloch boundary conditions are imposed on a reduced order linear model in the only dynamically active degrees-offreedom. Since the resonators can be designed to open and shift band gaps, an optimal design, focused on the largest possible gap in the low-frequency range, is achieved by solving a maximization problem in the bounded space of the significant geometrical and mechanical parameters. A local optimized solution, for a the lowest pair of consecutive dispersion curves, is found by employing the globally convergent version of the Method of Moving asymptotes, combined with Monte Carlo and quasi-Monte Carlo multi-start techniques.