Chiral two-dimensional periodic blocky materials with elastic interfaces: auxetic and acoustic properties

TL;DR

This paper introduces two novel chiral 2D periodic blocky materials with elastic interfaces, analyzing their auxetic and acoustic properties through a Lagrangian model, continuum approximation, and parametric analysis.

Contribution

It develops a new chiral lattice topology, derives an analytical micropolar continuum model, and links chirality and interface stiffness to auxetic and acoustic behaviors.

Findings

Chirality and interface stiffness influence auxetic behavior.

The micropolar model accurately predicts dispersion curves.

Parametric analysis reveals the effect of chirality angle and interface stiffness.

Abstract

Two novel chiral block lattice topologies are here conceived having interesting auxetic and acoustic behavior. The architectured chiral material is made up of a periodic repetition of square or hexagonal rigid and heavy blocks connected by linear elastic interfaces, whose chirality results from an equal rotation of the blocks with respect to the line connecting their centroids. The governing equation of the Lagrangian model is derived and a hermitian eigenproblem is formulated to obtain the frequency band structure. An equivalent micropolar continuum is analytically derived through a standard continualization approach in agreement with the procedure proposed by Bacigalupo and Gambarotta (2017) from which an approximation of the frequency spectrum is derived. Moreover, the overall elastic moduli of the equivalent Cauchy continuum are obtained in closed form via a proper condensation procedure. The parametric analysis involving the overall elastic moduli of the Cauchy equivalent continuum model and the frequency band structure is carried out to catch the influence of the chirality angle and of the ratio between the tangential and normal stiffness of the interface. Finally, it is shown how chirality and interface stiffness may affect strong auxeticity and how the equivalent micropolar model provides dispersion curves in excellent agreement with the current ones for a wide range of the wave vector magnitude.