Incremental auxetic response of composite lattices under isotropic prestress

TL;DR

This paper investigates how isotropic prestress influences the elastic and auxetic behavior of 2D and 3D lattice materials, revealing that prestress can induce auxetic responses in composite lattices with mixed material properties.

Contribution

It provides analytical formulas for elastic constants and demonstrates that prestress can significantly alter the stiffness and induce auxetic behavior in composite lattice materials.

Findings

Prestress can cause significant changes in elastic stiffness moduli.

Prestressed lattices can exhibit auxetic response with suitable material combinations.

Analytic expressions for elastic constants of stretching-dominated lattices are derived.

Abstract

This work studies the constitutive response of two- and three-dimensional lattice materials subject to isotropic prestress. The unit cell of the examined lattices is formed by an arbitrary number of junctions attached to a junction. Analytic formulae for second-order elastic constants and elastic stiffness coefficients of stretching-dominated lattices are provided. In addition, numerical results for the incremental elastic moduli of composite lattices equipped with hard and soft rods are presented. The given results highlight that isotropically pre-tensioned lattices may exhibit marked variations of the elastic stiffness moduli in the prestressed state, over the values competing to the stress-free configuration. This study also discloses that prestressed lattices may feature incremental auxetic response, when composite architectures suitably combining hard and soft materials are employed for their fabrication.