Incremental auxetic response of composite lattices under isotropic prestress

This work studies the constitutive response of two- and three-dimensional lattice materials subject to isotropic prestress, with a focus on the elastic stiffness moduli that can be directly measured through experimental tests. The elementary unit cell of the examined lattices is formed by an arbitrary number of junctions attached to a junction. Analytic formulae for the 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.