Auxeticity in truss networks and the role of bending versus stretching deformation

Auxetic behavior (i.e., a negative value of Poisson's ratio) has been reported for a variety of cellular networks including truss structures. Commonly, this implies that the geometric arrangement of truss members within a periodic unit cell is designed to achieve the negative Poisson effect, e.g., in the reentrant honeycomb configuration. Here, we show that elastic periodic truss lattices can be tuned to display auxeticity by controlling the ratio of bending to stretching stiffness. If the nodal stiffness (or the bending stiffness) is low compared to the stretching stiffness of individual truss members, then the lattice is expected to exhibit a positive Poisson's ratio, showing lateral expansion upon uniaxial compression. In contrast, if the nodal or bending stiffness is high (and buckling is prevented), the lattice may reveal auxetic behavior, contracting laterally under uniaxial compression. This effect is demonstrated in two dimensions for the examples of square and triangular lattices, and it is confirmed both analytically in the limit of small strains as well as numerically for finite elastic deformation. Under large deformation, instability additionally gives rise to auxetic behavior due to truss buckling