Tunable tension-compression asymmetry and auxeticity in lattice structures by harnessing unilateral contact

A novel lattice structure with tension-compression asymmetrical effective elastic properties is designed by harnessing unilateral contact and the Poisson effect. The initiation of unilateral contact induces a soft-to-hard state transition of the structure due to the change in nodal connectivity. The incremental Young's moduli and Poisson's ratios along the principal directions in both the soft and hard states and the critical strains for the initiation of unilateral contact are evaluated analytically and computationally. The influence of geometrical parameters and constituent material properties on these effective elastic constants is investigated in detail. The degree of tension-compression asymmetry measured by the difference in Young's modulus and Poisson's ratio is widely tunable. The structure can exhibit positive (nonauxetic) or negative (auxetic) Poisson's ratio in the soft as well as in the hard states.