Abstract
A direction-selective elastic micro-structured medium is proposed. The lattice model combines constitutive nonlinearity, a threshold activation displacement and the gyroscopic effect of an isolated spinner to induce a tunable wave deviation on a selected direction in a full non-reciprocal way. The direction-selective effect is quantified in terms of energy flux dependence on gyricity and propagation velocity of the incident wave. Three different regimes are identified, addressed as passing, highly directive and barrier. The nonlinear system sustains solitary waves, described both numerically and through an analytical approximation, which show that the wave is univocally determined by the propagation velocity. A final analysis demonstrates the non-reciprocal mechanism originated by the proposed micro-structured medium. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.