Negative refraction of elastic waves in two-dimensional inertial amplification metamaterials

Tailoring wave behaviors governed by dispersion relations is a huge challenge in wave manipulation. Inertial amplification (IA) mechanism has been introduced in metamaterials and phononic crystals to obtain a lowfrequency bandgap without adding mass to the system. In this work, we demonstrate unique wave propagation behaviors in two-dimensional inertial amplification metamaterials (2D IAMs). Through analytical derivations and numerical simulations, negative refraction and refractive steering of elastic waves are realized with the IA mechanism. The positive (negative) inertia of the system can be tuned by the IA angle, which determines whether the passband of the lattice is positive (negative) group velocity. By analyzing the dispersion relations of the 2D IAMs, we find that the IA angle 45 degrees is the critical point where the group velocity flips. Negative refraction occurs at the interface between two lattices, which have opposite signs of group velocity. We can also achieve a wide range of angles for wave steering in the system. The normalized displacement fields of 2D IAMs are measured via harmonic excitation. We believe that the research results may inspire the design of 'elastic lenses' and multifunctional metamaterial devices.