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

• The wave behaviors of 2D IAMs are regulated by the IA angle. • The negative refraction and refractive steering of elastic waves are realized with the IA mechanism. • The IA angle is the critical parameter that determines the sign of the effective stiffness, inertial and group velocity of the system. • The negative refraction and wave steering are verified in time-domain numerical simulation. 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 low-frequency 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° 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. [Display omitted] [ABSTRACT FROM AUTHOR]