Mechanical metamaterials: a state of the art

In this paper, we give a review of the state of the art in the study of mechanical metamaterials. The very attractive property of having a microstructure capable of determining exotic and specifically tailored macroscopic behaviour makes the study of metamaterials a field that is actually in expansion, from both a theoretical and a technological point of view. This work is divided into two sections, describing the phenomenological and theoretical aspects of metamaterials. We first give an overview of some existing metamaterials, such as pentamode materials, auxetic materials, materials with negative mechanical constitutive coefficients and materials with enhanced mechanical properties. We also focus on some emerging areas, such as origami. Then, we present some theoretical studies in the field of mechanical metamaterials, such as those related to first- and second-gradient theories.