Mechanical Metamaterials: a state of the art

In this paper we give a review on the state of the art about the study of mechanical metamaterials. The very attractive property of having a micro-structure capable to determine exotic and speci cally tailored macro-behavior makes metamaterials a eld which is actually in expansion both under a theoretical and a technological point of view. This work is divided in two di erent sections the phenomenological aspects and the theoretical ones. We will rstly give an overview of some existing metamaterials, such as penta-mode materials, auxetic materials, materials with negative mechanical constitutive coe cients and materials with enhanced mechanical properties. We will also focus on some emerging areas, as origami. After that, we will present some theoretical studies in the eld of mechanical metamaterials, like those related to rst and second gradient theories.