The scope of this volume is limited to metamaterials based on microstructural phenomena involving purely mechanical interactions. In general the exotic behavior of metamaterials is obtained by using multiscale architectured internal structures: it is assumed here that at the lowest considered scale a mechanical description is sufficient. The literature in the field being enormous, only a targeted selection of mechanical metamaterials has been considered, aiming to give an analysis of the literature relevant to the specific application developed in Chapter 3.

A most crucial aspect of the intellectual activity needed to comprehend the theory of metamaterials consists in the capacity to distinguish between the physical object which is studied and the possibly different models used to describe it, in different situations. A metamaterial is a material whose behavior is chosen "a priori" by fixing the mathematical model to be used to describe it, in a specific set of conditions. In a sense, ontologically, in the theory of metamaterials the models are used to define "a posteriori" some physical objects. In this context the "feasibility" or "possibility of existence" of a certain material represents a major conceptual problem. For these reasons a scientist working in this field must be aware of some basic concepts of Model Theory.