The Role of Homogenization in Metamaterials Analysis

The extremely rapid development of new metamaterials opens the way to many interesting engineering applications. However, the complexity of their microstructure makes the direct analysis of full-scale real systems made of metamaterials almost prohibitive. The two-scale asymptotic homogenization represents a promising tool for the design and optimization of such systems. In this paper, we will discuss the role of homogenization in the development of practical applications of metamaterials. Two examples will be presented: the optimization of auxetic materials for impact protection and the design of a system for energy localization that includes locally resonant materials. A significant computational advantage is obtained by substituting the metamaterial with an equivalent homogenized continuum.