Homogenization of periodic architected materials

New avant-garde architected materials endowed with extreme stiffness, strength and lightness may be conceived through appropriate choices of the microstructural topology, mostly aimed at optimizing the periodic distribution between the solid phases and the voids. Moreover, microstructure topologies may be designed to maximize exotic mechanical properties, such as auxeticity and chirality. The tailored design of these materials is also fueled by the recent extraordinary developments in the technological fields of high-precision micro-engineering and high-fidelity additive manufacturing. Several periodic architected materials, namely lattice-like materials and rigid blocky materials, may be accurately modeled through discrete Lagrangian systems. The periodicity of the microstructure determines considerable scale effects, implying boundary layer effects and dispersive propagation of elastic waves. The need to derive synthetic descriptions of the mechanical properties and to reduce the computational burdens may motivate the formulation of non-conventional non-local homogenization techniques able of accurately describing the static and dynamic response of these materials. Within this challenging research area, the present Chapter synthesizes the most recent theoretical contributions by the Authors to the mechanical modelling of architected materials with periodic microstructure, with a methodological focus on enhanced non-local homogenization schemes, as well as on innovative surrogate optimization techniques for the spectral design of a new generation of metafilters.