The advancement of additive manufacturing making possible the creation of complex multiscale architectures controlled from the nano / micro level led to a new paradigm in the design of materials. Architected materials (AM) derive their properties not from the ones of their base material, but rather from the design and topology of their microstructure. Amongst architected materials, the category called metamaterials indicate materials with pre-designed multiscale architecture that exhibit unusual static and dynamic properties associated with large local deformations, the presence of multiple metastable states, and instabilities.

For the effective mechanical and acoustic properties of AM to be determined, a link between the microstructural and the scale of an effective substitution medium needs to be set relying on suitable homogenization schemes; generalized continuum models like micromorphic or strain gradient media are sometimes needed to account for the special microstructural deformation modes.

Creating architectures of controlled anisotropy tuned to be ultra-soft or ultra-stiff and lightweight has become increasingly important in biomechanical, civil, and mechanical engineering applications. For instance, specific biological structural members such as tendons and ligaments exhibit Poisson’s ratio values well above the isotropic limits, thereby highlighting the need for biomimetic metamaterial microstructures, appropriate for tendon or ligament restoration processes. Fibrous materials are a class of AM that includes many biological and engineering examples, named collectively network materials. Connective tissue in human and animal bodies, paper, cellulose products, nonwovens, and textiles, are all network materials. Their behavior is highly non-linear and is defined by the presence of metastable states, instabilities, and ultimately, by the network architecture. Network materials are tough, damage resistant; they may be designed and built to exploit unusual static and dynamic properties and such systems belong to the class of metamaterials.

Topologically interlocked materials form a distinct class of AM. They are composed of periodic building blocks which are assembled to tesselate space. The contacts between blocks control the highly non-linear behavior of the ensemble on the macroscopic scale. These materials are damage-resistant and tough, and exhibit interesting behaviors in shear, indentation and under dynamics loads.