Rational designs of mechanical metamaterials: Formulations, architectures, tessellations and prospects

Mechanical Metamaterials (MMs) are artificially designed structures with extraordinary properties that are dependent on micro architectures and spatial tessellations of unit cells, rather than constitutive compositions. They have demonstrated promising and attractive application potentials in practical engineering. Recently, how to rationally design novel MMs and discover their multifunctional behaviors has received tremendous discussions with rapid progress, particularly in the last ten years with an enormous increase of publications and citations. Herein, we present a comprehensive overview of considerable advances of MMs, including critical focuses at different scales, forward and inverse design mechanisms with optimization formulations, micro architectures of unit cells, and their spatial tessellations in discovering novel MMs and future prospects. The implications in clarifying the four focuses at levels from the global to the physical in MMs are highlighted, that is, unique structures designed for unique functions, unique micro unit cells placed in unique locations, unique micro unit cells designed for unique properties and unique micro unit cells evaluated by unique mechanisms. We examine the inverse designs of MMs with intrinsic mechanisms of structure-property driven characteristics to achieve unprecedented behaviors, which are involved into material designs and multiscale designs. The former primarily optimizes micro architectures to explore novel MMs, and the latter focuses on micro architectures and spatial tessellations to promote multifunctional applications of MMs in engineering. Finally, we propose several promising research topics with serious challenges in design formulations, micro architectures, spatial tessellations and industrial applications.