Principle of Virtual Work As Foundational Framework for Metamaterial Discovery and Rational Design

Novel theories are needed for the discovery of innovative and exotic metamaterial and for their rational design. The current practice of mechanical analyses based upon moribund classical theories and experimental trial-error campaigns is caught in an inescapable vortex and illusion of inductive reasoning. The needed novel research paradigm is one in which the formulation of theoretical concepts precede their experimental validation. In the absence of theoretical understanding, the design experiments and collection of experimental evidence will remain unavoidably circumscribed. History of science can provide us guidance in the search for the needed powerful tools required for discovery. The principle of virtual work provides the necessary framework for development of theories that can lead to novel metamaterials, as it was the unifying principle which allowed the French-Italian School, headed by D’Alembert, Lagrange and Gabrio Piola, to found modern continuum mechanics. Based upon this framework we have conceived a metamaterial synthesis schema that exploits micro-macro identification traceable to the early days of the formulation of continuum theories for deformable solids. The schema is illustrated with application to metamaterials with pantographic and granular motifs based upon higher-gradient and higher-order theories.