Reciprocity is often treated as a fundamental principle in elastodynamics: if the locations of the source and receiver are interchanged, the recorded signal remains unchanged. Despite their intriguing power, reciprocity relations hold only when certain conditions are satisfied in the elastic medium. For example, breakdown of reciprocity may take place in nonlinear, active or rotating systems. Non-reciprocity leads to asymmetric wave propagation for opposite directions, which can be used to develop devices for rectification and control of elastic waves. Recent experiments have shown the feasibility of realizing such devices in mechanical metamaterials. In this light, we review the scenarios in which asymmetric wave propagation is possible in the context of 1D phononic systems and mechanical/acoustic metamaterials.
