Static nonreciprocity in mechanical metamaterials enabled by symmetry breaking: a perspective

Mechanical metamaterials enable unconventional direction-dependent actuation, vibration isolation, and signal routing. Beyond dynamic phenomena, static nonreciprocity can arise from geometric nonlinearities—curvature, contact, and buckling—or from material nonlinearity, challenging classical Maxwell–Betti reciprocity and Cauchy elasticity. This Perspective unifies direct, coupled, and odd elasticity, surveys symmetry-informed design strategies, nonlinear mechanisms, and constitutive models, and outlines pathways to programmable lattices. We propose a taxonomy linking nonreciprocity to symmetry-guided design.