<p>Hysterons are elementary units of hysteresis that underlie many complex behaviors of non-equilibrium matter. Because models of interacting hysterons can describe disordered matter, this suggests that artificial systems could respond to mechanical inputs in precise and targeted ways. Specifying the properties of hysterons and their interactions could thus be a general method for realizing arbitrary non-equilibrium behaviors. Elastic structures including slender beams, creased sheets, and shells are clear candidates for artificial hysterons, but complete control of their interactions has seemed impractical or impossible. Here we report a mechanical hysteron composed of rigid bars and linear springs, which has controllable properties and tunable interactions of general sign that can be reciprocal or non-reciprocal. We derive a mapping from the system parameters to the hysteron properties, and we show how collective behaviors of multiple hysterons can be targeted by adjusting geometric parameters on the fly. By transforming an abstract hysteron model into a physical design platform, our work demonstrates a route toward designed materials that can sense, compute, and respond to their mechanical environment.</p>