  Nonreciprocity can be passively achieved by harnessing material
nonlinearities. In particular, networks of nonlinear bistable elements with
asymmetric energy landscapes have recently been shown to support unidirectional
transition waves. However, in these systems energy can be transferred only when
the elements switch from the higher to the lower energy well, allowing for a
one-time signal transmission. Here, we show that in a mechanical metamaterial
comprising a 1D array of bistable arches nonreciprocity and reversability can
be independently programmed and are not mutually exclusive. By connecting
shallow arches with symmetric energy wells and decreasing energy barriers, we
design a reversible mechanical diode that can sustain multiple signal
transmissions. Further, by alternating arches with symmetric and asymmetric
energy landscapes we realize a nonreciprocal chain that enables propagation of
different transition waves in opposite directions.
