  Concepts from quantum topological states of matter have been extensively
utilized in the past decade in creating mechanical metamaterials with
topologically protected features, such as one-way edge states and topologically
polarized elasticity. Maxwell lattices represent a class of topological
mechanical metamaterials that exhibit distinct robust mechanical properties at
edges/interfaces when they are topologically polarized. Realizing topological
phase transitions in these materials would enable on-and-off switching of these
edge states, opening unprecedented opportunities to program mechanical response
and wave propagation. However, such transitions are extremely challenging to
experimentally control in Maxwell topological metamaterials due to mechanical
and geometric constraints. Here we create a Maxwell lattice with bistable units
to implement synchronized transitions between topological states and
demonstrate dramatically different stiffnesses as the lattice transforms
between topological phases both theoretically and experimentally. By combining
multistability with topological phase transitions, for the first time, this
metamaterial not only exhibits topologically protected mechanical properties
that swiftly and reversibly change, but also offers a rich design space for
innovating mechanical computing architectures and reprogrammable neuromorphic
metamaterials. Moreover, we design and fabricate a topological Maxwell lattice
using multi-material 3D printing and demonstrate the potential for
miniaturization via additive manufacturing. These design principles are
applicable to transformable topological metamaterials for a variety of tasks
such as switchable energy absorption, impact mitigation, wave tailoring,
neuromorphic metamaterials, and controlled morphing systems.
