Magnetically tunable topological states in translational-rotational coupling metamaterials

In this work, an approach for engineering translational-rotational coupling (TRC) metamaterials with magnetically tunable topological states is proposed. The metamaterial exhibits diverse nonlinear mechanical behaviors, remotely controlled and activated by an external magnetic field. The design is realized through a multi-material microstructure with highly deformable hinge configurations, targeting desirable strain-softening/stiffening characteristics. This 3D-printable hinge design eliminates the complex manual assembly processes typically required in current TRC metamaterials that are based on triangulated cylindrical origami. The stiffness transition property of the TRC metamaterials can be exploited to break the space-inversion symmetry and thus achieve tunable topological phase transition. Specifically, hard-magnetic active material is incorporated to enable untethered shape- and property-actuation in these metamaterials. The TRC metamaterial design is supported by a simplified analytical model whose stiffness parameters are directly linked to the hinge microstructure, offering a significant improvement over previous empirical model. The accuracy of the analytical model is demonstrated through the comparison with the finite element and experimental results. Through these methods, the deformations induced by a magnetic field and the dynamics of superimposed waves in the TRC metamaterial system are studied. Thanks to the magneto-mechanical coupling effect, the proposed TRC metamaterial design enables remote tunability of wave dispersions and topological invariants (including the Zak phase and winding number), in contrast to existing designs that require direct mechanical loading to achieve similar effects. This tunability extends to the control of topologically protected edge and interface states within the finite system. Our findings can potentially open new ways for designing remotely reconfigurable and switchable soft mechanical metamaterials with robust wave guiding and energy harvesting capabilities.