Multistable systems possessing multiple stable configurations can describe physical phenomena such as phase transformations, ferroelectric domain switching, structural snap-through buckling, among others. A transition wave can propagate through the system due to external stimuli or internal evolutions and alter the state of the system. Understanding the fundamentals of wave motion of these materials enables us to regulate the microstructure and design for a desired dynamical response from the system.

In this research, we focus on substrate-free metamaterials consisted of multistable unit cells located periodically capable of changing their geometry between stable configurations.  We outline a theoretical framework for the general treatment of dissipative and diffusive reconfigurable metamaterials governed by non-convex multi-well interaction potentials and derive a nonlinear energy scaling law for transition and elastic waves. This scaling law formulates the balance between energy release and energy dissipation and predicts the features of the propagating wave based on the material and geometrical properties of the system [1]. We extend our derivations to higher dimensions and present a framework capable of capturing phase transitions accurately. Borrowing from the continuum theory of solid-to-solid phase transformations, we propose a simple albeit powerful continuum model which captures the kinetics of substrate-free volumetrically bistable reconfigurable and is an efficient platform to study such systems numerically [2]. 

The scaling law and proposed continuum model [3] are of particular interest, e.g., for the design of material or structural behavior of substrate-free soft architectures, reconfigurable structures,  and mechanical metamaterials undergoing significant shape changes, for further applications in, e.g., energy harvesting or soft robotics.

References:
[1]  Khajehtourian,  R.,  Kochmann,  D. M.,  2020. Phase transformations in substrate-free dissipative multistable metamaterials. Extreme Mechanics Letters 37, 100700.
[2]  Jin, L., Khajehtourian, R., Mueller, J., Rafsanjani, A., Tournat, V., Bertoldi, K., Kochmann, D. M., 2020. Guided transition waves in multistable mechanical metamaterials. Proceedings of the National Academy of Sciences 117 (5), 2319‚Äì2325.
[3]  Khajehtourian,  R.,  Kochmann,  D. M.,  2020. A continuum description of substrate-free dissipative reconfigurable metamaterial. Under Review.


Substrate-free dissipative reconfigurable metamaterials

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