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Abstract Maxwell lattices possess distinct topological states that feature mechanically polarized edge behaviors and asymmetric dynamic responses protected by the topology of their phonon bands. Until now, demonstrations of non‐trivial topological behaviors from Maxwell lattices have been limited to fixed configurations or have achieved reconfigurability using mechanical linkages. Here, a monolithic transformable topological mechanical metamaterial is introduced in the form of a generalized kagome lattice made from a shape memory polymer (SMP). It is capable of reversibly exploring topologically distinct phases of the non‐trivial phase space via a kinematic strategy that converts sparse mechanical inputs at free edge pairs into a biaxial, global transformation that switches its topological state. All configurations are stable in the absence of confinement or a continuous mechanical input. Its topologically‐protected, polarized mechanical edge stiffness is robust against broken hinges or conformational defects. More importantly, it shows that the phase transition of SMPs that modulate chain mobility, can effectively shield a dynamic metamaterial's topological response from its own kinematic stress history, referred to as “stress caching”. This work provides a blueprint for monolithic transformable mechanical metamaterials with topological mechanical behavior that is robust against defects and disorder while circumventing their vulnerability to stored elastic energy, which will find applications in switchable acoustic diodes and tunable vibration dampers or isolators.
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Omnimodal topological polarization of bilayer networks: Analysis in the Maxwell limit and experiments on a 3D-printed prototype
Periodic networks on the verge of mechanical instability, called Maxwell lattices, are known to exhibit zero-frequency modes localized to their boundaries. Topologically polarized Maxwell lattices, in particular, focus these zero modes to one of their boundaries in a manner that is protected against disorder by the reciprocal-space topology of the lattice’s band structure. Here, we introduce a class of mechanical bilayers as a model system for designing topologically protected edge modes that couple in-plane dilational and shearing modes to out-of-plane flexural modes, a paradigm that we refer to as “omnimodal polarization.” While these structures exhibit a high-dimensional design space that makes it difficult to predict the topological polarization of generic geometries, we are able to identify a family of mirror-symmetric bilayers that inherit the in-plane modal localization of their constitutive monolayers, whose topological polarization can be determined analytically. Importantly, the coupling between the layers results in the emergence of omnimodal polarization, whereby in-plane and out-of-plane edge modes localize on the same edge. We demonstrate these theoretical results by fabricating a mirror-symmetric, topologically polarized kagome bilayer consisting of a network of elastic beams via additive manufacturing and confirm this finite-frequency polarization via finite element analysis and laser-vibrometry experiments.
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- Award ID(s):
- 1741618
- PAR ID:
- 10479663
- Publisher / Repository:
- National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 119
- Issue:
- 40
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2208051119
