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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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Topological floppy modes in models of epithelial tissues
Recent advances in topological mechanics have revealed unusual phenomena such as topologically protected floppy modes and states of self-stress that are exponentially localized at boundaries and interfaces of mechanical networks. In this paper, we explore the topological mechanics of epithelial tissues, where the appearance of these boundary and interface modes could lead to localized soft or stressed spots and play a role in morphogenesis. We consider both a simple vertex model (VM) governed by an effective elastic energy and its generalization to an active tension network (ATN) which incorporates active adaptation of the cytoskeleton. By analyzing spatially periodic lattices at the Maxwell point of mechanical instability, we find topologically polarized phases with exponential localization of floppy modes and states of self-stress in the ATN when cells are allowed to become concave, but not in the VM.
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- Award ID(s):
- 1741618
- PAR ID:
- 10349847
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 17
- Issue:
- 38
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 8624 to 8641
- 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/10.1039/D1SM00637A
