Defect Positioning in Combinatorial Metamaterials
Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system's response depends on the frustration (or its absence) due to the mutual orientations of the blocks within the lattice....
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Zusammenfassung: | Combinatorial mechanical metamaterials are made of anisotropic, flexible
blocks, such that multiple metamaterials may be constructed using a single
block type, and the system's response depends on the frustration (or its
absence) due to the mutual orientations of the blocks within the lattice.
Specifically, any minimal loop of blocks that may not simultaneously deform in
their softest mode defines a mechanical defect at the vertex (in two
dimensions) or edge (in three dimensions) that the loop encircles. Defects
stiffen the metamaterial, and allow to design the spatial patterns of stress
and deformation as the system is externally loaded. We study the ability to
place defects at arbitrary positions in metamaterials made of a family of block
types that we recently introduced for the square, honeycomb, and cubic
lattices. Alongside blocks for which we show that any defect configuration is
possible, we identify situations in which not all sets are realizable as
defects. One of the restrictions is that in three dimensions, defected edges
form closed curves. Even in cases when not all geometries of defect lines are
possible, we show how to produce defect lines of arbitrary knottedness. |
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DOI: | 10.48550/arxiv.2412.01227 |