The authors extend orbifold notation to three dimensions and provide a complete set of symbols for classifying all layer groups, demonstrated on knitted fabric motifs.
2025.arXiv preprint www.annualreviews.org • Textiles, Topology, and Mechanics 23
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A curvature-induced force threshold controls laddering onset and arrest in tensioned knits, with propagation velocity scaling linearly with fabric tension due to bending waves and friction.
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An Orbifold Framework for Classifying Layer Groups with an Application to Knitted Fabrics
The authors extend orbifold notation to three dimensions and provide a complete set of symbols for classifying all layer groups, demonstrated on knitted fabric motifs.
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Laddering of a knitted fabric: a topology-induced failure
A curvature-induced force threshold controls laddering onset and arrest in tensioned knits, with propagation velocity scaling linearly with fabric tension due to bending waves and friction.
- Textiles: from twisted yarn to topology and mechanics