Mechanics of a Model Frictional Knitted Fabric
Abstract
We present a study of the shapes and mechanical properties of a knitted loop made of elastic and frictional yarns. First, for non-frictional yarns, we investigate how the elastic energy of a loop varies with its shape. This allows us to quantify the energetic contributions of stretching and bending, and to identify energetically favorable loop configurations. We then consider the case of thin frictional yarns. In this case, the stability of a loop can be reduced, even in the presence of friction, to a simple planar \textit{elastica} problem. Friction gives rise to a multiplicity of stable loop shapes in a knitted fabric at rest, \textit{i.e.}, in the absence of externally applied forces. We show that, in the limit of thin yarns, a 2D \textit{elastica} model can predict these rest shapes. Furthermore, the force-deformation curves under uniaxial stretching can be obtained straightforwardly within this framework. Measurements of loop dimensions and forces during uniaxial stretching of nylon knitted fabrics allow us to assess the qualitative and quantitative validity of the planar \textit{elastica} model. Finally, we examine the limitations of this model for dense knitted fabrics.
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BibTeX
@misc{michel2026mechanics,
title = {{Mechanics of a Model Frictional Knitted Fabric}},
author = {Laura Michel and Antoine Faulconnier and Audrey Steinberger and Samuel Poincloux and Jérôme Crassous},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07372},
eprint = {2610.07372},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05783581v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mechanics of a Model Frictional Knitted Fabric
AU - Laura Michel
AU - Antoine Faulconnier
AU - Audrey Steinberger
AU - Samuel Poincloux
AU - Jérôme Crassous
PY - 2026
DA - 2026/10/05
PB - HAL
DO - 10.48550/arxiv.2610.07372
UR - https://hal.science/hal-05783581v1
AB - We present a study of the shapes and mechanical properties of a knitted loop made of elastic and frictional yarns. First, for non-frictional yarns, we investigate how the elastic energy of a loop varies with its shape. This allows us to quantify the energetic contributions of stretching and bending, and to identify energetically favorable loop configurations. We then consider the case of thin frictional yarns. In this case, the stability of a loop can be reduced, even in the presence of friction, to a simple planar \textit{elastica} problem. Friction gives rise to a multiplicity of stable loop shapes in a knitted fabric at rest, \textit{i.e.}, in the absence of externally applied forces. We show that, in the limit of thin yarns, a 2D \textit{elastica} model can predict these rest shapes. Furthermore, the force-deformation curves under uniaxial stretching can be obtained straightforwardly within this framework. Measurements of loop dimensions and forces during uniaxial stretching of nylon knitted fabrics allow us to assess the qualitative and quantitative validity of the planar \textit{elastica} model. Finally, we examine the limitations of this model for dense knitted fabrics.
ER -