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Geometry and Elasticity of a Knitted Fabric

Samuel Poincloux, Mokhtar Adda-Bedia, and Frédéric Lechenault
Phys. Rev. X 8, 021075 – Published 22 June 2018
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Abstract

Knitting is not only a mere art and craft hobby but also a thousand-year-old technology. Unlike weaving, it can produce loose yet extremely stretchable fabrics with almost vanishing rigidity, a desirable property exhibited by hardly any bulk material. It also enables the engineering of arbitrarily shaped two- and three-dimensional objects with tunable mechanical response. In contrast with the extensive body of related empirical knowledge and despite a growing industrial interest, the physical ingredients underlying these intriguing mechanical properties remain poorly understood. To make some progress in this direction, we study a model tricot made of a single elastic thread knitted into a common pattern called stockinette. On the one hand, we experimentally investigate its tensile response and measure local displacements of the stitches during deformation. On the other hand, we derive a first-principle mechanical model for the displacement field based on the yarn-bending energy, the conservation of its total length, and the topological constraints on the constitutive stitches. Our model solves both the shape and mechanical response of the knit and agrees quantitatively with our measurements. This study thus provides a fundamental framework for the understanding of knitted fabrics, paving the way to thread-based smart materials.

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  • Received 25 January 2018
  • Revised 16 May 2018

DOI:https://doi.org/10.1103/PhysRevX.8.021075

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

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Stitching Together a Knit Theory

Published 22 June 2018

A new model predicts how each stitch in a knitted fabric will respond to a stretching force.

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Authors & Affiliations

Samuel Poincloux1,*, Mokhtar Adda-Bedia2, and Frédéric Lechenault1

  • 1Laboratoire de Physique Statistique, École Normale Supérieure, PSL Research University, Sorbonne University, CNRS, F-75231 Paris, France
  • 2Université de Lyon, Ecole Normale Supérieure de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France

  • *spoincloux@lps.ens.fr

Popular Summary

Knitted fabrics can be easily stretched, whereas the constitutive yarn cannot. The geometry of the knitting pattern is therefore crucial to the mechanical response of the fabric. Designers and engineers have taken advantage of this quality to develop materials with tunable shapes and mechanical responses, with applications ranging from textiles to biomedical engineering. However, the fundamental physical ingredients linking geometry and elasticity are still obscure. We present a combination of experimental and theoretical work that unveils some of those ingredients and suggests a general framework for a study of thread-based smart materials.

Experimentally, we study the tensile response of a knitted nylon sheet. In the fabric, the yarn follows a repeated geometrical pattern, known as stitches, delimited by its self-crossing points. We stretch the fabric and track its morphology at the stitch level. While the stitches follow straight trajectories, the fabrics adopt a characteristic catenary shape.

We also model the fabric as a network with three ingredients: a dominant yarn-bending energy, an unaltered crossing-point pattern, and yarn-length conservation. Using this model, we find that minimization of the fabric energy under constraints allows us to capture the essential physical features of both the fabric shape and its elasticity.

We envision that our findings will connect the flourishing advanced-textile industry to fundamental work on geometrical and topological metamaterials.

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Vol. 8, Iss. 2 — April - June 2018

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