Discrete woven structure model: yarn-on-yarn friction

Bilel Ben Boubaker; Bernard Haussy; Jean-François Ganghoffer

doi:10.1016/j.crme.2007.02.006

Discrete woven structure model: yarn-on-yarn friction

Presented by: Évariste Sanchez-Palencia

Bilel Ben Boubaker ¹ ; Bernard Haussy ¹; Jean-François Ganghoffer ²

¹ ESEO, 4, rue Merlet de la Boulaye, 49009 Angers cedex 01, BP 926, France
² LEMTA, UMR 7563, ENSEM, 2, avenue de la forêt de Haye, B.P. 160, 54504 Vandoeuvre cedex, France

Comptes Rendus. Mécanique, Volume 335 (2007) no. 3, pp. 150-158.

Abstract
Résumé

A discrete model of a fabric has been developed from an analogical description, using a mass-spring system of discrete elements. An element of fabric is modeled by a set of grid nodes endowed with a mass and connected with flexional and stretching springs. This model describes the mechanical behavior of a woven structure at a mesoscopic scale. As a novel contribution, the interactions and the friction between yarns are introduced in the present work. An energy analysis of the discrete system of analogical elements is performed, taking into account the compression strain energy of the yarns and the work of the reaction forces exerted between yarns. A suitable discrete variational principle, accounting for the presence of the nonholonomic forces arising from friction, serves as a basis for a numerical implementation. Simulations of uniaxial tractions are performed, that show the effect of the yarn–yarn friction and yarn compressibility on the fabric response.

Un modèle discret d'une structure tissée d'armure toile a été développé, qui s'appuie sur une description analogique, mettant en œuvre un ensemble d'éléments masse-ressort. Le modèle est construit à partir d'un réseau de nœuds dotés de masses et de rigidités en rotation, connectés par des barres supposées élastiques. Le modèle décrit le comportement d'une nappe de fils à l'échelle mésoscopique. La nouveauté du présent travail réside dans la considération de la compressibilité des fils, ainsi que des interactions de frottement entre fils. Une étude énergétique du système discret est menée, en considérant l'énergie de compression des fils, ainsi que le travail des efforts de réaction exercé par les fils. Un principe variationnel discret est établi, tenant compte des forces non holonomes dues au frottement. Des simulations en traction uniaxiales mettent en évidence l'effet du frottement et de la compressibilité des fils sur la réponse du tissé.

Received: 2005-10-11
Accepted: 2007-02-22
Published online: 2007-03-01

DOI: 10.1016/j.crme.2007.02.006

Keywords: Solids and structures, Woven structures, Discrete models, Mechanical behavior, Yarn–yarn interaction, Traction behavior, Yarn–yarn friction
Mot clés : Solides et structures, Structures tissées, Modèles discrets, Comportement mécanique, Interaction entre fils, Frottement entre fils

Author's affiliations:

Bilel Ben Boubaker ¹; Bernard Haussy ¹; Jean-François Ganghoffer ²

¹ ESEO, 4, rue Merlet de la Boulaye, 49009 Angers cedex 01, BP 926, France
² LEMTA, UMR 7563, ENSEM, 2, avenue de la forêt de Haye, B.P. 160, 54504 Vandoeuvre cedex, France

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     title = {Discrete woven structure model: yarn-on-yarn friction},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {150--158},
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     doi = {10.1016/j.crme.2007.02.006},
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Bilel Ben Boubaker; Bernard Haussy; Jean-François Ganghoffer. Discrete woven structure model: yarn-on-yarn friction. Comptes Rendus. Mécanique, Volume 335 (2007) no. 3, pp. 150-158. doi : 10.1016/j.crme.2007.02.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.02.006/

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