Discrete models of fabric accounting for yarn interactions
Simulations of uniaxial and biaxial behaviour
Keywords:
woven structures, discrete models, draping simulations, stability analysis, mesoscopic approach, yarn-yarn interactions, uniaxial and biaxial loadingsAbstract
Discrete models of fabric have been elaborated at both macroscopic and mesoscopic scales, whereby nodes endowed with a mass and a rotational rigidity are mutually connected by extensible bars to form a two-dimensional trellis. At the macroscopic scale, the equilibrium shape of the structure is obtained as the minimum of its total potential energy versus the kinematic translational and rotational variables. Draping simulations are performed for fabric sheets lying on a fixed rigid surface. In the second part of the paper, a mesoscopic model of fabric is elaborated ; thereby, the undulations of the yarns are explicitly described within the unit cell, using a Fourier series development to represent the shape of each yarn. This methodology is applied to get the response of a set of intertwined yarns under biaxial loading, accounting for the contact reaction forces exerted by the transverse yarns.
Downloads
References
B. Ben Boubaker, B. Haussy, J.F. Ganghoffer, “Discrete models of woven structures ;
Draping and stability analysis”, CRAS, Série Mécanique, n° 330, 2002, p. 871-877.
B. Ben Boubaker, B. Haussy, J.F. Ganghoffer, “A discrete model for the coupling between
yarns in a woven fabric”, CRAS, Série Mécanique, n° 331, Issue 4, 2003, p. 295-302.
B. Ben Boubaker, Mise en oeuvre de modèles discrets du comportement mécanique de
structures tissées, PhD thesis, INPL (Nancy), 2004.
Boisse P., Borr M., Buet K., Cherouat A., “Finite element simulations of textile composite
forming including the biaxial fabric behaviour”, Composites, Part B 28B, 1997, p. 453-
Boisse P., Daniel J.L., Gasser A. , Hivet G., Soulat D., « Prise en compte du procédé de
fabrication dans la conception des structures composites minces », Mec. Ind., n° 1, 2001,
p. 303-311.
Bruckstein A.M., Netravali A.N., “On Minimal Energy Trajectories”, Computer Vision,
Graphics and Image Processing, n° 49, 1990, p. 283-296.
El Naschie M.S., Stress-Stability and Chaos in Structural Engineering: an Energy Approach,
London: McGraw-Hill, 1990.
Ganghoffer J.F., “New concepts in nonlocal continuum mechanics and new materials obeying
a generalised continuum behaviour”,. Int. J. Engng Sci., vol. 41, Issues 3-5, March 2003,
p. 291-304.
Gasser A., Boisse P., Hanklar S., “Mechanical behaviour of dry fabric reinforcements. 3D
simulations versus biaxial tests”, Computational Materials Science, vol. 17, 2000, p. 7-20.
Hing H., Grimsdale R.L, “Computer graphics techniques for modeling cloth”, IEEE
Computer Graphics and Applications, vol. 16, n° 5, 1996, p. 28-41.
Kapur K.K., Billy J., Asce M., “Stability of Plates Using the Finite Element Method”,
Journal of Engineering of Mechanics, Division (EM2), 1996, p. 77-195.
Kawabata S., Niwa M., Kawai H., Journal of the Textile Institute, vol. 64, n° 21,1973.
Kawabata S., “Nonlinear mechanics of woven and knitted materials”, Textile Structural
Composites, vol. 3, 1989, Amsterdam, Elsevier, p. 67-116.
Kikuchi F., Ishii K., “Unification of Kirchhoff and Reissner-Mindlin Plate Bending
Elements”, European Congress on Computational Methods in Applied Sciences and
Engineering, ECCOMAS 2000, Barcelona, 2001, 1-14 September.
Magno M., Lutz R; “Discrete buckling model for corrugated beam”, Eur. J. Mech. A/ Solids,
vol. 21, 2002, p. 669-682.
Magno M., Ganghoffer J.F., Postle R., Lallam A., “A mesoscopic wave model for textile
materials in large deformations”, Composites structures, vol. 57, 2002, p. 367-371.
Nemeth M.P., “Buckling Behavior of Long Symmetrically Laminated Plates Subjected to
Shear and Linearly Varying Axial Edge Loads”, Nasa TP-3659, July 1997.
Page J., Wang J., “Prediction of shear force using 3D non-linear FEM analyses for a plain
weave carbon fabric in a bias extension state”, FEAD, 38 (8),p. 755-764, 2002.
Provot X., “Deformation constraints in a mass-spring model to describe rigid cloth behavior”,
Graphics Interface, 1995, p. 147-155.
Realf M.L, Boyce M.C., Backer S., “A micromechanical approach to modelling tensile
behaviour of woven fabrics”, V.J. Stokes (Ed.), Use of Plastic and Plastic Composites:
Material and Mechanics Issue, vol. 46, 1993, ASME, New York, p. 285-293.
Silva A.R.D. et al., “Analysis of Plate Under Contact Constraints”, Computational Mechanics
New trends and Applications, 1998, CIMNE, Barcelona.
SNECMA Moteurs, Le Haillan, France, Internal Report, 2002.
Timoshenko S., Théorie de la Stabilité Elastique, Paris & Liège, Beranger, 1947.
Tollenaere H., Caillerie, D., « Continuous modeling of lattice structures by homogenization »,
Advances in Engineering Software, n° 7-9, 1998, p. 699-705.
Yu W.R., Kang T.J., Chung K., “Drape Simulation of Woven Cloth Using Explicit Dynamic
Analysis”, Journal of the Textile Institute, vol. 91, 2000, Part I n°.2, p. 285-301.
