Discrete models of fabric accounting for yarn interactions

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.

[1]  Philippe Boisse,et al.  Mechanical behaviour of dry fabric reinforcements. 3D simulations versus biaxial tests , 2000 .

[2]  Massimo Magno,et al.  Discrete buckling model for corrugated beam , 2002 .

[3]  P. Gonçalves,et al.  ANALYSIS OF PLATE UNDER CONTACT CONSTRAINTS , 1998 .

[4]  Richard L. Grimsdale,et al.  Computer graphics techniques for modeling cloth , 1996, IEEE Computer Graphics and Applications.

[5]  Stephen P. Timoshenko,et al.  Theorie de la stabilite elastique , 1966 .

[6]  Kwansoo Chung,et al.  Drape Simulation of Woven Fabrics by Using Explicit Dynamic Analysis , 2000 .

[7]  S. Kawabata,et al.  Nonlinear mechanics of woven and knitted materials , 1989 .

[8]  J. Ganghoffer.  New concepts in nonlocal continuum mechanics and new materials obeying a generalised continuum behaviour , 2003 .

[9]  Damien Soulat,et al.  Prise en compte du procédé de fabrication dans la conception des structures composites minces , 2000 .

[10]  Alfred M. Bruckstein,et al.  On Minimal Energy Trajectories , 1990, Comput. Vis. Graph. Image Process..

[11]  Jun Wang,et al.  Prediction of shear force using 3D non-linear FEM analyses for a plain weave carbon fabric in a bias extension state , 2002 .

[12]  Philippe Boisse,et al.  Finite element simulations of textile composite forming including the biaxial fabric behaviour , 1997 .

[13]  D. Caillerie,et al.  Continuous modeling of lattice structures by homogenization , 1998 .

[14]  M. P. Nemeth.  Buckling Behavior of Long Symmetrically Laminated Plates Subjected to Shear and Linearly Varying Axial Edge Loads , 1997 .

[15]  Mohammed S El Naschie,et al.  Stress, Stability and Chaos in Structural Engineering: An Energy Approach , 1990 .

[16]  R. Postle,et al.  A mesoscopic wave model for textile materials in large deformations , 2002 .

[17]  B. J. Hartz,et al.  Stability of Plates Using the Finite Element Method , 1966 .

[18]  Xavier Provot,et al.  Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior , 1995 .