Tarfaoui, M
ABSTRACT
This work is a theoretical study of the mechanical behavior of two different weave types: plain and twill. Traditional methods permit the study of plain weaves but prove quite difficult for twill weaves. Indeed, the difficulties related to modeling the mechanical behavior of the twill weave are due to its very complex geometry and its nonsymmetry, which require the application of the finite element method. This method requires first a mathematical formulation of the problem and then a mesh of the basic cells of the plain and twill fabrics. The next step is to simulate shearing and tensile tests. Analyzing the results has proved to be very hard and thus demands a study of the stress field of the basic cell.
In every model defined by its partial derivative equation of fabric mechanical behavior and whatever the method of homogenization employed to obtain a homogeneous model, one must solve a cellular problem. The three-dimensional structure of the basic cell of various fabrics is very complex. We begin this study by creating meshes for the different fabrics, which will enable us to take account of their geometry as well as the characteristic mechanics of the yam and the applied stresses. Then we present some models, neglecting one or another of both components.
For all models that deal with the mechanical behavior of textile structures independent of the method of homogenization, the problem has to be solved at the basic cell level before moving to the global model. After having defined the geometric form and created the meshes of the basic cells of the plain and twill fabrics, we then treat the problem from a mechanical point of view using the finite element method. Simulations of various shearing and tensile tests determine the model of the mechanical behavior of fabric. For a first approach, we suppose that the various components of the basic cell, ix., the yams, are homogeneous and isotropic. Many tests have been performed on stiff fabrics, and the results have shown that the linear model is the most accurate one.
The second part of this work consists of an evaluation of the strains in the yarns that constitute the basic cell; this will enable us to predict the most strained and most damaged areas.
Models and Methods
PIERCE'S GEOMETRIC MODEL
This model, developed in 1937 [9] by Pierce, is the most conventional and the oldest. In this model, the warp and weft yams show two-dimensional trajectories. Circular and compressible sections ideally represent these yarns, and segments and circles (Figure 1) represent their trajectories.
Due to this specific geometry, it is only possible to make calculations for the plain weave, because this model can treat only simple fabrics. Once the yarns are incompressible and perfectly flexible, the yam curvature is uniform and imposed by the cross section of the intersected yarns.
Literature Cited
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Manuscript rci-d September 10. 1999. 21, 2000.
M. TARFAOUI1 AND J. Y. DREAM1
Laboratoire de Physique et Mecanique Textiles, Ecole Nationale Superieure des Industries Textiles de Mulhouse, Universiti de Haute Alsace, 68093 Mulhouse Cedex, France
S. AKESBI2
Laboratoire de Mathematiques, Faculte de Sciences et Techniques, Universite de Haute Alsace, 68093 Mulhouse Cedex, France
1 m.tarfaoui@univ-mulhouse.fr and jy.drean@univ-mulhouse.fr 2 s.akesbi@univ-mulhouse.fr
