A Novel Approach to Three-Dimensional Modeling of Interlaced Fabric Structures

Abstract

This paper attempts the geometric modeling of woven and braided fabric structures in three dimensions using a computer aided geometric design (CAGD) technique. A new symbolic approach to fabric structure representation, which is useful to the textile CAD/CAM process and fabric design, is presented, and a basic model is proposed that treats a yarn as a three-dimensional solid object. Some traditional 2D fabric models are extended into 3D models and demonstrated in 3D form. The structures of various fabrics are demonstrated in graphic forms, including elementary weaves such as plain weave, twill, and satin; two layer fabrics; braided fabrics; and three-dimensional fabrics as reinforcements for composite materials.

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References

Ashenhurst, T.R. , "A Treatise on Textile Calculations and the Structure of Fabrics," Broadbent, Huddersfield, U. K., 1884.

Brierley, S. , Weaving Problems, Textile Mfr. 37, 3 (1931).

de Jong, S. , and Postle, R. , A General Energy Analysis of Fabric Mechanics Using Optimal-control Theory , Textile Res. J. 48, 127 (1978).

do Carmo, M.P. , "Differential Geometry of Curves and Surfaces," Prentice-Hall, Inc., Englewood Cliffs, NJ. 1976.

Dorkin, C.M.C. , Doctoral thesis, University of Leeds, 1954.

Ellis, P. , and Munden, D.L. , "A Theoretical Analysis and Experimental Study of the Plain Square-Weave, Part III, J. Textile Inst. 64, 564 (1973).

Grosberg, P. , and Park, B. J. The Mechanical Properties of Woven Fabrics, Part V: The Initial Modulus and the Frictional Restraint in Shearing of Plain-weave Fabrics, Textile Res. J. 36, 420 (1966).

Hamilton, J.B. , A General System of Woven Fabric Geometry , J. Textile Inst. 55, T66 (1964).

Kawabata, S. , Niwa, M. , and Kawai, H. , The Finite-deformation Theory of Plain-weave Fabrics, J. Textile Inst. 64, 862 (1976).

10.

Keefe, M. , Solid Modeling of Yarn and Fiber Assemblies, J. Textile Inst. 83, 185 (1992).

11.

Kemp, A. , An Extension of Peirce's Cloth Geometry to the Treatment of Non-circular Threads, J. Textile Inst. 49, T44 (1958 ).

12.

Law, W. , Worsted Fabric Structure. Wool Rec. 21, 968 (1922).

13.

Liao, T.Y. , The Structure Variation of Worsted Wool Fabric from Loom State to Finished Fabric, J. China Textile Res. 10, 32 (1989).

14.

Liao, T.Y. , The Relaxation Shrinkage of Worsted Wool Yarn And Its Effects on Fabric Structure And Performance, in "Proc. 8th International Wool Textile Research Conference, New Zealand," vol V, 1990, p. 128.

15.

Olofsson, B. , A General Model of Fabric as a Geometric Mechanical Structure, J. Textile Inst. 55, T541 ( 1964).

16.

Peirce, F.T. , Geometry of Cloth Structure, J. Textile Inst. 28, T45 (1937).

17.

Snowden, D.C. , in "Proc. Int. Wool Text. Res. Conf, Paris," vol. IV, 1965, p. 249.

18.

Snyder, J.M. , "Generative Modeling for Computer Graphics and CAD," Academic Press, Inc., San Diego, CA, 1992.

19.

Wolfram, S. , "The Mathematica Book," 3rd ed.. Cam-bridge University Press, U.K., 1996.