A reasonable microstructural model of fabrics is adopted, and an explicit. constitutive equation for such materials is derived. At infinitesimal strains the bulk stress tensor is directly proportional to the area fraction and the Young modulus of the fiber strands. Anisotropy is a direct consequence of the distribution of fiber strands. Two cases are considered: the completely random distribution, and a regular pattern of fiber strands. In the former case the material is not Hookean, in the sense that normal stresses are generated during a shear deformation; in the latter case material properties are strongly dependent on the pattern distribution itself.
Get full access to this article
View all access options for this article.
References
1.
Bird, R.B., Hassager, O., Armstrong, R.C., and Curtiss, C.F. "Dynamics of Polymeric Liquids, Vol. II: Kinetic Theory," Wiley, New York, 1977.
2.
Christoffersen, J., "Fabric: Orthotropic Materials with a Stress-Free Shear Mode," Report 150, The Danish Center for Applied Mathematics and Mechanics, Dec. 1978.
3.
Hashin, Z., Theory of Mechanical Behaviour of Heterogeneous Media, Appl. Mech. Rar.17, 1-9 (1964).
4.
Hearle, J.W.S. and Stevenson, P.J., Nonwoven Fabric Studies. Part III: The Anisotropy of Nonwoven Fabrics, Textile Res. J.42, 268-271 (1972).
5.
Hill, R., Report on Theories of the Elastic Properties of Reinforced Solids, British Iron and Steel Research Association, Rep. P/19/62 (1962), J. Meck. Phys. Solids11, 357-372 (1963).
6.
Phan-Thien, N., A Non-Linear Viscoelastic Model, J. Rheology22, 259-283 (1978).
7.
Phan-Thien, N., Atkinson, J.D., and Tanner, R.I., TheLangevin Approach to the Dumbbell Kinetic Problem in Rheology, J. Non-Nnewl . Fluid Mech.3, 309-330 (1978).
8.
Petterson, D.R. , "On the Mechanics of Nonwoven Fabrics," D. Sc. Thesis, Massachusetts Institute of Technology, 1958.
9.
Sengupta, A.K. , De, D., and Sarkar, B.P., Anisotropy in some Mechanical Properties of Woven Fabrics, Textile Res. J.42, 268-271 (1972).
10.
Treloar, L.R.G. , "The Physics of Rubber Elasticity," 3rd Edition, Clarendon Press, Oxford, 1975.
