Prediction of Elastic Properties of Plain Weave Fabric Using Geometrical Modeling

Fabrics are typical porous material and can be treated as mixtures of fibers and air. There is no clearly defined boundary and is different from a classical continuum for fabrics. It is complex to proceed with the theoretical analysis of fabric behavior. There are two main reasons (Hearle et al., 1969) for developing the geometrical structures of fabrics. One is to be able to calculate the resistance of the cloth to mechanical deformation such as initial extension, bending, or shear in terms of the resistance to deformation of individual fibers. The other is that the geometrical relationships can provide direct information on the relative resistance of cloths to the passage of air or light and similarly it can provide a guide to the maximum density of packing that can be achieved in a cloth. The most elaborate and detailed account of earlier work is contained in a classical paper by Peirce (Peirce, 1937). A purely geometrical model, which involves no consideration of internal forces, is set up by Peirce for the determination of the various parameters that were required. Beyond that, the geometrical structures of knits are another hot research issue, for instances, for plain-knitted fabric structure, Peirce (Peirce, 1947), Leaf and Glaskin (Leaf & Glaskin, 1955), Munden (Munden, 1961), Postle (Postle, 1971), DemirÖz and Dias (Demiröz & Dias, 2000), Kurbak (Kurbak, 1998), Semnani (Semnani et al., 2003), and Chamberlain (Chamberlain, 1949) et al. Lately, Kurbak & Alpyildiz propose a geometrical model for full (Kurbak & Alpyildiz, 2009) and half (Kurbak & Alpyildiz, 2009) cardigan structure. Both the knitted and woven fabrics are considered to be useful as a reinforcing material within composites. The geometrical structure of the plain woven fabric (WF) is considered in this study. Woven fabric is a two-dimension (2-D) plane formation and represents the basic structural element of every item of clothing. Fabrics are involved to various levels of load in transforming them from 2-D form into 3-D one for an item of clothing. It is important to know the physical characteristics and mechanical properties of woven fabrics to predict possible behavior and eventual problems in clothing production processes. Therefore, the prediction of the elastic properties has received considerable attention. Fabric mechanics is described in mathematical form based on geometry. This philosophy was the main objective of Peirce’s research on tensile deformation of weave fabrics. The load-extension behavior of woven fabrics has received attention from many researchers. The methods used to develop the models by the researches are quite varied. Some of the developed models are theorybased on strain-energy relationship e.g., the mode by Hearle and Shanahan (Hearle &