Bilinear Approximation of Anisotropic Stress-Strain Properties of Woven Fabrics

In the theoretical derivation of the anisotropic model of the woven fabric, Kilby (1963) achieved the symmetric anisotropy model. Yet, in practice, the warp behavior of a woven fabric is rarely identical to the weft behavior, even in the case of plain weave fabric of identical yarns in both warp and weft directions because of the manufacturing process. The closed form analytic solution of the asymmetric anisotropic behaviour is very difficult to find for real fabric, due to its nonlinear properties. Therefore, it is important to derive an efficient and accurate method to approximate the nonlinear fabric anisotropy. This paper discusses the issue of incorporating the tensile fabric properties and the bias angle effect into a bilinear stress-strain model. The stress-strain relationship is divided into two regions, below and above the elastic limit. Within each region, a basis function, based on three data points, is used to approximate the angular effect. The advantages of this method include: (1) its simplicity, (2) robust 2-step lookup operation to obtain the answer, (3) full coverage of both linear and nonlinear elastic regions, and (4) ability to achieve high degree of accuracy with only three data points.