Plain woven fabrics
This paper is concerned with the finite deformation of partially set plain woven fabrics subjected to biaxial stresses applied in the directions of the yarns. The configurations of the yarns in the stress-free state are assumed to consist of combinations of elasticas resulting from finitely deformed cantilevers under end loads. In our analysis, the yarns are treated as elastic curved rods subjected to combined extension and bending. As a result of fiber slippage, the moment-curvature relation of the yarn is regarded as bilinear with ideal Baushinger's effect. Residual stresses are found to exist in the fiber initially. A nonlinear boundary value problem can be formulated for the deformation of the fabric where the interyarn contact force is determined from the compatibility condition of displacements at the crimp for yarns in the warp and the weft directions. The effect of the contact deformation of yarns is included in this analysis. Numerical solutions are found for the problem of a uniaxial extension of the fabric and the problem of a biaxial extension of the fabric with equal stresses.