New concept of pseudo-continuum model for plain-weave fabrics

A new concept of pseudo-continuum model is proposed to analyze the complicated nonlinear behaviour of plain-weave fabrics. Subjected to an extension in an arbitrary direction, plain-weave fabric undergoes three kinds of thread deformation, that is, skewing, straightening and extension. On the assumption of no friction and no flexural rigidity with respect to the threads, a pseudo-continuum model is constituted by a new strain-displacement relationship which translates the three kinds of deformation to two kinds of strain, that is, axial extension and transverse compression of warp and weft. The finite element is formulated by means of the principle of virtual work in the total Lagrangian form. The mechanical nonlinearity and anisotropy of the plain-weave fabrics caused by geometrical nonlinearity of threads are elucidated through numerical examples concerning the uniaxial tensile tests.