Theory of Elasticity for Plain-Weave Fabrics (2nd Report, Finite Element Formulation)

A new breed of finite element is developed to analyze the nonlinear behavior of plain-weave fabrics in the in-plane problems of arbitrary boundary condition. A nondimensional parameter called crimp parameter is introduced as an unknown to represent the crimp condition of warp and weft, and handled as a component of the displacement vector. The plain-weave fabric is homogenized by means of a newly defined strain-displacement relationship including the crimp parameter for the sake of consistent dealing with the three types of thread deformations, that is, skewing, straightening and extension. This homogenized model called pseudo-continuum model induces the geometrical nonlinearity with respect to the finite rotation of the threads, and its finite element is formulated by the principle of virtual work in the total Lagrangian description. The mechanism of nonlinear behavior of the plain-weave fabrics is elucidated through several examples by the proposed finite element