A simplified constitutive and finite element model of plain weave fabric reinforcements for the biaxial loading

Soft matrices reinforced by textile preforms are considered as flexible composites that can undergo large elastic deformation. The mechanical behaviors of these composites are highly nonlinear, involving both material and geometric nonlinearities. To conduct a finite element analysis studying woven fabric structures, one of the desired approaches is to develop an equivalent continuum model representing the mechanical behavior of the fabric’s unit cell. During large deformation, significant fabric architecture rearrangement occurs. To include this geometrical nonlinearity into a continuum model, it is always a challenge. In this work, the constitutive model of weave fabrics under biaxial loadings has been derived considering the large nonlinear elastic deformations. This model assumes that the fabric consists of monofilaments, where the yarn is treated as a thin isotropic solid bar which follows the sinusoidal shape. The effects of the yarn’s crimp interchange, and bending are considered in the constitutive equations. One of the special advantages to use this constitutive model is that the geometry can be completely defined by the commonly given information for a fabric (i.e., crimps, number of yarns per unit fabric length). Good agreement has been found between predictions and experiments under various biaxial loadings. The theoretical predictions also agree well with FEA simulations of the mechanical behaviors of the unit cell.