A Shell Formulation to Model the Three-Dimensional Deformation Response of Woven Fabrics

We capture the out-of-plane mechanical response of woven fabrics through a nonlinear anisotropic shell implementation of a continuum constitutive model. For the membrane response, we rely on a previously developed model for the in-plane behavior of woven fabrics. This planar model captured both the macroscopic response and the interactions of the yarns at the structural level, but was limited to two dimensions. The two-dimensional model is here extended to capture three-dimensional modes of deformations through a shell formulation. We assume that the effects of out-of-plane bending and shear on the established in-plane behavior are negligible; however, we do consider the effects that in-plane deformation and the resulting evolution of the fabric structure have on the out-of-plane response. For example, the formulation accounts for the evolving anisotropy of the out-of-plane bending behavior, which reflects the changing orientations of the yarn families within the fabric surface. This three-dimensional model permits the analysis of complex modes of fabric deformation such as wrinkling at large shear strains or transverse identation. We present experiments and detailed finite element analyses used to understand and characterize the out-of-plane responses of the fabric, including bending and twist, and we discuss the underlying physical phenomena that control these responses. Finally, we compare model predictions of complex loading modes to experimental findings.