We capture the out-of-plane mechanical response of woven fabrics through a nonlinear anisotropic shell implementation of a multi-scale continuum constitutive model. For the membrane response, we rely on a previously developed model for the in-plane behavior of woven fabrics. The planar model captures both the macroscopic response and the interactions of the yarns at the mesostructural level. This model relies on the definition of a repeating unit cell representing the fabric mesostructure, where the macroscopic states of stress and strain are related to the internal loads carried by the yarns and to the configuration of the unit cell. The continuum model therefore retains information about the fabric mesostructural response without explicitly modeling discrete yarns. The two-dimensional model is extended to capture three-dimensional modes of deformation through a shell formulation, including out-of-plane bending, twist, and transverse shear. We assume that the effects of these deformations on the 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. This three-dimensional model permits the analysis of complex modes of fabric deformation such as draping, wrinkling, and transverse indentation. We discuss the mechanisms by which out-of-plane deformations are accommodated and present simple experiments used to characterize the out-of-plane response of the fabric. We compare model predictions of complex loading modes to experimental findings.
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