Nonlinear elastic stiffness behaviors of plain-weave textile-reinforced composites are considered in this work by modeling finite deformation effects at two scales: (1) at the fiber diameter scale within yarns (~10 microns); (2) at the yarn diameter scale within woven textiles (~1000 microns). To capture the effect of heterogeneous microscale stress and strain fields, symmetric, conjugate, stress and strain measures are first established. A transversely isotropic hyperelasticity model is then presented for modeling finite deformation behaviors of yarns. After the free parameters of this model are estimated using unit cell analysis at the fiber-diameter scale, it is then incorporated into plain-weave textile unit cell model. The textile mode is then subjected to finite strain deformation controlled loading to quantify nonlinearity in stiffness behaviors.

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