A continuum mechanics-based non-orthogonal constitutive model for woven composite fabrics

A non-orthogonal constitutive model is developed to characterize the anisotropic material behavior of woven composite fabrics under large deformation. A convected coordinate system, whose in-plane axes are coincident with the weft and warp yarns of woven fabrics, are embedded in the shell elements. Contravariant stress components and covariant strain components in a constitutive relation are introduced into the convected coordinate system. The transformations between the contravariant/covariant components and the Cartesian components of the stress and strain tensors provide an approach for deriving the global non-orthogonal constitutive relations for woven composite fabrics. By taking advantage of the tensile-shear decoupling in the constitutive equation under the convected coordinate system, the material characterization of woven fabrics is simplified. As an essential part for these transformations, a fiber orientation model is developed, by using some fundamental continuum mechanics concepts, to trace the yarn reorientation of woven fabrics during deformation. The proposed material characterization approach is demonstrated on a balanced plain weave composite fabric. The equivalent material properties are obtained by matching with experimental data of tensile and bias extension tests on the woven composite fabric. Model validation is provided by comparing numerical results with experimental data of bias extension test and shear test. The development of this non-orthogonal model is critical to the ultimate goal, i.e. using numerical simulations to optimize the forming of woven composite fabric sheets.