Measuring and modeling the anisotropic, nonlinear and hysteretic behavior of woven fabrics

The computational modeling of clothing has received increasing attention since the late 1980's with the desire to study and animate clothing-wearer interactions. Within a clothing modeling framework, it is necessary to model the mechanical behavior of woven fabrics. An important aspect of modeling the mechanics of woven fabrics is capturing realistic stress-strain behaviors which are invariably anisotropic, nonlinear, and hysteretic in that they feature irrecoverable deformation when loadings are removed from the fabric. The objective of this research is to develop a fabric constitutive model that captures the primary features of anisotropy, nonlinearity, and hysteresis, and that can be easily implemented in a nonlinear, large deformation shell finite element framework for general clothing-wearer interaction modeling.

To achieve the objective, biaxial responses of four different woven fabrics were experimentally measured under a battery of load-unload uniaxial stress tests performed in the fabrics' warp, weft, and bias 45° directions. Axial deformations were measured precisely using LVDTs, and transverse deformations were measured less precisely using photogrammetric methods. Such measurements yielded insight on the different fabrics' membrane properties such as nonlinear Young's moduli in the warp and weft directions, shear moduli, and Poisson's ratios. These membrane behaviors were captured in an incremental constitutive model that uses polynomial fitting of a fabric's loading warp and weft Young's moduli, and polynomial fitting of the membrane shear modulus. Measured membrane Poisson's ratios of the different fabrics were found to be asymmetrical and highly variable between fabric types. All of these effects were integrated in a nonsymmetrical incremental constitutive model that relates Piola-Kirchhoff stress to Green-Lagrangian strain.

For numerical implementation in a shell finite element framework, the woven fabric's warp and weft directions relative to an individual element's lamina coordinate system are specified in the undeformed configuration of the fabric and are denoted as the local material coordinate system. As the fabric undergoes arbitrary deformations, the local Piola-Kirchoff stress, the Green-Lagrange strain, and its increment at a point in the fabric are transformed to the material coordinate system in which the stress is updated. The updated state of Piola-Kirchoff stress in the material coordinate system is then rotated back into the local lamina coordinate system for usage in finite element force and stiffness calculations.

This new realistic material model for woven fabrics is successfully implemented and tested in a variety of computations such as simulation of quasi-static material tests, and dynamic fabric "drape" and "poke" tests.