A continuum constitutive model for the mechanical behavior of woven fabrics including slip and failure

Abstract

Woven fabrics are used in many applications, including ballistic armors and fabric-reinforced composites. Advances in small-scale technologies are enabling new applications including fabrics with embedded electronics, active yam materials, or microfluidics. In order to facilitate the design and improvement of such applications, we propose a modeling approach that relates the macroscopic response of the fabric to the behavior of the underlying yarns and weave. The resulting continuum model is more computationally efficient than a discrete model that represents every yam or fiber explicitly. Because it is physically based on the fabric mesostructure, the model can be used to predict the behavior of novel fabric designs. It can be easily tailored to a wide variety of different applications through the choice of suitable, physically motivated constitutive behaviors for the components that make up the assumed underlying mesostructure. We first describe a model suitable for slip-free planar deformations of a plain weave Kevlar® fabric in response to in-plane loads. We next extend this model to three dimensional behaviors through the development of an anisotropic shell implementation that includes the resistance of the fabric to bending and twist.

(cont.) The model predictions are validated against a number of experimental investigations. Yam friction and yam pullout experiments are used to study the phenomenon of yam slip and to characterize the frictional forces that oppose it. We propose a novel approach for capturing slip in a continuum fabric model, where a single deformation mapping describes the motion of the weave crossover points, and velocity fields describe the relative motion of the yarns past these crossover points. This approach allows the same modeling methodology that was developed for the slip-free case to be used in the presence of yam slip. The resulting theory is non-local-the characteristic unit cell representing the weave mesostructure evolves with the gradients of the slip velocities, and the slip velocities are driven in turn by the gradients of yam tensions. Consequently, implementing the slip formulation into a commercial finite element code presents significant challenges. Different implementation methods are discussed, and the model is validated by conducting analyses of load conditions where slip can be experimentally observed.