Three-scale modeling and numerical simulations of fabric materials

Based on the underlying structure of fabric materials, a three-scale model is developed to describe the mechanical behavior of fabric materials. The current model assumes that fabric materials take on an overall behavior of anisotropic membranes, thus the membrane-scale is taken as the macroscopic scale of the model. Since fabric materials exist only as thin structures and there is no corresponding bulk material having a similar constitutive property, the direct approach of the mechanics of surfaces is employed. Following the membrane-scale, a yarn-scale is introduced, in which yarns and their weaving structure are accounted for explicitly. Yarns are modeled as an extensible elasticae. A unit cell consisting of two overlapping yarns is used to formulate the weaving patterns and the interaction between the yarns, which governs the nonlinear constitutive behavior of fabric materials. The third scale, named fibril-scale, accounts for the fibrils constituting a yarn and incorporates their mechanical properties. Via a coupling (handshake) process between these three scales a couple model is introduced. The overall behavior and performance of various fabric products becomes predictable by the knowledge of the material properties of a single fibril and the weaving structure of the fabrics. In addition, potential damage during deformation is also captured in the current model through breakage of fibrils in the fibril-scale.