Mechanical Behavior of Regular Twill Weave Structures; Part I: 3D Meso-Scale Geometrical Modelling

Abstract

The mechanical behavior of fabrics with different configurations has been investigated in many works by various approaches including the force equilibrium or energy methods. However, representing a suitable geometrical model for fabric structure is prerequisite to apply these approaches. This paper introduces an analytic 3D meso-scale geometrical modelling of regular twill weaves, in terms of a few structural parameters in 2D biaxial orthogonal woven fabrics. The model is proposed for the fabrics in their fully relaxed state considering their inherent skewness. For this purpose, a three dimensional structure is used to show this phenomenon. In this model, the yarns cross-section is assumed to be circular and the yarns path is assumed to be straight line (saw-tooth) in the unit cell which leads to the results that are in reasonable agreement with experimental data. These assumptions will be helpful in finding a close form solution for the mechanical behavior of woven structures. The proposed model has been verified by comparing its output with some experimental data for its areal mass and thickness in 2/2 twill fabric as a case study. By applying this model, the geometrical structural parameters such as skewness and weave angles as well as their total consumed yarns can be predicted theoretically. This model is a framework which will be used for estimating the initial deformation behavior of regular twill woven structures under uniaxial tensile loads in our forthcoming works.