49—a General Model of a Fabric as a Geometric-Mechanical Structure

The need for a model of fabrics in the interpretation of their mechanical behaviour, especially in the low-stress range, is explained, and available models are criticized. A new model is evaluated by considering the yarn geometry to be a function of external forces and reaction forces in the fabric and assuming a relation between the curvature of the yarn in the fabric and in the released state. A new parameter, the form factor, is introduced. Important fabric parameters are calculated and different force combinations considered. A mathematical analysis is given of equilibrium conditions, of stress-strain relationships in extension and compression, and of energy in bending. Further applications and possibilities of the model are indicated.