Mathematical Modelling of Mechanical Properties of Textiles Subjected to Tension

Mathematical modelling of textiles subjected to one-directional tensile forces is presented. The models include the straightening of fibres at the beginning, accompanied by the compression of neighbouring fibres, and finally the elongation of the material of fibres when the straightening stops growing. As the result of fibres stretching, the transverse compressive forces hold all the fibres together and are responsible for maintaining the friction forces. Two models are proposed: the rhombus, representing perpendicular fibres, and the helix, representing parallel fibres. The final equations describing both models are found to be the same. Calculations demonstrating the behaviour of the model under dynamic loading were performed. The results are illustrated graphically and discussed.