Curvature evaluation of metal wires in plain weave structure via the elasto-plastic finite element analysis

Macroscopic deformation characteristics of plain weave structure, the most basic woven fabric, are significantly influenced by its mesoscale shape and internal stress state, depending on weaving process factors. This study analyses numerically the effects of the design variables, i.e. the wire pitch on the heddle/shuttle and the plasticity of the metal wires of plain weave, on the deflection state of the warp and weft wires. A model with continuity of the weave structure simulates the simple weaving process using the finite element method in anticipation of its application to homogenisation methods. Furthermore, the continuous curvature between contact points is analysed mathematically to evaluate the finished shape in plain woven structures. Considering internal stress by the weaving process and elastoplasticity of metal wires, the deflection curve is closer to straight lines than the ideal deflection curve in elasticity, owing to local yielding and tension caused by the plasticity effect and setting, respectively.