A simplified description of the stress-strain state of a warp-knitted fabric

A new technique for describing the deformation and failure of a warp-knitted fabric is proposed. The stress-strain state of the material is specified not by the principal stretch ratios, but by an effective strain, introduced as an analogue of the radial strain, and an angle characterizing the deformation regime. Within the framework of the approach suggested, the flexural stiffness of threads is ignored, which allows us to linearize the relation between the specific loads in the fabric and the effective strains, which is approximated by trigonometric functions (squares of sines and cosines). As a result, the mechanical properties of the fabric are characterized by ten parameters. They are determined by employing the method of separating a structural element, which has been elaborated previously. The results obtained are compared with those given by a more complex mathematical model without approximations and with experimental data found by the ball penetration method.