Discrete versus homogenized continuum modeling in finite deformation bias extension test of bi-pantographic fabrics

A 2D-continuum model describing finite deformations in plane of discrete bi-pantographic fabrics has been recently obtained by applying an asymptotic procedure based on a set of local generalized coordinates. Rectangular bi-pantographic prototypes were additively manufactured by selective laser sintering using polyamide as raw material. Displacement-controlled bias extension tests were performed on such specimens for total elastic deformations up to ca. 25%. Experimental force measurements, complemented by discrete displacement measurements obtained by local digital image correlation, were used to fit the continuum model. In the present paper, a global and minimal set of generalized coordinates, alternative to the one used for the homogenization, is introduced for the discrete model. The mechanical constitutive parameters appearing in the discrete model are then found by means of collected experimental data. Finally, a comparison between experiments, the discrete and the continuum model is presented. It is concluded that (a) the discrete model and the experimental data are in excellent agreement, and that (b) the continuum retains the relevant phenomenology of the discrete system even for a rather low number of cells.