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.

Symmetric-in-Plane Compression of Polyamide Pantographic Fabrics—Modelling, Experiments and Numerical Exploration

Symmetric in-plane compression of a pantographic lattice structure is modelled and simulated, and the results are compared to previously available experimental data. Said experimental results had shown a peculiar behaviour: depending on the fiber density, the deformed shape could present either one or two swellings under compression. The present article is a preliminary modelling attempt aiming at capturing that behaviour numerically.

Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation

Bi-pantographic fabrics are composed of two families of pantographic beams and correspond to a class of architectured materials that are described in plane as second-gradient 2D continua. On a discrete level, a pantographic beam is a periodic arrangement of cells and looks like an expanding barrier. The materialization of a bi-pantographic fabric made from polyamide was achieved by additive manufacturing techniques. Starting from a discrete spring system, the deformation energy of the corresponding continuum is derived for large strains by asymptotic homogenization. The obtained energy depends on the second gradient of the deformation through the rate of change in orientation and stretch of material lines directed along the pantographic beams. Displacement-controlled bias extension tests were performed on rectangular prototypes for total elastic extension up to 25%. Force–displacement measurements complemented by local digital image correlation analyses were used to fit the continuum model achieving excellent agreement.