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Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation. (English) Zbl 1446.74171

Summary: 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.

MSC:

74K99 Thin bodies, structures
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74Q05 Homogenization in equilibrium problems of solid mechanics
74-05 Experimental work for problems pertaining to mechanics of deformable solids
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