Pattern formation in the three-dimensional deformations of fibered sheets

Ivan Giorgio (1, 2) , Roman Grygoruk (3) , Francesco Dell’isola (1, 2) , David J. Steigmann (2, 4)

1 Dipartimento d'Ingegneria Strutturale & Geotecnica
2 International Research Centre for the Mathematics and Mechanics of Complex Systems
3 Warsaw University of Technology [Warsaw]
4 Department of Mechanical Engineering [Berkeley]

We simulate pattern formation in the deformations of a pantographic lattice using a model of elastic surfaces that accounts for the geodesic bending of the constituent fibers. The theory predicts an unusual arrangement of coexistent phases observed in an actual lattice, manufactured by a 3D printing process, in which the fibers undergo part-wise uniform shears separated by internal transition layers controlled by geodesic bending stiffness.

Mots clés: Strain gradients; Woven fabrics; Elastic surface theory

Domaines: Génie mécanique [physics.class-ph]; Mécanique [physics]; Mécanique des solides [physics.class-ph]

Ivan Giorgio, Roman Grygoruk, Francesco Dell’isola, David J. Steigmann. Pattern formation in the three-dimensional deformations of fibered sheets. Mechanics Research Communications, 2015, 69, pp.164-171. ⟨10.1016/j.mechrescom.2015.08.005⟩. ⟨hal-01194318⟩