Pattern formation in the three-dimensional deformations of fibered sheets

• Elastic fibered sheet, in which fibers are arranged in a pantographic lattice.
• Finite-element solution that illustrate the model.
• Bias test of pantographic sheet.
• Some simulations of a three-dimensional deformation.

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.