Self-organized rod undulations on pre-stretched textiles

Textile technology is a traditional approach to additive manufacturing based on one-dimensional yarn. Printing solid rods onto pre-stretched textiles creates internal stresses upon relaxation of the pre-stretch, which leads to buckling-induced out-of-plane deformation of the textile. Similar behaviours are well known to occur also in biological systems where differential growth leads to internal stresses that are responsible for the folding or wrinkling of leaves, for example. Our goal was to get a quantitative understanding of this wrinkling by a systematic experimental and numerical investigation of parallel rods printed onto a pre-stretched textile. We vary rod thickness and spacing to obtain wavelength and phase coherence of the wrinkles as a function of these parameters. We also derive a simple analytical description to rationalize these observations. The result is a simple analytical estimate for the phase diagram of behaviours that may be used for design purposes or to describe wrinkling phenomena in biological or bioinspired systems.