Pleat formation and the geometry of pure bending

We will discuss our recent attempts towards understanding the mechanics of pleat forming in soft textile sheets. This is an elastic-plastic bending process that we formulate as a variable-arc-length multi-point boundary value problem for an inextensible rod, with a moment-curvature constitutive relation as input. To determine this moment-curvature relation, we have developed a linkage mechanism that can impose an exact pure bending (constant curvature) state up to high curvatures. A simpler approximate mechanism that nearly matches the exact boundary conditions is nonetheless shown to result in significant curvature variations. Our approach is relevant to recent studies of crease formation in polymers that can inform models of folded deployable structures.