Spontaneous wrinkle branching by gradient stiffness.

The concept of coherency loss is proposed to understand wrinkle branching as a pathway toward hierarchical wrinkling pattern formation in a compressed film-substrate system with gradient stiffness of the film or substrate. A simple model indicates that the wrinkle branching arises when the characteristic length of the stiffness inhomogeneity zone is larger than the coherency persistent length, which depends on the amplitude of the stiffness inhomogeneity. Numerical simulations of nonlinear wrinkles based on the model of the Föppl-von Kármán plate on compliant substrates show how regulating the size and amplitude of the stiffness inhomogeneities results in branched wrinkles in striking agreement with the existing observations. The paper reveals the origin of such kinds of branched wrinkles and may provide a guideline for controllable hierarchical wrinkles by patterning the stiffness gradient.