Formation of twisted hierarchical patterns through sequential film depositions and wrinkles

Wrinkle patterns arising from surface instabilities are widespread in natural and engineered systems, with broad potential in electronics, optics, bionics and surface engineering. Although various methods—such as thermal expansion, swelling, mechanical loading, and light irradiation—have been developed to create diverse morphologies, generating complex hierarchical wrinkles with controllable features remains a challenge. Here, we report tunable hierarchical wrinkle patterns in film-substrate systems via multistep film deposition and sequential release of nonorthogonal biaxial prestretch. The first deposition and strain release yield unidirectional stripe wrinkles, while a second deposition followed by strain release along a nonorthogonal direction induces twisted hierarchical morphologies through the interaction of two wrinkle generations. The pattern formation process, morphology, and underlying mechanics are elucidated through experiments, theoretical analysis, and finite element simulations. This study elucidates the role of multistep deposition and sequential prestretch release in symmetry-breaking wrinkle formation and offers a simple yet versatile strategy for engineering ordered hierarchical wrinkles for practical applications.