Orientable wrinkles in stretched orthotropic films

Abstract

Tensional wrinkles are widely observed in elastic thin films, with mono-orientation of wrinkles being usually perpendicular to the stretching direction. Here, by changing material orthotropic direction, we present orientable wrinkles in uniaxially stretched orthotropic membranes. To quantitatively explore orthotropy-related wrinkles and their morphological evolution, we develop a mathematical model by introducing orthotropic, elastic constitution into the extended Föppl–von Kármán nonlinear plate theory that can describe large in-plane anisotropic deformations. We find that degree of orthotropy and shear modulus significantly affect the critical buckling strain, restabilization point and wrinkling amplitude. A 3D phase diagram on stability boundaries is drawn and we find that no wrinkles emerge when the orthotropic parameters are located in the stability region. Orientable oblique wrinkles, depending on the angle between orthotropy and stretching direction, are carefully examined, which could be used to guide effective designs of wrinkle-tunable membrane surfaces and structures.