A finite strain model predicts oblique wrinkles in stretched anisotropic films

Abstract

Transverse wrinkles commonly occur in a uniaxially tensile elastic membrane and can vanish upon excess stretching. The wrinkling direction is usually perpendicular to the stretching direction under isotropic elasticity. Here, we show that wrinkles are orientable by material anisotropy, such as in fiber-reinforced or fibrous films, and the wrinkling orientation can be tuned by varying the stiffness and direction of fibers. To quantitatively describe large anisotropic deformations and predict morphological evolution, we develop a finite strain model by introducing anisotropic, hyperelastic constitutive law into the geometrically extended Föppl-von Kármán nonlinear plate theory. We find that the shear modulus ratio between fibers and matrix significantly affects the critical buckling threshold, restabilization point and wrinkling amplitude. The shear modulus ratio above a critical value prevents the appearance of wrinkles. Effects of the angle between fibers and stretching direction on the oblique wrinkling orientation are carefully examined. The findings could provide an effective way to design wrinkle-tunable surfaces for fiber-reinforced or biomimetic membranes.