A consistent finite-strain plate model for wrinkling of stretched anisotropic hyperelastic films

Abstract

Stretch-induced wrinkles usually occur in a thin, clamped–clamped, hyperelastic film and eventually disappear upon excess stretching, with wrinkling direction being perpendicular to the stretching direction within isotropic elasticity framework. Here, we consider in-plane anisotropy induced by infilling fibers in thin films, which significantly affects the orientation and amplitude of wrinkles. To precisely predict the isola-center bifurcation (“birth” and “death” of wrinkles) and to capture wrinkling morphology evolution under large in-plane anisotropic deformations, we develop a consistent finite-strain plate model by accounting for anisotropic hyperelastic constitutive laws. Advantages of this plate model lie in its asymptotic consistency with the 3D field equations and its applicability to large deformations. A new type of rotational symmetric boundary conditions is proposed to reduce the computational cost and to achieve robust convergence. We reveal that the fiber orientation plays a critical role in the wrinkling and restabilization behavior of stretched films. The fibers parallel or perpendicular to the stretching direction can resist the appearance of wrinkles, while the oblique fiber orientation (15°∼75°) can advance wrinkle formation. Besides, oblique wrinkling patterns can be regulated by fiber/matrix shear modulus ratio, and we draw phase diagrams on stability boundary to demonstrate the interactive parametric effects. Our results could provide quantitative guidance to design wrinkle-tunable surfaces for fiber-composite or biomimetic films.