ANALYTICAL SOLUTIONS OF POLYMERIC GEL STRUCTURES UNDER BUCKLING AND WRINKLE

Abstract

One of the unique properties of polymeric gel is that the volume and shape of gel can dramatically change even at mild variation of external stimuli. Though a variety of instability patterns of slender and thin film gel structures due to swelling have been observed in various experimental studies, many are not well understood. This paper presents the analytical solutions of swelling-induced instability of various slender and thin film gel structures. We have adopted the well developed constitutive relation of inhomogeneous field theory of a polymeric network in equilibrium with a solvent and mechanical load or constraint with the incremental modulus concept for slender beam and thin film gel structures. The formulas of buckling and wrinkle conditions and critical stress values are derived for slender beam and thin film gel structures under swelling-induced instability using nonlinear buckling theories of beam and thin film structures. For slender beam structure, we construct the stability diagram with the distinct stable and unstable zones. The critical slenderness ratio and corresponding critical stresses are provided for different dimensionless material parameters. For thin film gel structures, we consider the thin film gel on an elastic foundation with different stiffness. The analytical solutions of critical stress and corresponding wrinkle wavelength, as well as buckling condition (or critical chemical potential) are given. These analytical solutions will provide a guideline for gel structure design used in polymeric gels MEMS and NEMS structures such as sensors and actuators. More importantly, the work provides a theoretical foundation of gel structure buckling and wrinkle, instability phenomena are different from normal engineering or material buckling.