Stability analysis of a cross-linked elastic gel that has absorbed the equilibrium amount of solvent and is attached to either a viscous or an elastic bottom layer atop a rigid substrate is considered. The effects of top and bottom layer moduli (Et and Eb), bottom-to-top layer thickness ratio (H/h), and polymer solvent interaction parameter (c) on the critical condition of wrinkling, wrinkle wavelength and amplitude are examined. When the bottom layer is viscous, the compressed top layer is always unstable, and wrinkling is rate-controlled. The viscous flow of the bottom layer governs the rate and determines the fastest growing wavelength, which is most likely to be observed when growth is arrested. As Et rises, the bending stiffness of the elastic layer does too and so the fastest growing wavelength (lm) rises and equilibrium amplitude (Ae) falls. As H/h rises, the constraint of the rigid substrate diminishes and so lm and Ae rise. As c falls, lm falls and Ae rises because better solvents create higher compressive strain that promote low wavelength, high amplitude wrinkles.
When the bottom layer is elastic, there is a critical compressive stress. If the generated compressive stress (s0,gen) is greater that the critical stress (s0,c), the top layer wrinkles. As the top layer modulus Et rises, s0,c rises and s0,gen peaks. Therefore, wrinkling is most likely at intermediate values of Et. Moreover, as Et rises, the equilibrium wrinkle amplitude (Ae) peaks because s0,gen peaks, and wrinkle wavelength (l) rises because bending stiffness rises. As Eb rises, s0,c rises but s0,gen does not change. Therefore, wrinkling is most likely when Eb is low. As the bottom layer modulus Eb rises, Ae and l fall because the constraint of the bottom layer rises. As the bottom-to-top layer thickness ratio H/h rises, s0,c falls but s0,gen does not change. Therefore, wrinkling is most likely when H/h is high. As H/h rises, Ae and l both rise because the wrinkling layer is relatively further from the rigid substrate that opposes wrinkling. As the polymer solvent interaction parameter c falls, s0,c does not change but s0,gen rises. Therefore, wrinkling is most likely when c is low. Moreover, as c falls, Ae rises because a better solvent generates more swelling and greater compressive strain energy, which promotes wrinkling, but does not change l significantly.