Buckling of a Stiff Thin Film Embedded Between Two Compliant Substrates

Layered structures consisting of stiff thin films and compliant matrixes are widely observed in flexible electronics, geology and composite materials. In this work, through analytic modelling and numerical simulations, we investigate the buckling instability of a stiff thin film embedded between two compliant substrates under uniaxial compression. Considering the shear stresses at the film/substrate interfaces and the finite geometry change of the film, the critical compressive strain, buckling wavelength and amplitude of sinusoidal wrinkles are analytically derived by the energy method. The analytic predictions agree well with the results obtained by finite element analysis. The post-buckling morphology may be sinusoidal or multiple-period, depending on the compressive strain and the modulus ratio of two compliant substrates. Our results aid in understanding the buckling of compliant substrate/film/compliant substrate tri-layer structures.