Wrinkling of stiff film on porous substrate

Film/substrate systems incorporating porous substrates are widespread in both natural and engineered materials, while the nonlinear constitutive behavior of the substrate induces complex wrinkling deformations in the overlying film. In this study, by integrating experimental observations, theoretical modeling, and finite element simulations, we conduct a systematic investigation of the wrinkling morphology and post-buckling evolution of a stiff film supported by a compliant porous substrate. Our results reveal that once the applied compressive strain exceeds a critical threshold, the system transitions from periodic wrinkling to localized folding, governed by a shift in the system’s minimum potential energy state. With continued loading, spatially heterogeneous compaction within the porous substrate increasingly constrains the film’s downward deformation, thereby triggering successive fold reconfigurations with stepwise increases in fold wavenumber. To elucidate the underlying mechanics, we develop a continuum framework based on von Kármán plate theory, which accurately predicts the critical buckling strain, wrinkle wavelength, and amplitude associated with both initial instability and the subsequent wrinkle-to-fold transition. Furthermore, a comprehensive phase diagram is constructed to clarify the morphological evolution of the film as a function of the applied eigenstrain and the film-to-substrate modulus ratio. These findings provide fundamental insights into instability-driven pattern formation in compliant systems, and offer design guidelines for engineering film/porous-substrate interfaces with tailored surface and mechanical properties.