Effects of tension-compression asymmetry on the surface wrinkling of film-substrate systems

摘要

Many soft materials and biological tissues are featured with the tension-compression asymmetry of constitutive relations. The surface wrinkling of a stiff thin film lying on a compliant substrate is investigated through theoretical analysis and numerical simulations. It is found that the tension-compression asymmetry of the soft substrate not only affects the critical strain of buckling but, more importantly, may also influence the wrinkling pattern that occurs in the film-substrate system under specified loading conditions. Due to this mechanism, the thin film subjected to equi-biaxial compression may first buckle into a hexagonal array of dimples or bulges, instead of the checkerboard pattern, and consequently evolve into labyrinths with further loading. Under non-equi-biaxial compression, the system may buckle either into a parallel bead-chain pattern or a stripe pattern, depending on the substrate nonlinearity and the loading biaxiality. Phase diagrams are established for the wrinkling patterns in a wide range of geometric and mechanical parameters, which facilitate the design of surface patterns with desired properties and functions.