Person:

Hutchinson, John

Wrinkling of thin stiff films on thick compliant elastomeric substrates subject to plane strain compression is considered for cases in which the substrate is pre-stretched prior to film attachment. Advanced wrinkling modes are investigated that evolve as the systems are compressed beyond the onset of the primary sinusoidal wrinkling mode. If the substrate pre-stretch is greater than about 40%, an advanced mode in the form of a series of well-spaced ridges separated by relatively flat film is observed in the simulations. Our experiments reveal a localization mode in the form of alternating packets of large and small amplitude wrinkles, but not ridges, while ridge formation has been observed in other recent experiments. Measurements of undulation amplitudes have been made for wrinkle fields of stiff films formed by oxidation of the surface of pre-stretched PDMS substrates. Simulations have been performed with a finite element model and an analytical film/substrate model. The formation of the ridge mode is a consequence of the altered nonlinearity of the substrate produced by the pre-stretch. The role of the tangential substrate stiffness in suppressing localization at the ridges is also highlighted. If there is no substrate pre-stretch, or if the substrate is pre-compressed, the primary sinusoidal mode gives way to an entirely different sequence of advanced modes usually entailing period doubling followed by folding. The nature of substrate nonlinearity that leads to ridges or folds is discussed.

Thin stiff films on compliant elastic substrates subject to equi-biaxial compressive stress states are observed to buckle into various periodic mode patterns including checkerboard, hexagonal and herringbone. An experimental setting in which these modes are observed and evolve is described. The modes are characterized and ranked by the extent to which they reduce the elastic energy of the film–substrate system relative to that of the unbuckled state over a wide range of overstress. A new mode is identified and analyzed having nodal lines coincident with an equilateral triangular pattern. Two methods are employed to ascertain the energy in the buckled state: an analytical upper-bound method and a full numerical analysis. The upper-bound is shown to be reasonably accurate to large levels of overstress. For flat films, except at small states of overstress where the checkerboard is preferred, the herringbone mode has the lowest energy, followed by the checkerboard, with the hexagonal, triangular, and one-dimensional modes lowering the energy the least. At low overstress, the hexagonal mode is observed in the experiments not the square mode. It is proposed that a slight initial curvature of the film may play role in selecting the hexagonal pattern accompanied by a detailed analysis. An intriguing finding is that the hexagonal and triangular modes have the same energy in the buckled state and, moreover, a continuous transition between these modes exists involving a linear combination of the two modes with no change in energy. Experimental observations of various periodic modes are discussed with reference to the energy landscape. Discrepancies between observations and theory are identified and open issues are highlighted.

The stability of the wrinkling mode experienced by a compressed half-space of neo-Hookean material is investigated using analytical and numerical methods to study the post-bifurcation behaviour of periodic solutions. It is shown that wrinkling is highly unstable owing to the nonlinear interaction among the multiple modes associated with the critical compressive state. Concomitantly, wrinkling is sensitive to exceedingly small initial imperfections that significantly reduce the compressive strain at which the instability occurs. The study provides insight into the connection between wrinkling and an alternative surface mode, the finite amplitude crease or sulcus. The shape of the critical combination of wrinkling modes has the form of an incipient crease, and a tiny initial imperfection can trigger a wrinkling instability that collapses into a crease.

Wrinkling modes are determined for a two-layer system comprised of a neo-Hookean film bonded to an infinitely deep neo-Hookean substrate with the entire bilayer undergoing compression. The full range of the film/substrate modulus ratio is considered from the limit of a traction-free homogeneous substrate to very stiff films on compliant substrates. The role of substrate prestretch is considered wherein an unstretched film is bonded to a prestretched substrate with wrinkling arising as the stretch in the substrate is relaxed. An exact bifurcation analysis reveals the critical strain in the film at the onset of wrinkling. Numerical simulations carried out within a finite element framework uncover advanced post-bifurcation modes including period-doubling, folding and a newly identified mountain ridge mode.

Two-dimensional ridge structures are induced by equi-biaxial compression with large equi-biaxial pre-stretch in a thin film by using a micro-fluidics technique. Whereas wrinkles tend to be uniformly distributed, ridges are localized. The wrinkle-to-ridge transition is unstable (subcritical), resulting in large amplitude changes. The nature and morphology of the ridges is studied and quantified by experiments and numerical simulations.