Abstract
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.
Highlights
Surface wrinkling of composite systems consisting of a hard skin on a soft underlayer has received considerable attention for several decades
Termed the mountain ridge mode, or, more briefly, the ridge mode, it was discovered through numerical simulation of wrinkling of thin stiff films on deep compliant neoHookean substrates (Cao & Hutchinson, 2012a)
When this film/substrate system is subject to incremental plane strain compression, the onset of wrinkling occurs as the classical sinusoidal mode at very small incremental compressive strain, typically on the order of 0.01 or less
Summary
Surface wrinkling of composite systems consisting of a hard skin on a soft underlayer has received considerable attention for several decades. To our knowledge the only experimental evidence for localized ridge formation is the recent work of Ebata, Croll & Crosby (2012) These authors attached films of polystyrene (with thicknesses varying from 5 to 180nm) to pre-stretched PDMS substrates. 3.2 Effect of pre-deformation on nonlinearity of substrate traction-displacement behavior Two subsidiary calculations have been carried out to give further insight into the role of substrate pre-stretch or pre-compression underlying the formation of the two distinct advanced modes, ridges and folds. These calculations help to expose the nature of the nonlinearity of a semi-infinite neo-Hookean substrate as dependent on a uniform pre-compression or pre-stretch, 1S. Bifurcation from the uniform state is governed by the linearized equation: Eh3 12 d 4W d4X
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