A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23:777-805.) predictedthe disappearance of the stretch-induced wrinkled pattern of thin, clamped,elastic sheets by numerical simulation of the F\"oppl-von K\'arm\'an equationsextended to the finite in-plane strain regime. It has also been revealed thatfor some aspect ratios of the rectangular domain wrinkles do not occur at allregardless of the applied extension. To verify these predictions we carried outexperiments on thin 20 micrometer thick adhesive covered), previouslyprestressed elastomer sheets with different aspect ratios under displacementcontrolled pull tests. On one hand the the adjustment of the materialproperties during prestressing is highly advantageous as in targeted strainregime the film becomes substantially linearly elastic (which is far not thecase without prestress). On the other hand a significant, non-ignorableorthotropy develops during this first extension. To enable quantitativecomparisons we abandoned the assumption about material isotropy inherent in theoriginal model and derived the governing equations for an orthotropic medium.In this way we found good agreement between numerical simulations andexperimental data. Analysis of the negativity of the second Piola-Kirchhoff stress tensorrevealed that the critical stretch for a bifurcation point at which thewrinkles disappear must be finite for any aspect ratio. On the contrary thereis no such a bound for the aspect ratio as a bifurcation parameter. Physicallythis manifests as complicated wrinkled patterns with more than one highlywrinkled zones on the surface in case of elongated rectangles. Thesearrangements have been found both numerically and experimentally. Thesefindings also support the new, finite strain model, since the F\"oppl-vonK\'arm\'an equations based on infinitesimal strains do not exhibit such abehavior.
展开▼
