Disappearance of stretch-induced wrinkles of thin sheets: A study of orthotropic films

作者：Sipos Andras A^*; Feher Eszter

来源：International Journal of Solids and Structures, 2016, 97-98: 275-283.

DOI：10.1016/j.ijsolstr.2016.07.021

• Foppl-von Karman plate theory
• Wrinkling of thin films
• Finite strain
• Disappearance of wrinkles
• Orthotropy

In a recent work (Healey et al., 2013. J. Nonlin. Sci. 23, 777-805.) it is predicted that stretch-induced wrinkled pattern in thin, clamped, elastic sheets eventually disappear as the imposed stretch is increased. The prediction stems from a precise bifurcation analysis of the Foppl-von Karman equations generalized for finite mid-plane strains. There it is also revealed that for some aspect ratios of the rectangular domain, wrinkles do not occur at all regardless of the applied extension. To verify these predictions we carried out experiments on thin (20 mu m thick adhesive covered), previously prestressed elastomer sheets with different aspect ratios under displacement controlled pull tests. On the one hand the adjustment of the material properties during prestressing is advantageous since in the targeted strain regime the film becomes substantially linearly elastic (which is not the case without prestress). On the other hand, a significant, non-negligible orthotropy develops during this first extension. To enable quantitative comparisons we abandon the assumption about material isotropy inherent in the original model and derive the governing equations for an orthotropic medium. We find good agreement between numerical simulations and experimental data by comparing measurements on prestressed specimen with predictions of the orthotropic model.
Analysis of the negativity of the second Piola-Kirchhoff stress tensor reveals that the critical stretch for the bifurcation point at which the wrinkles disappear must be finite for any aspect ratio of the domain. On the contrary, there is no such bound if the continuation parameter is the aspect ratio, which manifests as complicated wrinkled patterns with more than one highly wrinkled zone for elongated rectangles. These arrangements have been found both numerically and experimentally. These findings also support the new finite strain model, since the Foppl-von Karman equations based on infinitesimal strains do not exhibit such a behavior.

• 出版日期2016-10-15