The Mullins effect in the wrinkling behavior of highly stretched thin films

Recent work demonstrates that finite-deformation nonlinear elasticity is essential in the accurate modeling of wrinkling in highly stretched thin films. Geometrically exact models predict an isola-center bifurcation, indicating that for a bounded interval of aspect ratios only, stable wrinkles appear and then disappear as the macroscopic strain is increased. This phenomenon has been verified in experiments. In addition, recent experiments revealed the following striking phenomenon: For certain aspect ratios for which no wrinkling occurred upon the first loading, wrinkles appeared during the first unloading and again during all subsequent cyclic loading. Our goal here is to present a simple pseudo-elastic model, capturing the stress softening and residual strain observed in the experiments, that accurately predicts wrinkling behavior on the first loading that differs from that under subsequent cyclic loading. In particular for specific aspect ratios, the model correctly predicts the scenario of no wrinkling during first loading with wrinkling occurring during unloading and for all subsequent cyclic loading.Comment: 15 pages, 9 figure

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

A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23:777-805.) predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the F\"oppl-von K\'arm\'an equations extended to the finite in-plane strain regime. It has also been 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 micrometer thick adhesive covered), previously prestressed elastomer sheets with different aspect ratios under displacement controlled pull tests. On one hand the the adjustment of the material properties during prestressing is highly advantageous as in targeted strain regime the film becomes substantially linearly elastic (which is far not the case without prestress). On the other hand a significant, non-ignorable orthotropy develops during this first extension. To enable quantitative comparisons we abandoned the assumption about material isotropy inherent in the original model and derived the governing equations for an orthotropic medium. In this way we found good agreement between numerical simulations and experimental data. Analysis of the negativity of the second Piola-Kirchhoff stress tensor revealed that the critical stretch for a bifurcation point at which the wrinkles disappear must be finite for any aspect ratio. On the contrary there is no such a bound for the aspect ratio as a bifurcation parameter. Physically this manifests as complicated wrinkled patterns with more than one highly wrinkled zones on the surface in case of elongated rectangles. These arrangements have been found both numerically and experimentally. These findings also support the new, finite strain model, since the F\"oppl-von K\'arm\'an equations based on infinitesimal strains do not exhibit such a behavior.Comment: 16 pages, 5 figure

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

A recent paper [Healey et al., J. Nonlin. Sci., 2013, 23, 777-805.] predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the Föppl-von Kármán equations extended to the finite in-plane strain regime. It has also been 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 µm thick adhesive covered) elastomer sheets with different aspect ratios under displacement controlled pull tests. We found that the wrinkled shapes are strongly influenced by the emerging orthotropy during the extension. To carry out quantitative comparisons we abandoned the assumption about material isotropy and derived the governing equations for an orthotropic medium. In this way we found good agreement between numerical simulations and experimental data. Analysis of the negativity of the second Piola-Kirchhoff stress tensor showed that the critical stretch for a bifurcation point at which the wrinkles disappear must be finite for any aspect ratio. On the other hand, there is no such a bound for the aspect ratio as a bifurcation parameter. Physically this manifests as complicated wrinkled patterns with more than one highly wrinkled zones on the surface in case of elongated rectangles. These arrangements have been found both numerically and experimentally. These findings also support the new, finite strain model, since the Föppl-von Kármán equations based on infinitesimal strains do not exhibit such a behavior

Wrinkling patterns of thin films under finite membrane strain

There is a wide interest in understanding phenomena related to thin and ultrathin surfaces, such as wrinkling, cresting or folding. The classical Föppl-von Kármán plate theory is extensively used to model such phenomena. Significant in-plane strains demand the extension of the classical FvK model. The extended theory predicts the disappearance of wrinkling in the case of rectangular, clamped, stretched sheets, which was verified on thin, polyurethane sheets. In this talk we further develop the model for curved surfaces and present problems, where the extension to the finite tangential strains is essential to investigate the arising wrinkling pattern. By numerical simulation of the governing nonlinear system of PDEs, we investigate the effect of the curvature of the reference configuration on the emerging wrinkling pattern and demonstrate that disappearance of wrinkles takes place on curved surfaces, as well

An Existence Theorem for a Class of Wrinkling Models for Highly Stretched Elastic Sheets

We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small bending energy. Without bending energy, the stored-energy density is not rank-one convex for general spatial deformations but reduces to a polyconvex function when restricted to the plane, i.e., two-dimensional hyperelasticity. In addition, it grows unbounded as the local area ratio approaches zero. The small-bending component of the model is the same as that in the classical von K\'arm\'an model. Here we prove the existence of energy minima for a general class of such models

Mechanical Instability of Thin Solid Film Structures

Instability of thin film structures as buckling and wrinkling are important issues in various fields such as skin aging, mechanics of scars, metrology of the material properties of thin layers, coating of the surfaces and etc. Similar to the buckling, highly ordered patterns of wrinkles may be developed on the film‒substrate due to compressive stresses. They may cause a failure of the system as structural damage or inappropriate operation, however once they are well understood, it is possible to control and even use them properly in various systems such as the gossamer structures in the space, stretchable electronics, eyelike digital cameras and wound healing in surgery. In this thesis, the mechanical instability of the thin film is considered analytically and numerically by solving the eigenvalue problem for the governing equation of the system, and the effects of the different factors on the instability parameters such as load, amplitude, wavenumber and length of the wrinkles are studied. Different problems such as wrinkling within an area on the film, and buckling and wrinkling of the non‒uniform systems with variable geometry and material properties for both of the film and substrate are investigated. It is shown that the effects of the non‒uniformity of the system are very significant in localization of the wrinkles on the film; however, such a factor has been ignored by many researchers to simplify the problems. In fact, for the non‒uniform systems, the wrinkles accumulate around the weakest locations of the system with lower stiffness and the wrinkling parameters are highly affected by the non‒uniformity effects. Such effects are important especially in thin film technology where the thickness of the film is in the order of Micro/Nano scale and the uniformity of the system is unreliable. The results of this dissertation are useful in the design and applications of thin films in science, technology and industry. They consider the relation of the loading and structural stiffness with the wrinkling parameters and provide more insight into the physics of the localization of the wrinkling on the thin structures, how and why wrinkles are accumulated at some positions. Therefore, deliberate application of these results provides appropriate tools to control and use the buckling and wrinkling of thin films effectively in different fields