How does Gauss’ theorem ``materialize’’: Scarring, blistering, wrinkling and crumpling of adhesive films on curved topographies
Benny Davidovitch (UMass Amherst)
Soft Materials and Structures
Mon 2:40 - 4:00
Barus-Holley 158
Attaching a solid film to the surface of a curved foundation, such as sphere or saddle, generates elastic stresses. This is a consequence of Gauss’ theorema Egregium, which posits that there exists no isometric map between two surfaces of different Gaussian curvatures. Our group addresses the mechanisms by which this geometric principle ``materializes’’. We ask how the nature of the substrate, the film, and the adhesion, affect the structural instabilities that relieve curvature-induced stresses, and study the patterns that emerge from these instabilities [1-3]. If the substrate is highly rigid and the adhesion is very strong, a crystalline film (such as graphene) relieves stress through a periodic array of lattice defects [2]. In contrast, if the adhesion is weak, the film delaminates from the substrate and a pattern of blisters will form. Yet another instabilities, which involve a mutual wrinkling of the substrate and the film, come into play if the substrate is deformable and the film is sufficiently thin [1,3]. The wrinkling pattern may itself transform into several stress-focusing zones that resemble the shape of a crumpled paper [1]. We classify those distinct behaviors through a universal set of dimensionless parameters, that characterize the deformability of the substrate, the defectability and bendability of the film, and the degree of confinement exerted on it by the curved substrate. The phase diagram spanned by these parameters enables us to predict numerous types of novel transitions between distinct morphological types [1,2]. A particularly interesting prediction is a ``pro-lamination’’ effect, relevant for ultra-thin film, whereby delamination is suppressed through small-scale wrinkles without distorting the macroscopic shape of the substrate [3]. [1] H. King et al. Proc. Nat. Acad. Sci. 109, 9716 (2012). [2] G. Grason and B. Davidovitch, Proc. Nat. Acad. Sci. (under review). [3] E. Hohlfeld and B. Davidovitch (submitted).