Finite deformation mechanics in buckled thin films on compliant supports

Abstract

We present detailed experimental and theoretical studies of the mechanics of thin buckled films on compliant substrates. In particular, accurate measurements of the wavelengths and amplitudes in structures that consist of thin, single-crystal ribbons of silicon covalently bonded to elastomeric substrates of poly(dimethylsiloxane) reveal responses that include wavelengths that change in an approximately linear fashion with strain in the substrate, for all values of strain above the critical strain for buckling. Theoretical reexamination of this system yields analytical models that can explain these and other experimental observations at a quantitative level. We show that the resulting mechanics has many features in common with that of a simple accordion bellows. These results have relevance to the many emerging applications of controlled buckling structures in stretchable electronics, microelectromechanical systems, thin-film metrology, optical devices, and others.buckling ͉ stiff thin film ͉ compliant substrate ͉ stretchable electronics

In‐Plane Deformation Mechanics for Highly Stretchable Electronics

“…(a) wrinkling for very thin interconnects (sub-micrometer), as reported in prior studies [26,27] and also shown in Figure 1c for 300 nm and 1 µm; in this study, wrinkling is defined as out-of-plane buckling without significant twisting, with wavelength smaller than the length of the shortest straight segment (L/2 in Figure 1a); (b) coupled out-of-plane buckling and twisting with relatively long wavelengths (>L/2) for interconnects with moderate thickness (up to ≈45 µm), which we refer to as buckling and is shown in Figure 1c for 12.5 µm; similar transverse buckling behavior was observed in the study of Yang et al; [28] (c) pure in-plane bending for even thicker interconnects (> ≈45 µm), which we call scissoring (or non-buckling in comparison to previous studies on buckling interconnects) as shown in Figure 1c for 80 µm. Detailed deformation of the three modes (amplitudes, wavelengths, and twist angles) appear in Figure S2 (Supporting Information).…”

“…Transition from Wrinkling to Buckling: The mechanics of wrinkling of a thin metal film on an elastomer substrate gives [22,26,27] the wavelength at the onset of wrinkling as…”

Tunable Nanowrinkles on Shape Memory Polymer Sheets

“…[5,6] Flexible integrated circuits promising many new applications, such as wearable systems, have been demonstrated using thin buckled films of single-crystalline silicon based on elastomeric substrates. [7,8] Metal wrinkles, thin films of metal on polymer substrates, have promise for applications in molecular detection, optical devices, filters and sorters, high-surface-area conductors and actuators, and even metrology. [9][10][11][12] We have developed a rapid approach to create metal nanowrinkles of tunable size and demonstrable utility on a shape memory polymer, [13,14] pre-stressed polystyrene (PS) sheets commercially available as the children's toy Shrinky-Dinks.…”

The Mexican hat effect on the delamination buckling of a compressed thin film

“…Even before the film buckling load is reached, the nonlinear Green-Lagrange strain tensor due to the finite deformation effect needs to be considered for a very soft substrate [2,23]. (2) The nonlinear stress-strain relation of the substrate, which is characterized by the neo-Hookean constitutive law [23] or the bilinear [24] and exponential [25] elastic foundation models. (3) The fact that the substrate responds differently to tension and compression [20,26,27].…”