Vibration Analysis of Post-Buckled Thin Film on Compliant Substrates

Buckling stability of thin films on compliant substrates is universal and essential in stretchable electronics. The dynamic behaviors of this special system are unavoidable when the stretchable electronics are in real applications. In this paper, an analytical model is established to investigate the vibration of post-buckled thin films on a compliant substrate by accounting for the substrate as an elastic foundation. The analytical predictions of natural frequencies and vibration modes of the system are systematically investigated. The results may serve as guidance for the dynamic design of the thin film on compliant substrates to avoid resonance in the noise environment.

Spontaneous bending of pre-stretched bilayers

We discuss spontaneously bent configurations of pre-stretched bilayer sheets that can be obtained by tuning the pre-stretches in the two layers. The two-dimensional nonlinear plate model we use for this purpose is an adaptation of the one recently obtained for thin sheets of nematic elastomers, by means of a rigorous dimensional reduction argument based on the theory of Gamma-convergence (Agostiniani and DeSimone in Meccanica. doi:10.1007/s11012-017-0630-4, 2017, Math Mech Solids. doi:10.1177/1081286517699991, arXiv:1509.07003, 2017). We argue that pre-stretched bilayer sheets provide us with an interesting model system to study shape programming and morphing of surfaces in other, more complex systems, where spontaneous deformations are induced by swelling due to the absorption of a liquid, phase transformations, thermal or electro-magnetic stimuli. These include bio-mimetic structures inspired by biological systems from both the plant and the animal kingdoms.

Wrinkling membranes with compliant boundaries

Wrinkled patterns are useful for a wide variety of technological applications ranging from microfluidics to microelectronics. In order to use wrinkled patterns for these applications, both the location and the morphology, i.e. wavelength and amplitude of the wrinkled features, must be precisely controlled. In this paper, a surface was fabricated by placing a thin, flat, continuous glassy film on a topographically-patterned elastomeric substrate to control different wrinkling morphologies and mechanisms on a single surface. With this configuration, we achieved unique surfaces with two distinct regions of wrinkling morphology without changing the film material properties; a region where the film is unsupported and the wrinkling mechanics is dictated only by the film property and the pattern geometry, and a region where the film is supported and wrinkling length scales are dictated by the film and elastomer properties. We demonstrated that the wrinkling wavelength and amplitude scales with geometry and applied strain differently and can be independently controlled in each of the distinct regions.

The topography of steady sandpiles on arbitrary domains

If sand is continually and slowly added onto a table, a pile will grow and reach some steady state, whereupon any further sand added to the pile will fall off the table, leaving the surface of the pile unchanged. A construction that gives the surface of a unique steady pile for a table of any given shape was proposed by Arpad L. Nadai. Here, we show that Nadai's construction can be justified mathematically on the basis of a few plausible assumptions on the mechanical behaviour of sand. We also show that the surface of the steady pile given by the construction is the maximal topography supported on the domain of the table; that the surface may contain smooth patches, valleys, peaks and ridges; that any smooth patch is developable; that any valley is smooth, straight and without tributaries, and has a slope equal to the angle of repose of the sand; that any peak is sharp; and that any ridge is sharp and has a slope less than the angle of repose of the sand. Lastly, we perform simple experiments and verify that actual steady piles look similar to those given by the construction, with a precision that depends on the type of sand and how carefully the sand is poured to form a pile.

Oscillatory thermomechanical instability of an ultrathin catalyst

Because of the small thermal capacity of ultrathin ( approximately 200 nanometers) metal single crystals, it is possible to explore the coupling of catalytic and thermal action at low pressures. We analyzed a chemothermomechanical instability in this regime, in which catalytic reaction kinetics interact with heat transfer and mechanical buckling to create oscillations. These interacting components are separated and explored through experimentation, mathematical modeling, and scientific computation, and an explanation of the phenomenon emerges from their synthesis.