We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of two parts, describing the two main physical effects. The first part represents the elastic energy of the film, which is approximated using the von Kármán plate...

The local, eigenfunction-weighted acoustic phonon density of states (DOS) tensor is calculated for a model substrate consisting of a semi-infinite isotropic elastic continuum with a stress-free surface. On the surface, the local DOS is proportional to the square of the frequency v, as for the three-dimensional Debye model, but with a constant of proportionality that is considerably enhanced com...

We present an asymptotic analysis of the thickness of the liquid film that coats a smooth solid substrate when it is withdrawn from a bath of non-Newtonian fluid, and compare our results with experimental measurements. The film thickness is, to a good approximation, uniform above the point where the film is withdrawn from the fluid bath, and depends on the rotation rate, the fluid properties an...

The interaction of atoms and molecule with surfaces is of great technological relevance. For a reliable theoretical description of the interaction dynamics of light atoms and molecules such as hydrogen or helium with surfaces, quantum effects have to be taken into account. In this article, I will discuss quantum effects in the interaction dynamics of both the substrate as well as the incident p...

The morphological evolution during spinodal decomposition of a binary alloy thin film elastically constrained by a substrate is studied. Elastic solutions, derived for elastically anisotropic thin films subject to the mixed stress-free and constraint boundary conditions, are employed in a three-dimensional phase-field model. The Cahn–Hilliard diffusion equation for a thin film boundary conditio...

In this paper we study some key effects of a discontinuous forcing term in fourth order wave equation on bounded domain, modeling the adhesion an elastic beam with substrate through elastic-breakable interaction. By using spectral decomposition method show that main induced by nonlinearity at transition from attached to detached states can be traced loss regularity solution and migration total ...

a new three-dimensional unit cell model has been developed for modeling three constituent phases including inclusion, interphase and matrix. the total elastic modulus of nano-composite is evaluated.  numerical results are in good agreement with the previous proposed theoretical modeling. higher matrix and inclusion elastic modulus both can dramatically influence the total elastic modulus.

background substrates in medical science are hydrophilic polymers undergoing volume expansion when exposed to culture medium that influenced on cell attachment. although crosslinking by chemical agents could reduce water uptake and promote mechanical properties, these networks would release crosslinking agents. in order to overcome this weakness, silicone rubber is used and reinforced by nanocl...

Transfer printing by kinetically switchable adhesion to an elastomeric stamp shows promise as a powerful micromanufacturing method to pickup microstructures and microdevices from the donor substrate and to print them to the receiving substrate. This can be viewed as the competing fracture of two interfaces. This paper examines the mechanics of competing fracture in a model transfer printing sys...