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Thin films buckle easily and form wrinkled states in regions of well defined size. The extent of a wrinkled region is typically assumed to reflect the zone of in-plane compressive stresses prior to buckling, but recent experiments on…
We study the non-Euclidean (incompatible) elastic energy functionals in the description of prestressed thin films, at their singular limits ($\Gamma$-limits) as $h\to 0$ in the film's thickness $h$. Firstly, we extend the prior results…
Residual stress and plastic strain in additive manufactured materials can exhibit significant microscopic variation at the powder scale, profoundly influencing the overall properties of printed components. This variation depends on…
Glasses have a wide range of technological applications. The recent discovery of ultrastable glasses that are obtained by depositing the vapor of a glass-forming liquid onto the surface of a cold substrate has sparked renewed interest in…
Self-assembly of ordered nanometer-scale patterns is interesting in itself, but its practical value depends on the ability to predict and control pattern formation. In this paper we demonstrate theoretically and numerically that engineering…
Polymer glasses have numerous advantageous mechanical properties in comparison to other materials. One of the most useful is the high degree of toughness that can be achieved due to significant yield occurring in the material. Remarkably,…
We analyze a linear 3D/3D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic plate-like structure with the aim of deriving a simplified reduced model. Based on suitable energy dissipation…
Classical molecular-dynamics simulations have been carried out to investigate densification mechanisms in silicon dioxide thin films deposited on an amorphous silica surface, according to a simplified ion-beam assisted deposition (IBAD)…
We consider a variational model for periodic partitions of the upper half-space into three regions, where two of them have prescribed volume and are subject to the geometrical constraint that their union is the subgraph of a function, whose…
Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain, which is theoretically well understood. Here and in the companion paper, we extend this…
For the contact of two finite portions of interacting rigid crystalline surfaces, we compute the dependence of the pinning energy barrier on the misfit angle and contact area. The resulting data are used to investigate the distribution of…
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…
A minimal athermal model for the flow of dense disordered materials is proposed, based on two generic ingredients: local plastic events occuring above a microscopic yield stress, and the non-local elastic release of the stress these events…
In recent years, functional oxide-metal based vertically aligned nanocomposite (VAN) thin films have gained interest due to their intriguing physical properties and multifunctionalities stemming from the complex interactions between the two…
We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic…
This is the second paper devoted to energetic rigidity, in which we apply our formalism to examples in two dimensions: underconstrained random regular spring networks, vertex models, and jammed packings of soft particles. Spring networks…
The model introduced in [Kholmatov-Piovano 2020] in the framework of the theory on Stress-Driven Rearrangement Instabilities (SDRI) [Asaro-Tiller 1972; Grinfeld 1993} for the morphology of crystalline materials under stress is considered.…
The apparently intractable shape of a fold in a compressed elastic film lying on a fluid substrate is found to have an exact solution. Such systems buckle at a nonzero wavevector set by the bending stiffness of the film and the weight of…
The influence of surface constraints on the self-assembly of liquid droplets is investigated. A semi-quantitative explanation for large scale pattern formation consisting of small scale closely arranged droplets inside the large scale…
We propose a model for predicting the fluctuations of electron states in thin films as function of film thickness. The model was derived based on the assumption of the existence of potential barrier fluctuations on the film surface. Since…