Related papers: Solutions for a free-boundary problem modeling mul…
Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. The cantilever experiment allows the stress in a drying film that has been deposited onto a thin plate…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…
We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface…
We investigate the role of architected thin films in the interfacial failure properties of bi-layer composites. Our results show that, while graded structures can be used to prescribe failure at the interface, they do not offer significant…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
We present a thermodynamic theory of plane coherent solid-solid interfaces in multicomponent systems subject to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated separately using…
Free interfaces of liquid crystals tend to minimise both capillarity and anchoring forces. Here we study nematic films in planar and radial geometries with antagonistic anchoring boundary conditions and one deformable interface. Assuming a…
Electrohydrodynamic instabilities of fluid-fluid interfaces can be exploited in various microfluidic applications in order to enhance mixing, replicate well-controlled patterns or generate drops of a particular size. In this work, we study…
We investigate theoretically the morphology of a thin nematic film adsorbed at flat substrate patterned by stripes with alternating aligning properties, normal and tangential respectively. We construct a simple "exactly-solvable" effective…
The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the…
This note summarizes recent results in which modern techniques of the calculus of variations are used to obtain qualitative features of film-substrate interfaces for a broad class of interfacial energies. In particular, we show that the…
We consider two-layers of immiscible liquids confined between an upper and a lower rigid plate. The dynamics of the free liquid-liquid interface is described for arbitrary amplitudes by a single evolution equation derived from the basic…
This work presents a mathematical model for the optimal control of thin-film flows over a flexible topography influenced by an external force. Our thin-film model allows for the rupture of films as well as the coalescence of bubbles. The…
We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…
An equilibrium phase diagram for the shape of compressively strained free-hanging films is developed by total strain energy minimization. For small strain gradients {\Delta}{\epsilon}, the film wrinkles, while for sufficiently large…
I study numerically the problem of delamination of a thin film elastically attached to a rigid substrate. A nominally flat elastic thin film is modeled using a two-dimensional triangular mesh. Both compression and bending rigidities are…
This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed…
A boundary element formulation is developed to determine the complex stress intensity factors associated with cracks on the interface between dissimilar materials. This represents an extension of the methodology developed previously by the…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…