Related papers: Blister patterns and energy minimization in compre…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…
A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to…
This work is devoted so show the appearance of different cracking modes in linearly elastic thin film systems by means of an asymptotic analysis as the thickness tends to zero. By superposing two thin plates, and upon suitable scaling law…
This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical…
We study the behavior of thin elastic sheets that are bent and strained under the influence of weak, smooth confinement. We show that the emerging shapes exhibit the coexistence of two types of domains that differ in their characteristic…
We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional…
Gels are used to design bilayered structures with high residual stresses. The swelling of a thin layer on a compliant substrate leads to compressive stresses. The post-buckling of this layer is investigated experimentally; the wavelengths…
Frustration arises for a broad class of physical systems where confinement (geometric) or the presence of a perturbation (kinematic) prevents equilibration to a minimum energy state. By varying the diameter ratio and packing fraction in…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
Using numerical simulations, we study the dynamical evolution of particles interacting via competing long-range repulsion and short-range attraction in two dimensions. The particles are compressed using a time-dependent quasi-one…
This work tackles the problem of achieving consistent drying rates of a solution film deposited on a $20\,\rm{cm}$-wide substrate ($\approx $ silicon-wafer size) that is driven under a narrow air flow ejected by a slot nozzle (or "air…
The V2O3 phase diagram contains two insulating phases and one metallic phase with different lattice structures. The stability of these phases is very sensitive to pressure, offering a mechanism to tune phase transitions by inducing strain…
Wrinkling patterns at the metallized surface of thin polymer films are shown to be sensitive to the sticky or slippery character of the polymer/substrate interface (titanium coating, polystyrene film and coated silicon substrate). Selective…
The spontaneous emergence of heterogeneous dislocation patterns is a conspicuous feature of plastic deformation and strain hardening of crystalline solids. Despite long-standing efforts in the materials science and physics of defect…
It has been claimed that quasistatic granular materials, as well as nanoscale materials, exhibit departures from elasticity even at small loadings. It is demonstrated, using 2D and 3D models with interparticle harmonic interactions, that…
A new approach for generating stress-constrained topological designs in continua is presented. The main novelty is in the use of elasto-plastic modeling and in optimizing the design such that it will exhibit a linear-elastic response. This…
Partial localization is the phenomenon of self-aggregation of mass into high-density structures that are thin in one direction and extended in the others. We give a detailed study of an energy functional that arises in a simplified model…
Inspired by the observation that many naturally occurring adhesives arise as textured thin films, we consider the displacement controlled peeling of a flexible plate from an incision-patterned thin adhesive elastic layer. We find that crack…
During coating processes, dust deposition can lead to an uneven thickness in the resulting film, posing significant problems in industrial processes. Our study explores the effects of solid defects using a vertical cylindrical fiber…
We study the linearized Fopl - von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle $2 \alpha$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness…