Related papers: Elastic sheets, phase surfaces and pattern univers…
We consider a physical model where the total energy is governed by surface tension and attractive screened Coulomb potential on the 3-dimensional space. We obtain different periodic equilibrium patterns i.e. stationary sets for this energy,…
Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ($\mbox{Re}$) numbers. Our direct numerical simulations show that elastic…
Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were…
We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplished by extending the…
We study free-discontinuity functionals in nonlinear elasticity, where discontinuities correspond to the phenomenon of cavitation. The energy comprises two terms: a volume term accounting for the elastic energy; and a surface term…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales…
A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry…
We consider a thin elastic sheet in the shape of a disk whose reference metric is that of a singular cone. I.e., the reference metric is flat away from the center and has a defect there. We define a geometrically fully nonlinear free…
A consistent treatment of the coupling of surface energy and elasticity within the multi-phase- field framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases…
The alignment of fibers and cells in living tissues affect their mechanical properties and functionality. In this context, one can draw an analogy between tissues and nematic liquid crystal elastomers. We explore this analogy by growing…
We propose an alternative physical mechanism to explain the observed accelerated expansion of the Universe based on the configuration entropy of the cosmic web and its evolution. We show that the sheets, filaments and clusters in the cosmic…
Starting from some relevant facts concerning the behaviour of the universe over large scale and time span, the analogy between the geometric approach of General Relativ- ity and the classical description of an elastic strained material…
An instantaneous sub-surface disturbance in a two-dimensional elastic half-space is considered. The disturbance propagates through the elastic material until it reaches the free surface, after which it propagates out along the surface. In…
We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior…
In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, three- and fivefold straight screw- and…
We analyze scalar field dark energy models minimally and non-minimally coupled to gravity, postulating that a Yukawa-like interacting term is \emph{in form} equivalent for general relativity, teleparallel and symmetric-teleparallel…
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…
We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…