Related papers: Energy minimising configurations of pre-strained m…
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…
In this paper we derive, by means of $\Gamma$-convergence, the periodically wrinkled plate model starting from three dimensional nonlinear elasticity. We assume that the thickness of the plate is $h^2$ and that the mid-surface of the plate…
We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By $\Gamma$-convergence we derive a one-dimensional limit theory and show that…
We study the effective elastic behaviour of the incompatibly prestrained thin plates, characterized by a Riemann metric $G$ on the reference configuration. We assume that the prestrain is "weak", i.e. it induces scaling of the incompatible…
We consider a single disclination in a thin elastic sheet of thickness $h$. We prove ansatz-free lower bounds for the free elastic energy in three different settings: First, for a geometrically fully non-linear plate model, second, for…
We derive von-K\'arm\'an plate theory from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a $\Gamma$-limit when considering the limit where the interatomic distance…
We discuss the limiting behavior (using the notion of \Gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales…
The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…
We apply a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology to derive a viscoelastic plate model of von K\'arm\'an type. We start from time-discrete solutions to a…
We study the static and dynamic structure of thermally fluctuating elastic thin sheets by investigating the overdamped dynamic F\"oppl-von K\'arm\'an equation, in which the F\"oppl-von K\'arm\'an equation from elasticity theory is driven by…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
We rigorously derive a Kirchhoff plate theory, via $\Gamma$-convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin sheet. The heterogeneity in the elastic properties of…
Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller studied a branching pattern with optimal scaling of the energy with respect to its parameters.…
A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element,…
We present an alternative to the Kohn-Sham formulation of density functional theory for the ground-state properties of strongly interacting electronic systems. The idea is to start from the limit of zero kinetic energy and systematically…
The paper is dedicated to the investigation of simultaneous homogenization and dimension reduction of textile structures as elasticity problem with an energy in the von-K{\'a}rm{\'a}n-regime. An extension for deformations is presented…
Variety of statistically steady energy spectra in elastic wave turbulence have been reported in numerical simulations, experiments, and theoretical studies. Focusing on the energy levels of the system, we have performed direct numerical…
We derive, via simultaneous homogenization and dimension reduction, the Gamma-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the…
We consider a two phase elastic thin film with soft inclusions subject to bending dominated deformations. The soft (void) phase may comprise asymptotically small droplets within the elastic matrix. We perform a dimension reduction analysis…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…