相关论文: On the derivation of homogenized bending plate mod…

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…

Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004), we consider a variational plate model for an elastic cone under compression in the direction of the cone symmetry axis. Assuming radial symmetry,…

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 study the homogenization of nonlocal micromagnetic functionals incorporating both symmetric and antisymmetric exchange contributions under the physical constraint that the magnetization field takes values in the unit sphere. Assuming…

We are interested in the thermal insulation of a bounded open set $\Omega$ surrounded by a set whose thickness is locally described by $\varepsilon h$, where $h$ is a non-negative function defined on the boundary $\partial\Omega$. We study…

We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice spacing tends to zero. We assume that the atoms are part of a (maybe) non-periodic lattice close to a flat set in a lower dimensional space, typically a…

We use the method of $\Gamma$-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach…

We derive the effective energy density of thin membranes of liquid crystal elastomers as the Gamma-limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic…

The purpose of this paper is to present a new mathematical model for the deformation of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner plate theory, takes into account the transverse…

We study equilibrium configurations of non-Euclidean plates, in which the reference metric is uniaxially periodic. This work is motivated by recent experiments on thin sheets of composite thermally responsive gels [1]. Such sheets bend…

We prove compactness with respect to $\Gamma$-convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free…

Using $\Gamma$-convergence arguments, we construct a nonlinear membrane-like Cosserat shell model on a curvy reference configuration starting from a geometrically nonlinear, physically linear three-dimensional isotropic Cosserat model. Even…

We prove that that for nonlinear elastic energies with strong enough energetic control of the outer distortion of admissible deformations, almost everywhere global invertibility as constraint can be obtained in the $\Gamma$-limit of the…

We study investigate a long, thin rectangular elastic membrane that is bent through an angle $2 \alpha$, using the Foppl--von Karman ansatz in a geometrically linear setting. We study the associated variational problem, and show the…

We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite systems of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy,…

A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret & Raoult. Specific characterizations of the 2D elastic…

We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not…

We derive a class of two-dimensional shell energies for thin elastic bodies exhibiting small-length scale effects modeled via strain-gradient elasticity. Building on the final author's earlier work on plate models, the kinetic and stored…

We derive a von K\'arm\'an plate theory from a three-dimensional quasistatic nonlinear model for nonsimple thermoviscoelastic materials in the Kelvin-Voigt rheology, in which the elastic and the viscous stress tensor comply with a frame…

We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…