相关论文: Dimension reduction for thin films with transversa…

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…

We study wrinkling patterns in a thin elastic annulus subjected to radial stretching within the framework of the F\"oppl--von K\'arm\'an theory. Building on the analysis of the Lam\'e problem in Bella and Kohn, we investigate the asymptotic…

We consider a geodesic $\gamma$ of length $2L$ in an oriented Riemannian manifold $(\mathcal M, g)$ and a thin tube $\Omega^*_h$ around $\gamma$ of radius $h$. We study an 'elastic' energy per unit volume $E_h(u)$ of maps $u$ from…

We show the existence of global minimizers for a geometrically nonlinear isotropic elastic Cosserat 6-parameter shell model. The proof of the main theorem is based on the direct methods of the calculus of variations using essentially the…

We consider a geometrically fully nonlinear variational model for thin elastic sheets that contain a single disclination. The free elastic energy contains the thickness $h$ as a small parameter. We give an improvement of a recently proved…

We consider a nonlinear, frame indifferent Griffith model for nonsimple brittle materials where the elastic energy also depends on the second gradient of the deformations. In the framework of free discontinuity and gradient discontinuity…

This paper is motivated by the complex blister patterns sometimes seen in thin elastic films on thick, compliant substrates. These patterns are often induced by an elastic misfit which compresses the film. Blistering permits the film to…

Motivated by experiments and formal asymptotic expansions in the physics literature, Maor and Shachar (J. Elasticity 134 (2019), 149-173) studied the behaviour of a model elastic energy of maps between manifolds with incompatible metrics.…

We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness $h$ and around the mid-surface $S$ of arbitrary geometry, converge as $h\to 0$ to the critical points of the von K\'arm\'an functional…

We consider a thin elastic strip of thickness h and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is of order h^2 converge to stationary points of the Euler-Bernoulli functional. The proof…

We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness…

$3d-2d$ dimensional reduction for hyperelastic thin films modeled through energies with point dependent growth, assuming that the sample is clamped on the lateral boundary, is performed in the framework of $\Gamma$-convergence. Integral…

The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and {\delta}_h,…

The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…

A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…

In this work we consider a new class of oscillatory instabilities that pertain to thermocapillary destabilization of a liquid film heated by a solid substrate. We assume the substrate thickness and substrate-film thermal conductivity ratio…

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…

For a comprehensive characterization of mechanical reliability of metallization layers on polymer substrates both electrical and mechanical degradation should be taken into account. Although it is evident that cracking of a conductive film…

We study the transition from flat to wrinkled region in uniaxially stretched thin elastic film. We set up a model variational problem, and study energy of its ground state. Using known scaling bounds for the minimal energy, the minimal…

The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal…