Related papers: Dimension reduction via Gamma-convergence for soft…
Using the theory of $\Gamma$-convergence, we derive from three-dimensional elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e. ribbons exhibiting spontaneous curvature and twist. We apply the models to…
In the context of finite elasticity, we propose plate models describing the spontaneous bending of nematic elastomer thin films due to variations along the thickness of the nematic order parameters. Reduced energy functionals are deduced…
We compute effective energies of thin bilayer structures composed by soft nematic elastic-liquid crystals in various geometrical regimes and functional configurations. Our focus is on order-strain interaction in elastic foundations composed…
The problem of the rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in a variational setting. Considering different scalings of the three-dimensional energy and passing to the limit as the…
We study thin films with residual strain by analyzing the $\Gamma-$limit of non-Euclidean elastic energy functionals as the material's thickness tends to $0.$ We begin by extending prior results \cite{bhattacharya2016plates}…
We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of $\Gamma$-convergence. Hereby, we generalize the results of the purely elastic setting [57] to a framework of free discontinuity problems. The…
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external…
$3d-2d$ 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 reduced models for a thin plate by means of {\Gamma}-convergence, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we analyse the case where…
We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a "natural" curvature tensor. This tensor either denotes the second fundamental…
Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…
In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…
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,…
We study the $\Gamma$-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.
We investigate an extension of 2D nonlinear gauge theory from the Poisson sigma model based on Lie algebroid to a model with additional two-form gauge fields. Dimensional reduction of 3D nonlinear gauge theory yields an example of such a…
Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control…
The rigorous derivation of linear elasticity from finite elasticity by means of Gamma-convergence is a well-known result, which has been extended to different models also beyond the elastic regime. However, in these results the applied…
We consider three-dimensional reshaping of thin nemato-elastic sheets containing half-charged defects upon nematic-isotropic transition. Gaussian curvature, that can be evaluated analytically when the nematic texture is known, differs from…
We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also…
This paper presents a new method for modelling the dynamic behaviour of developable ribbons, two dimensional strips with much smaller width than length. Instead of approximating such surface with a general triangle mesh, we characterize it…