Related papers: Nonlinear weakly curved rod by Gamma convergence

This paper is devoted to describe the asymptotic behavior of a structure made by a thin plate and a thin rod in the framework of nonlinear elasticity. We scale the applied forces in such a way that the level of the total elastic energy…

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 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…

We derive, via simultaneous homogenization and dimension reduction, the $\Gamma$-limit for thin elastic plates of thickness $h$ whose energy density oscillates on a scale $\eh$ such that $ \eh^2 \ll h\ll \eh$. We consider the energy scaling…

In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…

We analyze the asymptotic behavior of a junction problem between a plate and a perpendicular rod made of a nonlinear elastic material. The two parts of this multi-structure have small thicknesses of the same order $\delta$. We use the…

We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter $\varepsilon$. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous.…

We consider the equilibrium shapes of a thin, annular strip cut out in an elastic sheet. When a central fold is formed by creasing beyond the elastic limit, the strip has been observed to buckle out-of-plane. Starting from the theory of…

Starting from three-dimensional nonlinear elasticity under the restriction of incompressibility, we derive reduced models to capture the behavior of strings in response to external forces. Our $\Gamma$-convergence analysis of the…

We derive a new version of the von K\'arm\'an energy and the corresponding Euler-Langrange equations, in the context of thin prestrained plates, under the condition of incompressibility relative to the given prestrain. Our derivation uses…

We derive Griffith functionals in the framework of linearized elasticity from nonlinear and frame indifferent energies in brittle fracture via Gamma-convergence. The convergence is given in terms of rescaled displacement fields measuring…

We show that solutions for a specifically scaled nonlinear wave equation of nonlinear elasticity converge to solutions of a linear Euler-Bernoulli beam system. We construct an approximation of the solution, using a suitable asymptotic…

We study the $\Gamma$-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.

We study the asymptotic behaviour, in the sense of $\Gamma$-convergence, of a thin incompressible magnetoelastic plate, as its thickness goes to zero. We focus on the linearized von K\'arm\'an regime. The model features a mixed…

A weakly nonlinear study is numerically conducted to determine the behaviour near the onset of convection in rotating spherical shells. The mathematical and numerical procedure is described in generality, with the results presented for an…

The three-dimensional shapes of thin lamina such as leaves, flowers, feathers, wings etc, are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric, given on the…

We study the $\Gamma$-limit of sequences of variational problems for straight, transversely curved shallow shells, as the width of the planform $\varepsilon$ goes to zero. The energy is of von K\'arm\'an type for shallow shells under…

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…

The geometrically rigorous nonlinear analysis of elastic shells is considered in the context of finite, but small, strain theory. The research is focused on the introduction of the full shell metric and examination of its influence on the…

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…