相关论文: Derivation of the Reissner-Mindlin model from nonl…
The linear Reissner-Mindlin shell theory is reformulated in the frame of the tangential differential calculus (TDC) using a global Cartesian coordinate system. The rotation of the normal vector is modelled with a difference vector approach.…
The classical flexure problem of non-linear incompressible elasticity is revisited assuming that the bending angle suffered by the block is specified instead of the usual applied moment. The general moment-bending angle relationship is then…
We propose a method for deriving equivalent one-dimensional models for slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, finite rotations, arbitrary cross-sections…
We obtain linear elasticity as $\Gamma$-limit of finite elasticity under incompressibility assumption and Dirichlet boundary conditions. The result is shown for a large class of energy densities for rubber-like materials.
Starting from the three-dimensional Cosserat elasticity, we derive a two-dimensional model for isotropic elastic shells. For the dimensional reduction, we employ a derivation method similar to that used in classical shell theory, as…
We develop a general framework based on the functional derivative to extract nonlinear dynamical response functions from the temporal evolution of physical quantities, without explicitly computing multipoint correlation functions. We…
The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling…
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…
In this paper, we derive a dimensionally reduced model for a thin film prestrained with a given incompatible Riemannian metric: $$G^h(x',x_3)=I_3+2h^{\gamma}\,S(x')+2h^{\gamma/2}\,x_3B(x')+h.o.t, \,\,\,\gamma>2,$$ where $0<h\ll 1$ is the…
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 effective elastic behavior of incompatibly prestrained plates, where the prestrain is independent of thickness as well as uniform through the thickness. We model such plates as three-dimensional elastic bodies with a prescribed…
We investigate the problem of dimension reduction for plates in nonlinear magnetoelasticity. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed set in the actual space. We consider…
We derive homogenized bending shell theories starting from three dimensional nonlinear elasticity. The original three dimensional model contains three small parameters: the two homogenization scales $\varepsilon$ and $\varepsilon^2$ of the…
The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This…
The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based…
By means of a variational approach we rigorously deduce three one-dimensional models for elastic ribbons from the theory of von K\'arm\'an plates, passing to the limit as the width of the plate goes to zero. The one-dimensional model found…
In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a…
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 consider a variational problem modeling transition between flat and wrinkled region in a thin elastic sheet, and identify the $\Gamma$-limit as the sheet thickness goes to 0, thus extending the previous work of the first author [Bella,…
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,…