相关论文: Effective theories for incompressible magnetoelast…
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…
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 use variational convergence to derive a hierarchy of one-dimensional rod theories, starting out from three-dimensional models in nonlinear elasticity subject to local volume-preservation. The densities of the resulting $\Gamma$-limits…
Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
In this paper we derive, by means of $\Gamma$-convergence, the shallow shell models starting from non linear three dimensional elasticity. We use the approach analogous to the one for shells and plates. We start from the minimization…
A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical fields are generalised to the magnetic variables to derive a…
We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference…
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 develop a reduced model for hard-magnetic, thin, linear-elastic shells that can be actuated through an external magnetic field, with geometrically exact strain measures. Assuming a reduced kinematics based on the Kirchhoff-Love…
Starting from the three-dimensional setting, we derive a limit model of a thin magnetoelastic film by means of {\Gamma}-convergence techniques. As magnetization vectors are defined on the elastically deformed configuration, our model…
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…
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…
This paper studies a nonlinear shallow shell model proposed by Donnell, Vlasov, Mushtari, Galimov, and Koiter. More specifically, we address the question concerning the asymptotic behavior of minimizing solutions. Our result can be applied…
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…
This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an…
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 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…
In this paper a we derive by means of $\Gamma$-convergence a macroscopic strain-gradient plasticity from a semi-discrete model for dislocations in an infinite cylindrical crystal. In contrast to existing work, we consider an energy with…
An asymptotically exact two-dimensional theory of elastic-piezoceramic sandwich shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application,…