Related papers: Multiscale homogenization in Kirchhoff's nonlinear…
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 derive, via simultaneous homogenization and dimension reduction, the Gamma-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the…
We derive a hierarchy of plate theories for heterogeneous multilayers from three dimensional nonlinear elasticity by means of $\Gamma$-convergence. We allow for layers composed of different materials whose constitutive assumptions may vary…
We rigorously derive a Kirchhoff plate theory, via $\Gamma$-convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin sheet. The heterogeneity in the elastic properties of…
This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Vel\v{c}i\'c in 2014. Thereby, a nonlinear bending energy…
We study the asymptotic behavior of thin heterogeneous elastoplastic plates in the framework of linearized elastoplasticity, focusing on the regime where the plate thickness vanishes much faster than the characteristic scale of the…
In this paper, we derive a linearized Kirchhoff model from three dimensional nonlinear elastic energy of plates with incompatible prestrain as its thickness $h$ tends to zero and its elastic energy scales like $h^{\beta}$ with $2<\beta<4.$…
This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…
In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional non-linear elasticity via homogenization and dimension reduction. We compare effective models obtained by either…
In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of thickness. We study two different cases. First, we…
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…
We use the notion of stochastic two-scale convergence to solve the problem of stochastic homogenization of the elastic plate in the bending regime.
In the framework of linearized elasticity, we study thin elastic composite plates with thickness $\delta$. The plates contain small, rigid rectangular plates distributed periodically along $\varepsilon$. Between two neighboring rigid plates…
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…
This paper focuses on the simultaneous homogenization and dimension reduction of periodic composite plates within the framework of non-linear elasticity. The composite plate in its reference (undeformed) configuration consists of a periodic…
The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication…
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…
We consider the two-dimensional Kirchhoff-Love plate equation in the context of elasticity modeling the stresses and deformations in thin plates subjected to forces and moments. We establish global recovery of the material parameters like…
The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values…
We investigate a finite element discretization of an elastic bending-plate model with an effective prestrain. The model has been obtained via homogenization and dimension reduction by B\"onlein at al. (2023). Its energy functional is the…