Related papers: Multiscale homogenization in Kirchhoff's nonlinear…
We rigorously derive a Blake-Zisserman-Kirchhoff theory for thin plates with material voids, starting from a three-dimensional model with elastic bulk and interfacial energy featuring a Willmore-type curvature penalization. The effective…
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 carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Gamma-convergence. In contrast to what one naturally would expect, our result shows that the limiting…
Thin growing tissues (such as plant leaves) can be modelled by a bounded domain $S\subset R^2$ endowed with a Riemannian metric $g$, which models the internal strains caused by the differential growth of the tissue. The elastic energy is…
The paper addresses the homogenization of a micro-model of poroelasticity coupled with thermal effects for two-constituent media and with imperfect interfacial contact.The homogenized model is obtained by means of the two-scale convergence…
We perform the periodic homogenization (i.e. $\eps\to 0$) of the non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where $\eps$ is a suitable scale parameter. The objective is to investigate the influence of…
A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined…
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 identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the…
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…
This article develops duality principles applicable to the non-linear Kirchhoff-Love model of plates. The results are obtained through standard tools of convex analysis, functional analysis, calculus of variations and duality theory. The…
In this paper, we derive a dynamic surface elasticity model for the two-dimensional midsurface of a thin, three-dimensional, homogeneous, isotropic, nonlinear gradient elastic plate of thickness $h$. The resulting model is parameterized by…
In this paper we study the effects of simultaneous homogenization and dimension reduction in the context of convergence of stationary points for thin nonhomogeneous rods under the assumption of the von K\'arm\'an scaling. Assuming…
A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element,…
We study the dimensional reduction from three to two dimensions in hyperelastic materials subject to a live load, modeled as a constant pressure force. Our results demonstrate that this loading has a significant impact in higher-order…
For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…
A thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base is considered; the diameter of $\theta_{h}$ is of the same order as the plate relative thickness $h\ll1$. In…
In this paper, we introduce a nonlocal, variational model for thin films. We consider convolution-type functionals defined on a thin domain whose thickness is of order $\gamma$, where the effective interactions range between points is of…
We study equilibrium configurations of non-Euclidean plates, in which the reference metric is uniaxially periodic. This work is motivated by recent experiments on thin sheets of composite thermally responsive gels [1]. Such sheets bend…
In the celebrated work of Friesecke, James and M\"uller '06 the authors derive a hierarchy of models for plates by carefully analyzing the $\Gamma$-convergence of the rescaled nonlinear elastic energy. The key ingredient of their proofs is…