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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.…

Mathematical Physics · Physics 2021-08-23 Marco Picchi Scardaoni , Roberto Paroni

We derive, by means of Gamma-convergence, the equations of homogenized bending rod starting from $3D$ nonlinear elasticity equations. The main assumption is that the energy behaves like h^2 (after dividing by the order h^2 of vanishing…

Analysis of PDEs · Mathematics 2014-02-20 Maroje Marohnic , Igor Velcic

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…

Analysis of PDEs · Mathematics 2024-10-14 Elisa Davoli , Chiara Gavioli , Valerio Pagliari

We prove an homogenization result, in terms of $\Gamma$-convergence, for energies concentrated on rectifiable lines in $\R^3$ without boundary. The main application of our result is in the context of dislocation lines in dimension $3$. The…

Analysis of PDEs · Mathematics 2023-04-25 Martino Fortuna , Adriana Garroni

We perform a simultaneous homogenization and linearization analysis for a magnetoelastic energy functional featuring a mixed Eulerian-Lagrangian structure. Neglecting Zeeman and anisotropic contributions, we characterize the asymptotic…

Analysis of PDEs · Mathematics 2025-12-01 Mikhail Cherdantsev , Elisa Davoli , Lorenza D'Elia , Samuele Riccò

We study the homogenisation of geometrically nonlinear elastic composites with high contrast. The composites we analyse consist of a perforated matrix material, which we call the "stiff" material, and a "soft" material that fills the pores.…

Analysis of PDEs · Mathematics 2017-03-02 Mikhail Cherdantsev , Kirill Cherednichenko , Stefan Neukamm

We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior…

Mathematical Physics · Physics 2017-04-03 Francois Murat , Roberto Paroni

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…

Analysis of PDEs · Mathematics 2019-02-20 Elisa Davoli

We derive a homogenized mechanical model of a masonry-type structure constituted by a periodic assemblage of blocks with interposed mortar joints. The energy functionals in the model under investigation consist in (i) a linear elastic…

Optimization and Control · Mathematics 2019-05-20 Andrea Braides , Nicola A. Nodargi

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…

Analysis of PDEs · Mathematics 2016-04-13 Fabian Christowiak , Carolin Kreisbeck

We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…

Analysis of PDEs · Mathematics 2024-06-03 Timothy J. Healey , Gokul G. Nair

A two phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the…

Mathematical Physics · Physics 2013-04-29 Shane Cooper

Homogenization is studied for a nonlinear elliptic boundary-value problem with a large nonlinear potential. More specifically we are interested in the asymptotic behavior of a sequence of p-Laplacians of the form $$…

Analysis of PDEs · Mathematics 2012-08-16 Hermann Douanla , Nils Svanstedt

In this paper we investigate rods made of nonlinearly elastic, composite--materials that feature a micro-heterogeneous prestrain that oscillates (locally periodic) on a scale that is small compared to the length of the rod. As a main result…

Analysis of PDEs · Mathematics 2019-10-15 Robert Bauer , Stefan Neukamm , Mathias Schäffner

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…

Numerical Analysis · Mathematics 2012-10-23 Dominique Blanchard , Georges Griso

In this paper we study the homogenization of a class of energies concentrated on lines. In dimension $2$ (i.e., in codimension $1$) the problem reduces to the homogenization of partition energies studied by \cite{AB}. There, the key tool is…

Analysis of PDEs · Mathematics 2020-09-21 Adriana Garroni , Pietro Vermicelli

In this work we consider the elasticity problem for two domains separated by a heterogeneous layer. The layer has an $\varepsilon-$periodic structure, $\varepsilon\ll1$, including a multiple micro-contact between the structural components.…

Analysis of PDEs · Mathematics 2015-11-25 Georges Griso , Anastasia Migunova , Julia Orlik

We consider a thin elastic sheet in the shape of a disk whose reference metric is that of a singular cone. I.e., the reference metric is flat away from the center and has a defect there. We define a geometrically fully nonlinear free…

Analysis of PDEs · Mathematics 2016-03-23 Heiner Olbermann

This paper is devoted to study of the limiting behaviour of an elastic material with periodically distributed rigid inclusions of size {\epsilon}, as the small parameter {\epsilon} goes to zero. We address here the case with inclusions of…

Analysis of PDEs · Mathematics 2024-10-29 Lazarus Signing

The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…

Mathematical Physics · Physics 2018-11-16 Hermann Douanla , Cyrille Kenne