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Related papers: A homogenization result in finite plasticity

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We obtain a compactness result for $\Gamma$-convergence of integral functionals defined on $\mathcal{A}$-free vector fields. This is used to study homogenization problems for these functionals without periodicity assumptions. More…

Analysis of PDEs · Mathematics 2026-03-10 Gianni Dal Maso , Rita Ferreira , Irene Fonseca

We study wrinkling patterns in a thin elastic annulus subjected to radial stretching within the framework of the F\"oppl--von K\'arm\'an theory. Building on the analysis of the Lam\'e problem in Bella and Kohn, we investigate the asymptotic…

Analysis of PDEs · Mathematics 2026-05-20 Roberta Marziani

We analyse a problem of two-dimensional linearised elasticity for a two-component periodic composite, where one of the components consists of disjoint soft inclusions embedded in a rigid framework. We consider the case when the contrast…

Mathematical Physics · Physics 2018-11-06 Kirill D. Cherednichenko , James A. Evans

A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with…

Optimization and Control · Mathematics 2019-07-01 Francesco Maddalena , Danilo Percivale , Franco Tomarelli

Two classes of non-linear elastic materials are derived via two-dimensional homogenization. These materials are equivalent to a periodic grid of axially-deformable and axially-preloaded structural elements, subject to incremental…

Classical Physics · Physics 2025-03-25 Davide Bigoni , Andrea Piccolroaz

Nowadays, nonhomogeneous and periodic ferromagnetic materials are the subject of a growing interest. Actually such periodic configurations often combine the attributes of the constituent materials, while sometimes, their properties can be…

Analysis of PDEs · Mathematics 2016-02-17 François Alouges , Giovanni Di Fratta

We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…

Analysis of PDEs · Mathematics 2020-02-04 Manuel Friedrich , Francesco Solombrino

At the microscopic level, plastic flow of a jammed, disordered material consists of a series of particle rearrangements that cannot be reversed by subsequent deformation. An infinitesimal deformation of the same material has no…

Soft Condensed Matter · Physics 2014-01-22 Nathan C. Keim , Paulo E. Arratia

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 study thin films with residual strain by analyzing the $\Gamma-$limit of non-Euclidean elastic energy functionals as the material's thickness tends to $0.$ We begin by extending prior results \cite{bhattacharya2016plates}…

Analysis of PDEs · Mathematics 2022-04-26 David Padilla-Garza

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…

Analysis of PDEs · Mathematics 2025-12-02 Amartya Chakrabortty , Georges Griso , Julia Orlik

We compute the $\Gamma$-limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic membrane. We work in the regime of infinitesimal…

Analysis of PDEs · Mathematics 2017-12-08 Pierluigi Cesana , Andrés A. León Baldelli

Long range order and symmetry in heterogeneous materials architected on crystal lattices lead to elastic and inelastic anisotropies and thus limit mechanical functionalities in particular crystallographic directions. Here, we present a…

Soft Condensed Matter · Physics 2025-11-17 Jehoon Moon , Gisoo Lee , Jaehee Lee , Hansohl Cho

We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…

Analysis of PDEs · Mathematics 2019-10-02 Annika Bach , Andrea Braides , Marco Cicalese

In this paper, we deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal in exam, so that the mathematical formulation…

Mathematical Physics · Physics 2008-08-19 Adriana Garroni , Giovanni Leoni , Marcello Ponsiglione

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…

Analysis of PDEs · Mathematics 2023-01-18 Klaus Böhnlein , Stefan Neukamm , David Padilla-Garza , Oliver Sander

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

A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity…

Analysis of PDEs · Mathematics 2015-08-21 Elisa Davoli , Irene Fonseca

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are…

Mathematical Physics · Physics 2008-03-07 Lucia Scardia

We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor…

Analysis of PDEs · Mathematics 2015-05-20 Stefan Müller , Stefan Neukamm