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Some variational problems for a Foppl-von Karman plate subject to general equilibrated loads are studied. The existence of global minimizers is proved under the assumption that the out-of-plane displacement fulfils homogeneous Dirichlet…

Optimization and Control · Mathematics 2018-01-17 Francesco Maddalena , Danilo Percivale , Franco Tomarelli

We show that a smooth giant voltage actuation of soft dielectric plates is not easily obtained in practice. In principle one can exploit, through pre-deformation, the snap-through behavior of their loading curve to deliver a large stretch…

Soft Condensed Matter · Physics 2018-08-01 Yipin Su , Hannah Conroy Broderick , Weiqiu Chen , Michel Destrade

We prove a compactness result with respect to $\Gamma$-convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the…

Analysis of PDEs · Mathematics 2022-12-23 Andrea Braides , Gianni Dal Maso

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 are interested in the thermal insulation of a bounded open set $\Omega$ surrounded by a set whose thickness is locally described by $\varepsilon h$, where $h$ is a non-negative function defined on the boundary $\partial\Omega$. We study…

Analysis of PDEs · Mathematics 2024-05-24 Paolo Acampora , Emanuele Cristoforoni , Carlo Nitsch , Cristina Trombetti

Periodic wrinkling of a rigid capping layer on a deformable substrate provides a useful method for templating surface topography for a variety of novel applications. Many experiments have studied wrinkle formation during the compression of…

Soft Condensed Matter · Physics 2020-04-21 John F. Niven , Gurkaran Chowdhry , James S. Sharp , Kari Dalnoki-Veress

This paper deals with the introduction of a decomposition of the deformations of curved thin beams, with section of order $\delta$, which takes into account the specific geometry of such beams. A deformation $v$ is split into an elementary…

Numerical Analysis · Mathematics 2011-09-13 Dominique Blanchard , Georges Griso

In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that the $\Gamma$-limit of suitable scaled versions of the model…

Analysis of PDEs · Mathematics 2024-07-08 Annika Bach , Marco Cicalese , Adriana Garroni , Gianluca Orlando

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…

Analysis of PDEs · Mathematics 2009-12-22 Helmut Abels , Maria Giovanna Mora , Stefan Müller

We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of $\Gamma$-convergence. Hereby, we generalize the results of the purely elastic setting [57] to a framework of free discontinuity problems. The…

Analysis of PDEs · Mathematics 2023-11-30 Manuel Friedrich , Leonard Kreutz , Konstantinos Zemas

Decay in time of undriven weakly collisional kinetic plasma turbulence in systems large compared to the ion kinetic scales is investigated using fully electromagnetic particle-in-cell simulations initiated with transverse flow and magnetic…

Plasma Physics · Physics 2015-06-16 P. Wu , M. Wan , W. H. Matthaeus , M. A. Shay , M. Swisdak

The propagation of waves in soft dielectric elastomer layers is investigated. To this end incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined. First we examine…

Soft Condensed Matter · Physics 2011-11-22 Gal Shmuel , Massimiliano Gei , Gal deBotton

We study the $\Gamma$-convergence of sequences of free discontinuity functionals with linear growth defined in the space ${\rm BD}$ of functions with bounded deformation. We prove a compactness result with respect to $\Gamma$-convergence…

Analysis of PDEs · Mathematics 2026-01-28 Gianni Dal Maso , Davide Donati

Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004), we consider a variational plate model for an elastic cone under compression in the direction of the cone symmetry axis. Assuming radial symmetry,…

Analysis of PDEs · Mathematics 2019-12-13 Sergio Conti , Heiner Olbermann , Ian Tobasco

We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite systems of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy,…

Analysis of PDEs · Mathematics 2023-05-04 Roberto Alicandro , Lucia De Luca , Mariapia Palombaro , Marcello Ponsiglione

The three-dimensional shapes of thin lamina such as leaves, flowers, feathers, wings etc, are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric, given on the…

Analysis of PDEs · Mathematics 2014-01-09 Marta Lewicka , L. Mahadevan , Mohammad Reza Pakzad

We consider sparse inhomogeneous Erd\H{o}s-R\'enyi random graph ensembles where edges are connected independently with probability $p_{ij}$. We assume that $p_{ij}= \varepsilon_N f(w_i, w_j)$ where $(w_i)_{i\ge 1}$ is a sequence of…

Probability · Mathematics 2023-12-06 Luca Avena , Rajat Subhra Hazra , Nandan Malhotra

Partial localization is the phenomenon of self-aggregation of mass into high-density structures that are thin in one direction and extended in the others. We give a detailed study of an energy functional that arises in a simplified model…

Mathematical Physics · Physics 2007-05-23 Mark A. Peletier , Matthias Roeger

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

Thin elastic sheets supported on compliant media form wrinkles under lateral compression. Since the lateral pressure is coupled to the sheet's deformation, varying it periodically in time creates a parametric excitation. We study the…

Soft Condensed Matter · Physics 2021-06-25 Haim Diamant