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Related papers: Gamma-convergence results for nematic elastomer bi…

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We analyze the $\Gamma$-convergence of sequences of free-discontinuity functionals arising in the modeling of linear elastic solids with surface discontinuities, including phenomena as fracture, damage, or material voids. We prove…

Analysis of PDEs · Mathematics 2020-10-15 Manuel Friedrich , Matteo Perugini , Francesco Solombrino

Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In…

Soft Condensed Matter · Physics 2017-10-25 Paul Plucinsky , Marius Lemm , Kaushik Bhattacharya

The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…

Disordered Systems and Neural Networks · Physics 2020-09-29 Jishnu N. Nampoothiri , Yinqiao Wang , Kabir Ramola , Jie Zhang , Subhro Bhattacharjee , Bulbul Chakraborty

Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…

Mathematical Physics · Physics 2009-11-11 A. Majumdar , J. M. Robbins , M. Zyskin

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

In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…

Analysis of PDEs · Mathematics 2019-09-04 Fabian Christowiak , Carolin Kreisbeck

Nematic elastomers with a locked-in anisotropy direction exhibit semi-soft elastic response characterized by a plateau in the stress-strain curve in which stress does not change with strain. We calculate the global phase diagram for a…

Soft Condensed Matter · Physics 2009-11-13 Fangfu Ye , Ranjan Mukhopadhyay , Olaf Stenull , T. C. Lubensky

I put forward a continuum theory for active nematic gels, defined as fluids or suspensions of orientable rodlike objects endowed with active dynamics, that is based on symmetry arguments and compatibility with thermodynamics. The starting…

Soft Condensed Matter · Physics 2017-11-15 Stefano S Turzi

We study thermal fluctuations of a free-standing bilayer graphene subject to vanishing external tension. Within a phenomenological theory, the system is described as a stack of two continuum crystalline membranes, characterized by finite…

Mesoscale and Nanoscale Physics · Physics 2020-12-01 Achille Mauri , David Soriano , Mikhail I. Katsnelson

Reproducing the key features of fracture behavior under multiaxial stress states is essential for accurate modeling. Experimental evidence indicates that three intrinsic material properties govern fracture nucleation in elastic materials:…

Numerical Analysis · Mathematics 2025-11-04 Eleonora Maggiorelli , Matteo Negri , Francesco Vicentini , Laura De Lorenzis

We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in $\mathbb{R}^3$ equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and…

Analysis of PDEs · Mathematics 2015-09-30 Luca Lussardi , Matthias Röger

Liquid crystal elastomers (LCEs) marry the large deformation response of a cross-linked polymer network with the nematic order of liquid crystals pendent to the network. Of particular interest is the actuation of LCE sheets where the…

Soft Condensed Matter · Physics 2024-10-02 Lucas Bouck , David Padilla-Garza , Paul Plucinsky

In this paper we show the emergence of polycrystalline structures as a result of elastic energy minimisation. For this purpose, we introduce a variational model for two-dimensional systems of edge dislocations, within the so-called core…

Analysis of PDEs · Mathematics 2023-04-26 Silvio Fanzon , Mariapia Palombaro , Marcello Ponsiglione

Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales…

Analysis of PDEs · Mathematics 2008-11-17 Marta Lewicka , Maria Giovanna Mora , Mohammad Reza Pakzad

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

We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental…

Soft Condensed Matter · Physics 2018-10-04 Yipin Su , Bin Wu , Weiqiu Chen , Michel Destrade

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…

Analysis of PDEs · Mathematics 2025-07-22 Marco Bresciani , Martin Kružík

Liquid crystal elastomers realize a fascinating new form of soft matter that is a composite of a conventional crosslinked polymer gel (rubber) and a liquid crystal. These {\em solid} liquid crystal amalgams, quite similarly to their…

Soft Condensed Matter · Physics 2009-09-29 Xiangjun Xing , Leo Radzihovsky

The effect of AC electric fields on the elasticity of supported lipid bilayers has been investigated at the microscopic level using grazing incidence synchrotron x-ray scattering. A strong decrease in the membrane tension up to 1mN/m and a…

Soft Condensed Matter · Physics 2016-06-08 Arnaud Hemmerle , Thierry Charitat , Giovanna Fragneto , Jean Daillant

For a given family of smooth closed curves $\gamma^1,...,\gamma^\alpha\subset\mathbb{R}^3$ we consider the problem of finding an elastic \emph{connected} compact surface $M$ with boundary $\gamma=\gamma^1\cup...\cup\gamma^\alpha$. This is…

Optimization and Control · Mathematics 2021-09-30 Matteo Novaga , Marco Pozzetta