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Related papers: A hierarchy of multilayered plate models

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In the present work, the overall nonlinear elastic behavior of a 1D multi-modular structure incorporating possible imperfections at the discrete (micro-scale) level, is derived with respect to both tensile and compressive applied loads. The…

Soft Condensed Matter · Physics 2019-04-10 S. Palumbo , L. Deseri , D. R. Owen , M. Fraldi

We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of…

Mathematical Physics · Physics 2015-06-16 Patrizio Neff , Ionel-Dumitrel Ghiba , Angela Madeo , Luca Placidi , Giuseppe Rosi

A consistent treatment of the coupling of surface energy and elasticity within the multi-phase- field framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases…

Mesoscale and Nanoscale Physics · Physics 2018-01-17 Raphael Schiedung , Ingo Steinbach , Fathollah Varnik

In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven…

Analysis of PDEs · Mathematics 2024-01-29 Randy Llerena , Paolo Piovano

The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an…

Numerical Analysis · Mathematics 2017-03-14 David Mora , Gonzalo Rivera , Iván Velásquez

Within the linearized three-dimensional theory of polymer gels, we consider a sequence of problems formulated on a family of cylindrical domains whose height tends to zero. We assume that the fluid pressure is controlled at the top and…

Soft Condensed Matter · Physics 2017-02-14 Roberto Paroni , Giuseppe Tomassetti

In this paper, I presented the analysis and numerical results for free transverse vibration of thin rectangular plates having arbitrarily varying non-homogeneity with the in-plane coordinates along the two concurrent edges. For finding the…

Classical Physics · Physics 2018-10-16 Avinash Kumar

We consider a nonlinear, frame indifferent Griffith model for nonsimple brittle materials where the elastic energy also depends on the second gradient of the deformations. In the framework of free discontinuity and gradient discontinuity…

Analysis of PDEs · Mathematics 2019-09-25 Manuel Friedrich

We study the effective behavior of heterogeneous energies arising in the modeling of material voids in geometrically linear elastic materials. Specifically, we consider functionals featuring bulk terms depending on the symmetrized gradient…

Analysis of PDEs · Mathematics 2026-02-20 Stefano Almi , Antonio Flavio Donnarumma , Manuel Friedrich

The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…

Materials Science · Physics 2007-05-23 L. N. Maurin , I. S. Tikhomirova

Starting from three-dimensional elasticity we derive a rod theory for biphase materials with a prescribed dislocation at the interface. The stored energy density is assumed to be non-negative and to vanish on a set consisting of two copies…

Analysis of PDEs · Mathematics 2012-01-23 Stefan Müller , Mariapia Palombaro

Kinetically constrained models (KCM) are systems with trivial thermodynamics but often complex dynamical behavior due to constraints on the accessible paths followed by the system. Exploring these properties, the Kob-Andersen (KA) model was…

Soft Condensed Matter · Physics 2010-05-12 Jeferson J. Arenzon

Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived…

Soft Condensed Matter · Physics 2010-10-14 Yimin Jiang , Mario Liu

A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each…

Soft Condensed Matter · Physics 2020-12-08 Yipin Su , Ray W. Ogden , Michel Destrade

We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small…

Analysis of PDEs · Mathematics 2023-09-06 Timothy J. Healey

We prove convergence of critical points $u^h$ of the nonlinear elastic energies $E^h$ of thin incompressible plates $\Omega^h=\Omega \times (-h/2, h/2)$, which satisfy the von K\'arm\'an scaling: $E^h(u^h)\leq Ch^4$, to critical points of…

Analysis of PDEs · Mathematics 2012-11-19 Marta Lewicka , Hui Li

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the…

Mathematical Physics · Physics 2017-06-16 Giulio G. Giusteri , Luca Lussardi , Eliot Fried

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

An effective model is identified for thin perfectly plastic plates whose microstructure consists of the periodic assembling of two elastoplastic phases, as the periodicity parameter converges to zero. Assuming that the thickness of the…

Analysis of PDEs · Mathematics 2022-12-06 Marin Bužančić , Elisa Davoli , Igor Velčić

A numerical scheme is proposed to identify low energy configurations of a F\"oppl-von K\'arm\'an model for bilayer plates. The dependency of the corresponding elastic energy on the in-plane displacement $u$ and the out-of-plane deflection…

Numerical Analysis · Mathematics 2025-02-25 Sören Bartels , Bernd Schmidt , Philipp Tscherner