Displaying similar documents to “Spatial heterogeneity in 3D-2D dimensional reduction”

Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity

Elisa Davoli (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of -convergence, in the framework of finite plasticity. Denoting by the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order , with ≥ 3. According to the value of , partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory...

Dimension reduction for −Δ1

Maria Emilia Amendola, Giuliano Gargiulo, Elvira Zappale (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

A 3D-2D dimension reduction for −Δ is obtained. A power law approximation from −Δ as  → 1 in terms of -convergence, duality and asymptotics for least gradient functions has also been provided.

FETI-DP domain decomposition methods for elasticity with structural changes: -elasticity

Axel Klawonn, Patrizio Neff, Oliver Rheinbach, Stefanie Vanis (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor := sym ( ∇) is redefined to include a matrix valued inhomogeneity () which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field induces a structural change of the elasticity equations. For such...

A Variational Problem Modelling Behavior of Unorthodox Silicon Crystals

J. Hannon, M. Marcus, Victor J. Mizel (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical...

FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity

Axel Klawonn, Patrizio Neff, Oliver Rheinbach, Stefanie Vanis (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor := sym ( ∇) is redefined to include a matrix valued inhomogeneity () which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field induces a structural change of the elasticity equations. For...

Dimension reduction for functionals on solenoidal vector fields

Stefan Krömer (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study integral functionals constrained to divergence-free vector fields in on a thin domain, under standard -growth and coercivity assumptions, 1    ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject...

An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin, Peter Maass (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in -norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate information of smoothness/sparsity on the inhomogeneity...