Displaying similar documents to “Analytical results on a model for damaging in domains and interfaces”

Analytical results on a model for damaging in domains and interfaces

Elena Bonetti, Michel Frémond (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions...

A minimum principle in the dynamics of elastic materials with voids

Michele Ciarletta, Edoardo Scarpetta (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In the context of the linear, dynamic problem for elastic bodies with voids, a minimum principle in terms of mechanical energy is stated. Involving a suitable (Reiss type) function in the minimizing functional, the minimum character achieved in the Laplace-transform domain is preserved when going back to the original time domain. Initial-boundary conditions of quite general type are considered.

Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device

Iñigo Arregui, J. Jesús Cendán, Carlos Vázquez (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The aim of this work is to deduce the existence of solution of a coupled problem arising in elastohydrodynamic lubrication. The lubricant pressure and concentration are modelled by Reynolds equation, jointly with the free-boundary Elrod-Adams model in order to take into account cavitation phenomena. The bearing deformation is solution of Koiter model for thin shells. The existence of solution to the variational problem presents some difficulties: the coupled character of the equations,...

Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part I – Model Development

D. A. Hadjiloizi, A.L. Kalamkarov, Ch. Metti, A. V. Georgiades (2014)

Curved and Layered Structures

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A comprehensive micromechanical model for the analysis of a smart composite piezo-magneto-thermoelastic thin plate with rapidly-varying thickness is developed in the present paper. A rigorous three-dimensional formulation is used as the basis of multiscale asymptotic homogenization. The asymptotic homogenization model is developed using static equilibrium equations and the quasi-static approximation of Maxwell’s equations. The work culminates in the derivation of a set of differential...

On the accuracy of Reissner–Mindlin plate model for stress boundary conditions

Sheng Zhang (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear...

A frictionless contact problem for elastic-viscoplastic materials with internal state variable

Lynda Selmani (2013)

Applicationes Mathematicae

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We study a mathematical model for frictionless contact between an elastic-viscoplastic body and a foundation. We model the material with a general elastic-viscoplastic constitutive law with internal state variable and the contact with a normal compliance condition. We derive a variational formulation of the model. We establish existence and uniqueness of a weak solution, using general results on first order nonlinear evolution equations with monotone operators and fixed point arguments....

Quasistatic frictional problems for elastic and viscoelastic materials

Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)

Applications of Mathematics

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We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution...

Unilateral contact applications using FEM software

M. Stavroulaki, G. Stavroulakis (2002)

International Journal of Applied Mathematics and Computer Science

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Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engineering applications, a rubber-coated roller contact problem and a masonry wall, solved with...

A piezoelectric contact problem with normal compliance

Mircea Sofonea, Youssef Ouafik (2005)

Applicationes Mathematicae

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We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an insulator foundation. We use a nonlinear electroelastic constitutive law to model the piezoelectric material and the normal compliance condition associated to a version of Coulomb's friction law to model the contact. We derive a variational formulation for the model which is in the form of a coupled system involving the displacement and the electric potential fields. Then...