A Dynamic Contact Model for Viscoelastic Plates

Sofonea, Mircea; Bartosz, Krzysztof

doi:10.1093/qjmam/hbw013

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…We also refer to Sofonea and Bartosz (2017) where the analysis of a dynamic contact problem for viscoelastic plates was provided. There, the model considered was two-dimensional and was derived from the full three-dimensional problem by using very similar arguments.…”

Section: The Modelmentioning

confidence: 99%

Modeling and simulations for quasistatic frictional contact of a linear 2D bar

Barboteu¹,

Djehaf²,

Shillor³

et al. 2017

jtam

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This work considers a mathematical model that describes quasistatic evolution of an elastic 2D bar that may come in frictional contact with a deformable foundation. We present the model and some of its underlying assumptions. In particular, the novelty in the model is that both vertical and horizontal motions are taken into account, which makes it especially useful when frictional contact is concerned. Contact is described with the normal compliance condition and friction with the Coulomb law of dry friction. We introduce a hybrid variational formulation of the problem and a numerical discretization based on a uniform time step and the finite element method in space. The numerical algorithm has been implemented, and we present computer simulations that illustrate the mechanical behavior of the system with emphasis on frictional aspects of the problem.

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Section: The Modelmentioning

confidence: 99%

Modeling and simulations for quasistatic frictional contact of a linear 2D bar

Barboteu¹,

Djehaf²,

Shillor³

et al. 2017

jtam

Self Cite

View full text Add to dashboard Cite

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A nonlinear history-dependent boundary value problem

Sofonea

Benseghir

2016

Quart. Appl. Math.

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We consider a nonlinear boundary value problem with unilateral constraints in a two-dimensional rectangle. We derive a variational formulation of the problem which is in the form of a history-dependent variational inequality. Then, we establish the existence of a unique weak solution to the problem. We also prove two convergence results. The first one provides the continuous dependence of the solution with respect to the unilateral constraint. The second one shows the convergence of the solution of the penalized problem to the solution of the original problem, as the penalization parameter converges to zero.

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A Dynamic Contact Model for Viscoelastic Plates

Cited by 2 publications

References 21 publications

Modeling and simulations for quasistatic frictional contact of a linear 2D bar

Modeling and simulations for quasistatic frictional contact of a linear 2D bar

A nonlinear history-dependent boundary value problem

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