Journal of Applied Mathematics

On the frictionless unilateral contact of two viscoelastic bodies

M. Barboteu, T.-V. Hoarau-Mantel, and M. Sofonea

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We consider a mathematical model which describes the quasistatic contact between two deformable bodies. The bodies are assumed to have a viscoelastic behavior that we model with Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the classical Signorini condition with zero-gap function. We derive a variational formulation of the problem and prove the existence of a unique weak solution to the model by using arguments of evolution equations with maximal monotone operators. We also prove that the solution converges to the solution of the corresponding elastic problem, as the viscosity tensors converge to zero. We then consider a fully discrete approximation of the problem, based on the augmented Lagrangian approach, and present numerical results of two-dimensional test problems.

Article information

J. Appl. Math., Volume 2003, Number 11 (2003), 575-603.

First available in Project Euclid: 8 December 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 74M15: Contact 74S05
Secondary: 35K85


Barboteu, M.; Hoarau-Mantel, T.-V.; Sofonea, M. On the frictionless unilateral contact of two viscoelastic bodies. J. Appl. Math. 2003 (2003), no. 11, 575--603. doi:10.1155/S1110757X03212043.

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