Open Access
2 December 2003 On the frictionless unilateral contact of two viscoelastic bodies
M. Barboteu, T.-V. Hoarau-Mantel, M. Sofonea
J. Appl. Math. 2003(11): 575-603 (2 December 2003). DOI: 10.1155/S1110757X03212043


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.


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M. Barboteu. T.-V. Hoarau-Mantel. M. Sofonea. "On the frictionless unilateral contact of two viscoelastic bodies." J. Appl. Math. 2003 (11) 575 - 603, 2 December 2003.


Published: 2 December 2003
First available in Project Euclid: 8 December 2003

zbMATH: 1121.74422
MathSciNet: MR2029354
Digital Object Identifier: 10.1155/S1110757X03212043

Primary: 74M15 , 74S05
Secondary: 35K85

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 11 • 2 December 2003
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