Numerical modelling of a dynamic contact problem with normal damped response and unilateral constraint

• Autorzy: Barboteu M. , Ouafik Y. , Sofonea M.

Identyfikatory

DOI

10.15632/jtam-pl.56.2.483

• Języki publikacji: EN

Abstrakty

EN

We consider a mathematical model which describes the dynamic evolution of a viscoelastic body in frictional contact with an obstacle. The contact is modelled with normal damped response and unilateral constraint for the velocity field, associated to a version of Coulomb’s law of dry friction. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we use a penalty method to approximate the constraint. Then, we provide numerical simulations in the study of a two-dimensional example and compare the penalty model with the original one.

Słowa kluczowe

EN

dynamic contact; viscoelastic material; frictional contact; normal damped response; unilateral constraint; penalty method; numerical simulations

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2018
• Tom: Vol. 56 nr 2
• Strony: 483--496
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Barboteu M.

• Laboratoire de Math´ematiques et Physique, University of Perpignan Via Domitia, Perpignan, France

autor

Ouafik Y.

• Universit´e Cadi Ayyad, ENSA Safi, Maroc

autor

Sofonea M.

• Laboratoire de Math´ematiques et Physique, University of Perpignan Via Domitia, Perpignan, France

Bibliografia

• 1. Alart P., Curnier A., 1991, A mixed formulation for frictional contact problems prone to Newton like solution methods, Computer Methods in Applied Mechanics and Engineering, 92, 3, 353-375
• 2. Barboteu M., Bartosz K., Kalita P., 2015, A dynamic viscoelastic contact problem with normal compliance, finite penetration and nonmonotone slip rate dependent friction, Nonlinear Analysis: Real World Applications, 22, 452-472
• 3. Barboteu M., Cheng X.L., Sofonea M., 2016a, Analysis of a contact problem with unilateral constraint and slip-dependent friction, Mathematics and Mechanics of Solids, 21, 791-811
• 4. Barboteu M., Danan D., 2016, Analysis of a dynamic viscoelastic contact problem with normal compliance, normal damped response, and nonmonotone slip rate dependent friction, Advances in Mathematical Physics, 2016, http://dx.doi.org/10.1155/2016/1562509
• 5. Barboteu M., Danan D., Sofonea M., 2016b, Analysis of a contact problem with normal damped response and unilateral constraint, Zeitschrift f¨ur Angewandte Mathematik and Mechanik, 96, 408-428
• 6. Chouly F., Hild P., 2013, On convergence of the penalty method for unilateral contact problems, Applied Numerical Mathematics, 65, 27-40
• 7. Duvaut G., Lions J.L., 1976, Inequalities in Mechanics and Physics, Springer Verlag, Berlin
• 8. Han J., Migórski S., Zeng H., 2016, Analysis of a dynamic viscoelastic unilateral contact problem with normal damped response, Nonlinear Analysis: Real World Applications, 28, 229-250
• 9. Han W., Shillor M., Sofonea M., 2001, Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage, Journal of Computational and Applied Mathematics, 137, 377-398
• 10. Han W., Sofonea M., 2002, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, American Mathematical Society-International Press
• 11. Hlavacek I., Haslinger J., Necas J., Lov isek J., 1988, Solution of Variational Inequalities in Mechanics, Springer, New York, NY, USA.
• 12. Khenous H.B., Laborde P., Renard Y., 2006, On the discretization of contact problems in elastodynamics, [In:] Analysis and Simulation of Contact Problems, 27, 31-38, Lecture Notes in Applied and Computational Mechanics, Springer, Berlin, Germany
• 13. Kikuchi N., Song Y., 1981, Penalty finite element approximations of a class of unilateral problems in linear elasticity, Quarterly of Applied Mechanics, 39, 1-21
• 14. Laursen T.A., 2002, Computational Contact and Impact Mechanics, Springer, Berline, Germany
• 15. Oden J.T., Martins J.A.C., 1985, Models and computational methods for dynamic friction phenomena, Computer Methods in Applied Mechanics and Engineering, 52, 527-634
• 16. Shillor M., Sofonea M., Telega J., 2004, Models and Variational Analysis of Quasistatic Contact, 655, Lecture Notes in Physics, Springer, Berlin, Germany
• 17. Sofonea M., Matei A., 2012, Mathematical Models in Contact Mechanics, 398, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge
• 18. Wriggers P., 2002, Computational Contact Mechanics, John Wiley & Sons, Chichester, UK

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).