A Model for Adhesive Frictional Contact

• Autorzy: Sofonea M. , Lerguet Z.
• Konferencja: French-Polish Seminar on Mechanics ; 14. ; International Conference on Modelling and Simulation of the Friction Phenomena in the Physical and Technical Systems "FRICTION 2006" ; 4. (5.06.2006 ; Warsaw, Poland)
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to present a mathematical model which describes the quasistatic process of adhesive frictional contact between a deformable body and an obstacle, the so-called foundation. The material's behavior is assumed to be elastic, with a nonlinear constitutive law; the adhesive contact is modelled with a surface variable, the bonding field, associated to the normal compliance condition and the static version of Coulomb's law of dry friction. We describe the assumptions which lead to the mathematical model of the process and derive a variational formulation of the problem; then, under a smallness assumption on the coefficient of friction, we prove the uniqueness of the solution for the model.

Słowa kluczowe

EN

applied mathematics; quantistatic contact; numerical approximation; finite element method; FEM; Coulomb's frictional law

PL

matematyka; quasistatyka; analiza numeryczna; metoda elementów skończonych; FEM; prawo Coulomba

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Problems
• Rocznik: 2006
• Tom: Vol. 30, No. 2
• Strony: 158--168
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Sofonea M.

autor

Lerguet Z.

• Universite de Perpignan, Laboratoire de Mathematiques et Physique pour les Systemes, France,

Bibliografia

• Andrews, K. T., Shillor, M., 2003, Dynamic adhesive contact of a membrane, Adv. Math. Sci. Appl, 13, 343-356.
• Chau, O., Fernandez, J. R., Shillor, M., Sofonea, M., 2003, Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion, J. Comput. Appl. Math., 159, 431-465.
• Chau, O., Shillor, M., Sofonea, M., 2004, Dynamic frictionless contact with adhesion, J. Appl. Math. Phys. (ZAMP), 55, 32-47.
• Cocou, M., Rocca, R., 2000, Existence results for unilateral quasistatic contact problems with friction and adhesion, Math. Model. Num. Anal., 34, 981-1001.
• Fernandez J. R., Shillor, M., Sofonea, M., 2003, Analysis and numerical simulations of a dynamic contact problem with adhesion, Math. Comput. Modelling, 37, 1317-1333.
• Fremond, M., 1982, Equilibre des structures qui adherent a leur support, C. R. Acad. Sci. Paris, Serie II, 295, 913-916.
• Fremond, M., 1987, Adherence des solides, J. Mecanique Theorique et Appliquee 6, 383-407.
• Fremond, M., 2002, Non-Smooth Thermomechanics, Springer, Berlin.
• Han, W., Kuttler, K. L., Shillor, M., Sofonea, M., 2002, Elastic beam in adhesive contact, Int. J. Solids Structures, 39, 1145-1164.
• Raous M., Cangemi, L., Cocou, M., 1999, A consistent model coupling adhesion, friction, and unilateral contact, Comput. Meth. Appl. Mech. Engng., 177, 383-399.
• Rojek, J., Telega, J. J., 2001, Contact problems with friction, adhesion and wear in orthopaedic biomechanics, I: General developments, J. Theor. Appl. Mech., 39, 655-677.
• Rojek, J., Telega, J. J., Stupkiewicz, S., 2001, Contact problems with friction, adhesion and wear in orthopaedic biomechanics, II: Numerical implementation and application to implanted knee joints, J. Theor. Appl. Mech., 39, 679-706.
• Shillor, M., Sofonea, M., Telega, J. J., 2004, Models and Variational Analysis of Quasistatic Contact, Lect. Notes Phys. 655, Springer, Berlin Heidelberg.
• Sofonea, M., Han, W., Shillor, M., 2006, Analysis and Approximation of Contact Problems with Adhesion or Damage, Pure and Applied Mathematics, 276, Chapman-Hall/CRC Press, New York.