A Dynamic Piezoelectric Contact Problem

• Autorzy: Barboteu M. , Sofonea M.
• Konferencja: International Conference on Modelling and Simulation of the Friction Phenomena in the Physical and Technical Systems "FRICTION 2008" (5 ; 31.05-1.06.2008 ; Warsaw, Poland) ; French-Polish Seminar of Mechanics (16 ; 31.05-1.06.2008 ; Warsaw, Poland)
• Języki publikacji: EN

Abstrakty

EN

We consider a mathematical model, which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. The material's behavior is modeled with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We state the variational formulation for the problem, and then we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of a two-dimensional test problem.

Słowa kluczowe

EN

piezoelectric structure; piezoelectrics; viscoplasticity; numerical approximation; discrete approximation; numerical simulatios; electrical conductivity; finite element method; FEM; mathematical model

PL

struktura piezoelektryczna; piezoelektryki; lepkoplastyczność; dyskretna aproksymacja; symulacja numeryczna; przewodnictwo elektryczne; metoda elementów skończonych; MES (metoda elementów skończonych); model matematyczny

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Problems
• Rocznik: 2008
• Tom: Vol. 32, No. 1
• Strony: 23--32
• Opis fizyczny: Bibliogr. 12 poz., wykr.

Twórcy

autor

Barboteu M.

autor

Sofonea M.

• Université de Perpignan, Laboratoire de Mathematiques, Physique et Systemes, France,

Bibliografia

• Alart, P., Curnier, A., 1991, A mixed formulation for frictional contact problems prone to Newton like solution methods, Comput. Methods Appl. Mech. Engrg, 92, 353-375.
• Barboteu, M., Sofonea, M., Solvability of a dynamic contact problem between a piezoelectric body and a conductive foundation, submitted to Applied Mathematics and Computation.
• Batra, R.C., Yang, J.S., 1995, Saint-Venant's principle in linear piezoelectricity, Journal of' Elasticity, 38, 209-218.
• Bisegna, P., Lebon, F., Maceri, F., 2002, The unilateral frictional contact of a piezoelectric body with a rigid support, in Contact Mechanics, J.A.C. Martins and Manuel D.P. Monteiro Marques (Eds.), Kluwer, Dordrecht, 347-354.
• Han, W., Sofonea, M., 2002, Quasistatic Contact Problems in Yiscoelasticity and Viscoplasticity, Studies in Advanced Mathematics, 30, American Mathematical Society, Providence, RI- Intl. Press, Sommerville, MA.
• Lerguet, Z., Shillor, M., Sofonea, M., 2007, A frictional contact problem for an electro-viscoelastic body, Electronic Journal of Differential Equations, paper 170, 1-16.
• Maceri, F., Bisegna, P., 1998, The unilateral frictionless contact of a piezoelectric body with a rigid support, Mathematical and Computer Modelling, 28, 19-28.
• Martins, J.A.C., Odeń, J.T., 1987, Existence and uniqueness results for dynamic contact problems with non-linear normal and friction interface laws, Non-linear Analysis TAM, 11, 407-428.
• Minors, S., 2006, Hemivariational inequality for a frictional contact problem in elasto-piezoelectricity, Discrete and Continuous Dynamical Systems - Series B, 6, 1339-1356.
• Patron V.Z., Kudryavtsev, B.A., 1988, Electromagnetoelasticity, Piezoelectrics and Electrically Conductive Solids, Gordon & Breach, London.
• Shillor, M., Sofonea, M., Telega, J.J., 2004, Models and Variational Analysis of Quasistatic Contact, Lect. Notes Phys., 655, Springer, Berlin Heidelberg.
• Sofonea, M., Essoufl, El H., 2004, Quasistatic frictional contact of a viscoelastic piezoelectric body, Adv. Math. Sci. Appl., 14, 613-631.