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A Damageable Spring

Identyfikatory
Warianty tytułu
Konferencja
French-Polish Seminar of Mechanics (19 ; 8-11.06. 2011 ; Perpignan, France)
Języki publikacji
EN
Abstrakty
EN
The evolution of material damage in a nonlinear spring is modeled, analyzed, and numerically simulated. The material damage is described by a damage function whose evolution depends on the mechanical energy in the system and the damage threshold. The model is in the form of two coupled nonlinear ordinary differential equations. The existence of the unique solution is proved using arguments for evolutionary equations with maximal monotone operators, differential equations, and fixed points. The scaling properties of the model are discussed. A numerical algorithm for the problem is presented and four simulations of the system behavior depicted. In particular, the changes in the oscillations of the system as damage progresses are shown.
Rocznik
Strony
82--96
Opis fizyczny
Bibliogr. 19 poz., wykr.
Twórcy
autor
autor
autor
Bibliografia
  • Andrews, K. T., Anderson, S., Menike, R. S. R., Shillor, M., Swaminathan, R., Yuzwalk, J., 2007, Vibrations of a damageable string, in "Fluids and Waves - Recent Trends in Applied Analysis," F. Botelho, T. Hagen, and J. Jamison (Eds.), Contemporary Mathematics, 440, AMS, Rhode Island, 1-14.
  • Andrews, K. T., Fernandez, J. R., Shillor, M., 2005, Numerical analysis of dynamic thermo-viscoelastic contact with damage of a rod, IMA J. Appl. Math., 70, 768-795.
  • Andrews, K. T., Kuttler, K. L., Rochdi M., Shillor, M., 2002, One-dimensional dynamic thermoviscoelastic contact with damage, J. Math. Anal. Appl., 272, 249-275.
  • Andrews, K. T., Shillor, M., 2006, Thermomechanical behaviour of a damageable beam in contact with two stops, Applicable Analysis, 85, 845-865.
  • Barbu, V., 1976, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei, Bucharest-Noordhoflf, Leyden.
  • Bonetti, E., Fremond, M., 2003, Damage theory: microscopic effects of vanishing macroscopic motions, Comp. Appl. Math., 22, 313-333.
  • Bonetti, E., Schimperna, G., 2004, Local existence for Fremond's model of damage in elastic materials, Comp. Mech. Thermodyn,. 16, 319-335.
  • Brezis, H., 1973, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Mathematics Studies, North Holland, Amsterdam.
  • Burden, R. L., Faires, J. D., 2001, Numerical analysis (7-th edition), Brooks/Cole.
  • Edwards, C. H., Penney, D. E., 1993, Elementary Differential Equations with Boundary Value Problems (3d edition), Prentice Hall, Englewood Cliffs, New Jersey.
  • Fremond, M., 2002, Non-Smooth Thermomechanics, Springer, Berlin.
  • Kachanov, L. M., 1986, Introduction to the Theory of Damage, Martinus Nijhoff, the Hague (new revised printing 1990).
  • Kuttler, K. L., 2005, Quasistatic evolution of damage in an elastic-viscoplastic material, Electron, J. Diff. Eqns., 147, 1-25.
  • Kuttler, K. L., Shillor, M., 2006, Quasistatic Evolution of damage in an Elastic Body, Nonlinear Analysis RWA, 1, 674-699.
  • Kuttler, K. L., Shillor, M., Fernandez, J. R., 2006, Existence and regularity for dynamic viscoelastic adhesive contact with damage, Appl. Math. Optim., 53, 31-66.
  • Lemaitre, J., Chaboche, J.-L., 1990, Mechanics of Solid Materials, Cambridge University Press.
  • Maugin, G. A., 1992, The Thermomechanics of Plasticity and Fracture, Cambridge University Press.
  • Shillor, M., Sofonea, M., Telega, J. J., 2004, Models and Analysis of Quasistatic Contact, Lecture Notes in Physics, 655, Springer, Berlin.
  • 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, Boca Raton, Florida.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA0-0054-0016
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