Quasi-static evolution for fatigue debonding

Alessandro Ferriero

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 2, page 233-253
  • ISSN: 1292-8119

Abstract

top
The propagation of fractures in a solid undergoing cyclic loadings is known as the fatigue phenomenon. In this paper, we present a time continuous model for fatigue, in the special situation of the debonding of thin layers, coming from a time discretized version recently proposed by Jaubert and Marigo [C. R. Mecanique333 (2005) 550–556]. Under very general assumptions on the surface energy density and on the applied displacement, we discuss the well-posedness of our problem and we give the main properties of the evolution process.

How to cite

top

Ferriero, Alessandro. "Quasi-static evolution for fatigue debonding." ESAIM: Control, Optimisation and Calculus of Variations 14.2 (2008): 233-253. <http://eudml.org/doc/250317>.

@article{Ferriero2008,
abstract = { The propagation of fractures in a solid undergoing cyclic loadings is known as the fatigue phenomenon. In this paper, we present a time continuous model for fatigue, in the special situation of the debonding of thin layers, coming from a time discretized version recently proposed by Jaubert and Marigo [C. R. Mecanique333 (2005) 550–556]. Under very general assumptions on the surface energy density and on the applied displacement, we discuss the well-posedness of our problem and we give the main properties of the evolution process. },
author = {Ferriero, Alessandro},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Variational models; quasistatic evolution; rate-independent processes; fatigue; fractures; variational models},
language = {eng},
month = {3},
number = {2},
pages = {233-253},
publisher = {EDP Sciences},
title = {Quasi-static evolution for fatigue debonding},
url = {http://eudml.org/doc/250317},
volume = {14},
year = {2008},
}

TY - JOUR
AU - Ferriero, Alessandro
TI - Quasi-static evolution for fatigue debonding
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/3//
PB - EDP Sciences
VL - 14
IS - 2
SP - 233
EP - 253
AB - The propagation of fractures in a solid undergoing cyclic loadings is known as the fatigue phenomenon. In this paper, we present a time continuous model for fatigue, in the special situation of the debonding of thin layers, coming from a time discretized version recently proposed by Jaubert and Marigo [C. R. Mecanique333 (2005) 550–556]. Under very general assumptions on the surface energy density and on the applied displacement, we discuss the well-posedness of our problem and we give the main properties of the evolution process.
LA - eng
KW - Variational models; quasistatic evolution; rate-independent processes; fatigue; fractures; variational models
UR - http://eudml.org/doc/250317
ER -

References

top
  1. V. Barbu and T. Precupanu, Convexity and optimization in Banach spaces. D. Reidel Publishing Co., Dordrecht (1986).  Zbl0594.49001
  2. B. Dacorogna, Direct methods in the calculus of variations. Springer-Verlag, Berlin (1989).  Zbl0703.49001
  3. G. Dal Maso and R. Toader, A model for the quasi-static evolution of brittle fractures: existence and approximation results. Arch. Rational Mech. Anal162 (2002) 102–135.  Zbl1042.74002
  4. G. Dal Maso, G.A. Francfort and R. Toader, Quasi-static crack growth in finite elasticity. Arch. Rational Mech. Anal176 (2005) 165–225.  Zbl1064.74150
  5. G.A. Francfort and A. Garroni, A variational view of partial brittle damage evolution. Arch. Rational Mech. Anal182 (2006) 125–152.  Zbl1098.74006
  6. G.A. Francfort and C. Larsen, Existence and convergence for quasi-static evolution in brittle fractures. Comm. Pure Applied Math56 (2003) 1495–1500.  Zbl1068.74056
  7. G.A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids46 (1998) 1319–1342.  Zbl0966.74060
  8. G.A. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies. J. reine angew. Mathematik595 (2006) 55–91.  Zbl1101.74015
  9. A. Friedman, Variational principles and free-boundary problems. Wiley-Interscience (1982).  Zbl0564.49002
  10. A. Griffith, The phenomena of rupture and flow in solids. Philos. Trans. Roy. Soc. London Ser A 221 (1920) 163–198.  
  11. A. Jaubert and J.-J. Marigo, L'approche variationnelle de la fatigue: des premiers résultats. C. R. Mecanique333 (2005) 550–556.  
  12. D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math42 (1989) 577–685.  Zbl0691.49036
  13. J. Neveu, Bases mathématiques du calcul des probabilités. Masson Cie, Paris (1970).  Zbl0203.49901
  14. R. Wheeden and A. Zygmund, Measure and integral. Marcel Dekker (1977).  Zbl0362.26004

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.