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Quasi-static evolution for fatigue debonding

Published online by Cambridge University Press:  20 March 2008

Alessandro Ferriero
Alessandro Ferriero*
Affiliation:
CMAP, École Polytechnique, 91128 Palaiseau, France; [email protected]
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Abstract

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

Keywords

Variational modelsquasistatic evolutionrate-independent processesfatiguefractures
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 2 , April 2008 , pp. 233 - 253
Copyright
© EDP Sciences, SMAI, 2008

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References

V. Barbu and T. Precupanu, Convexity and optimization in Banach spaces. D. Reidel Publishing Co., Dordrecht (1986).
B. Dacorogna, Direct methods in the calculus of variations. Springer-Verlag, Berlin (1989).
Dal Maso, G. and Toader, R., A model for the quasi-static evolution of brittle fractures: existence and approximation results. Arch. Rational Mech. Anal 162 (2002) 102–135. CrossRef
Dal Maso, G., Francfort, G.A. and Toader, R., Quasi-static crack growth in finite elasticity. Arch. Rational Mech. Anal 176 (2005) 165–225. CrossRef
Francfort, G.A. and Garroni, A., A variational view of partial brittle damage evolution. Arch. Rational Mech. Anal 182 (2006) 125–152. CrossRef
Francfort, G.A. and Larsen, C., Existence and convergence for quasi-static evolution in brittle fractures. Comm. Pure Applied Math 56 (2003) 1495–1500. CrossRef
Francfort, G.A. and Marigo, J.-J., Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 1319–1342. CrossRef
Francfort, G.A. and Mielke, A., Existence results for a class of rate-independent material models with nonconvex elastic energies. J. reine angew. Mathematik 595 (2006) 55–91.
A. Friedman, Variational principles and free-boundary problems. Wiley-Interscience (1982).
A. Griffith, The phenomena of rupture and flow in solids. Philos. Trans. Roy. Soc. London Ser A 221 (1920) 163–198.
Jaubert, A. and Marigo, J.-J., L'approche variationnelle de la fatigue: des premiers résultats. C. R. Mecanique 333 (2005) 550–556. CrossRef
Mumford, D. and Shah, J., Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math 42 (1989) 577–685. CrossRef
J. Neveu, Bases mathématiques du calcul des probabilités. Masson Cie, Paris (1970).
R. Wheeden and A. Zygmund, Measure and integral. Marcel Dekker (1977).