Quasi-static evolution for fatigue debonding
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 233-253.

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. Mecanique 333 (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.

DOI : https://doi.org/10.1051/cocv:2007046
Classification : 74R10,  49M99,  49J40
Mots clés : variational models, quasistatic evolution, rate-independent processes, fatigue, fractures
@article{COCV_2008__14_2_233_0,
     author = {Ferriero, Alessandro},
     title = {Quasi-static evolution for fatigue debonding},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {233--253},
     publisher = {EDP-Sciences},
     volume = {14},
     number = {2},
     year = {2008},
     doi = {10.1051/cocv:2007046},
     zbl = {1133.74041},
     mrnumber = {2394509},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2007046/}
}
TY  - JOUR
AU  - Ferriero, Alessandro
TI  - Quasi-static evolution for fatigue debonding
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2008
DA  - 2008///
SP  - 233
EP  - 253
VL  - 14
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2007046/
UR  - https://zbmath.org/?q=an%3A1133.74041
UR  - https://www.ams.org/mathscinet-getitem?mr=2394509
UR  - https://doi.org/10.1051/cocv:2007046
DO  - 10.1051/cocv:2007046
LA  - en
ID  - COCV_2008__14_2_233_0
ER  - 
Ferriero, Alessandro. Quasi-static evolution for fatigue debonding. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 233-253. doi : 10.1051/cocv:2007046. http://www.numdam.org/articles/10.1051/cocv:2007046/

[1] V. Barbu and T. Precupanu, Convexity and optimization in Banach spaces. D. Reidel Publishing Co., Dordrecht (1986). | MR 860772 | Zbl 0594.49001

[2] B. Dacorogna, Direct methods in the calculus of variations. Springer-Verlag, Berlin (1989). | MR 990890 | Zbl 0703.49001

[3] G. Dal Maso and R. Toader, A model for the quasi-static evolution of brittle fractures: existence and approximation results. Arch. Rational Mech. Anal 162 (2002) 102-135. | MR 1897378 | Zbl 1042.74002

[4] G. Dal Maso, G.A. Francfort and R. Toader, Quasi-static crack growth in finite elasticity. Arch. Rational Mech. Anal 176 (2005) 165-225. | MR 2186036 | Zbl 1064.74150

[5] G.A. Francfort and A. Garroni, A variational view of partial brittle damage evolution. Arch. Rational Mech. Anal 182 (2006) 125-152. | MR 2247954 | Zbl 1098.74006

[6] G.A. Francfort and C. Larsen, Existence and convergence for quasi-static evolution in brittle fractures. Comm. Pure Applied Math 56 (2003) 1495-1500. | MR 1988896 | Zbl 1068.74056

[7] G.A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 1319-1342. | MR 1633984 | Zbl 0966.74060

[8] G.A. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies. J. reine angew. Mathematik 595 (2006) 55-91. | MR 2244798 | Zbl 1101.74015

[9] A. Friedman, Variational principles and free-boundary problems. Wiley-Interscience (1982). | MR 679313 | Zbl 0564.49002

[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. Mecanique 333 (2005) 550-556.

[12] D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math 42 (1989) 577-685. | MR 997568 | Zbl 0691.49036

[13] J. Neveu, Bases mathématiques du calcul des probabilités. Masson Cie, Paris (1970). | MR 272004 | Zbl 0203.49901

[14] R. Wheeden and A. Zygmund, Measure and integral. Marcel Dekker (1977). | MR 492146 | Zbl 0362.26004

Cité par Sources :