A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [G. Dal Maso and C. Zanini, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007) 253-279] is recovered. In this case, the convergence of the discrete time approximations is improved.
Mots-clés : variational models, energy minimization, free discontinuity problems, crack propagation, Young measures, quasistatic evolution, rate-independent processes
@article{COCV_2011__17_1_1_0,
author = {Cagnetti, Filippo and Toader, Rodica},
title = {Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a {Young} measures approach},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1--27},
publisher = {EDP-Sciences},
volume = {17},
number = {1},
year = {2011},
doi = {10.1051/cocv/2009037},
mrnumber = {2775184},
zbl = {1210.49046},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2009037/}
}
TY - JOUR AU - Cagnetti, Filippo AU - Toader, Rodica TI - Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 1 EP - 27 VL - 17 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009037/ DO - 10.1051/cocv/2009037 LA - en ID - COCV_2011__17_1_1_0 ER -
%0 Journal Article %A Cagnetti, Filippo %A Toader, Rodica %T Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 1-27 %V 17 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009037/ %R 10.1051/cocv/2009037 %G en %F COCV_2011__17_1_1_0
Cagnetti, Filippo; Toader, Rodica. Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 1, pp. 1-27. doi : 10.1051/cocv/2009037. http://www.numdam.org/articles/10.1051/cocv/2009037/
[1] , The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7 (1962) 55-129. | MR
[2] , A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path. Math. Models Methods Appl. Sci. 18 (2008) 1027-1071. | MR | Zbl
[3] , Measure theory. Reprint of the 1980 original, Birkhäuser, Boston, USA (1993). | MR | Zbl
[4] and , A model for the quasi-static growth of brittle fractures: existence and approximation results. Arch. Ration. Mech. Anal. 162 (2002) 101-135. | MR | Zbl
[5] and , Quasi-static crack growth for a cohesive zone model with prescribed crack path. Proc. Roy. Soc. Edinburgh Sect. A 137 (2007) 253-279. | MR | Zbl
[6] , and , Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal. 176 (2005) 165-225. | MR | Zbl
[7] and , Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 1319-1342. | MR | Zbl
[8] , Evolution of rate-independent systems, in Handbook of differential equations, evolutionary equations 2, C.M. Dafermos and E. Feireisl Eds., Elsevier, Amsterdam, The Netherlands (2005) 461-559. | MR | Zbl
[9] , Discrete-Parameter Martingales. American Elsevier, Amsterdam, The Netherlands (1975). | MR | Zbl
[10] , Young measures, in Methods of nonconvex analysis (Varenna, 1989) 1446, Lect. Notes Math., Springer, Berlin, Germany (1990) 152-188. | MR | Zbl
Cité par Sources :
