Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach

Filippo Cagnetti; Rodica Toader

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 1, page 1-27
  • ISSN: 1292-8119

Abstract

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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. A137 (2007) 253–279] is recovered. In this case, the convergence of the discrete time approximations is improved.

How to cite

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Cagnetti, Filippo, and 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 17.1 (2011): 1-27. <http://eudml.org/doc/197293>.

@article{Cagnetti2011,
abstract = { 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. A137 (2007) 253–279] is recovered. In this case, the convergence of the discrete time approximations is improved. },
author = {Cagnetti, Filippo, Toader, Rodica},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Variational models; energy minimization; free discontinuity problems; crack propagation; Young measures; quasistatic evolution; rate-independent processes; variational models; crack propagation; rate-independent},
language = {eng},
month = {2},
number = {1},
pages = {1-27},
publisher = {EDP Sciences},
title = {Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach},
url = {http://eudml.org/doc/197293},
volume = {17},
year = {2011},
}

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
DA - 2011/2//
PB - EDP Sciences
VL - 17
IS - 1
SP - 1
EP - 27
AB - 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. A137 (2007) 253–279] is recovered. In this case, the convergence of the discrete time approximations is improved.
LA - eng
KW - Variational models; energy minimization; free discontinuity problems; crack propagation; Young measures; quasistatic evolution; rate-independent processes; variational models; crack propagation; rate-independent
UR - http://eudml.org/doc/197293
ER -

References

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  1. G.I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech.7 (1962) 55–129.  
  2. F. Cagnetti, 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.  Zbl1154.49005
  3. D.L. Cohn, Measure theory. Reprint of the 1980 original, Birkhäuser, Boston, USA (1993).  
  4. G. Dal Maso and R. Toader, A model for the quasi-static growth of brittle fractures: existence and approximation results. Arch. Ration. Mech. Anal.162 (2002) 101–135.  Zbl1042.74002
  5. G. Dal Maso and C. Zanini, Quasi-static crack growth for a cohesive zone model with prescribed crack path. Proc. Roy. Soc. Edinburgh Sect. A137 (2007) 253–279.  Zbl1116.74004
  6. G. Dal Maso, G.A. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal.176 (2005) 165–225.  Zbl1064.74150
  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. A. Mielke, Evolution of rate-independent systems, in Handbook of differential equations, evolutionary equations2, C.M. Dafermos and E. Feireisl Eds., Elsevier, Amsterdam, The Netherlands (2005) 461–559.  Zbl1120.47062
  9. J. Neveu, Discrete-Parameter Martingales. American Elsevier, Amsterdam, The Netherlands (1975).  Zbl0345.60026
  10. M. Valadier, Young measures, in Methods of nonconvex analysis (Varenna, 1989)1446, Lect. Notes Math., Springer, Berlin, Germany (1990) 152–188.  Zbl0738.28004

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