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

top
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.

How to cite

top

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/272788>.

@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. A 137 (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; rate-independent},
language = {eng},
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/272788},
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
PY - 2011
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. A 137 (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; rate-independent
UR - http://eudml.org/doc/272788
ER -

References

top
  1. [1] G.I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech.7 (1962) 55–129. MR149728
  2. [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. Zbl1154.49005MR2435184
  3. [3] D.L. Cohn, Measure theory. Reprint of the 1980 original, Birkhäuser, Boston, USA (1993). Zbl0860.28001MR1454121
  4. [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. Zbl1042.74002MR1897378
  5. [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. Zbl1116.74004MR2360770
  6. [6] G. Dal Maso, G.A. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal.176 (2005) 165–225. Zbl1064.74150MR2186036
  7. [7] G.A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids46 (1998) 1319–1342. Zbl0966.74060MR1633984
  8. [8] A. Mielke, 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. Zbl1120.47062MR2182832
  9. [9] J. Neveu, Discrete-Parameter Martingales. American Elsevier, Amsterdam, The Netherlands (1975). Zbl0345.60026MR402915
  10. [10] M. Valadier, Young measures, in Methods of nonconvex analysis (Varenna, 1989) 1446, Lect. Notes Math., Springer, Berlin, Germany (1990) 152–188. Zbl0738.28004MR1079763

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.