An Artificial Viscosity Approach to Quasistatic Crack Growth

Rodica Toader; Chiara Zanini

Bollettino dell'Unione Matematica Italiana (2009)

  • Volume: 2, Issue: 1, page 1-35
  • ISSN: 0392-4041

How to cite

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Toader, Rodica, and Zanini, Chiara. "An Artificial Viscosity Approach to Quasistatic Crack Growth." Bollettino dell'Unione Matematica Italiana 2.1 (2009): 1-35. <http://eudml.org/doc/290554>.

@article{Toader2009,
author = {Toader, Rodica, Zanini, Chiara},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {1-35},
publisher = {Unione Matematica Italiana},
title = {An Artificial Viscosity Approach to Quasistatic Crack Growth},
url = {http://eudml.org/doc/290554},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Toader, Rodica
AU - Zanini, Chiara
TI - An Artificial Viscosity Approach to Quasistatic Crack Growth
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/2//
PB - Unione Matematica Italiana
VL - 2
IS - 1
SP - 1
EP - 35
LA - eng
UR - http://eudml.org/doc/290554
ER -

References

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  1. CASADO-DIAZ, J. - DAL MASO, G., A simplified model for the evolution of a fracture in a membrane, Preprint (2000). Zbl0959.49014
  2. CHAMBOLLE, A., A density result in two-dimensional linearized elasticity, and applications. Arch. Rational Mech. Anal., 167 (2003), 211-233. Zbl1030.74007MR1978582DOI10.1007/s00205-002-0240-7
  3. DAL MASO, G., FRANCFORT, G.A. AND TOADER, R., Quasistatic Crack Growth in Nonlinear Elasticity, Arch. Rational Mech. Anal., 176 (2005), 165-225. Zbl1064.74150MR2186036DOI10.1007/s00205-004-0351-4
  4. DAL MASO, G. - TOADER, R., A model for the quasi-static growth of brittle fractures: existence and approximation results, Arch. Rational Mech. Anal., 162 (2002), 101-135. Zbl1042.74002MR1897378DOI10.1007/s002050100187
  5. DAL MASO, G. - TOADER, R., A model for the quasi-static growth of brittle fractures based on local minimization, Math. Models Methods Appl. Sci., 12 (2002), 1773-1799. Zbl1205.74149MR1946723DOI10.1142/S0218202502002331
  6. DEIMLING, K., Ordinary Differential Equations in Banach Spaces. Lect. Notes Math.596, Springer-Verlag, Berlin-New York, 1977. Zbl0361.34050MR463601
  7. FRANCFORT, G.A. - LARSEN, C.J., Existence and convergence for quasi-static evolution in brittle fracture. Comm. Pure Appl. Math., 56 (2003), 1465-1500. Zbl1068.74056MR1988896DOI10.1002/cpa.3039
  8. FRANCFORT, G. A. - MARIGO, J.-J., Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46 (1998), 1319-1342. Zbl0966.74060MR1633984DOI10.1016/S0022-5096(98)00034-9
  9. FRIEDMAN, A. - HU, B. - VELAZQUEZ, J. J. L., The evolution of stress intensity factors in the propagation of two dimensional cracks, European J. Appl. Math., 11 (2000), 453-471. Zbl0969.74056MR1799921DOI10.1017/S0956792500004265
  10. GRIFFITH, A. A., The Phenomena of Rupture and Flow in Solids, Philos. Trans. R. Soc. London Ser. A, 221 (1920), 163-198. 
  11. GRISVARD, P., Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, 24. Pitman (Advanced Publishing Program), Boston, MA, 1985. Zbl0695.35060MR775683
  12. GRISVARD, P., Singularities in Boundary Value Problems, Recherches en Mathématiques Appliquées [Research in Applied Mathematics], 22. Masson, Paris; Springer-Verlag, Berlin, 1992. MR1173209
  13. HALE, J., Ordinary Differential Equations, Pure and Applied Mathematics, XXI, Krieger, Florida, 1980. MR587488
  14. KNEES, D. - MIELKE, A., Energy release rate for cracks in finite-strain elasticity. Math. Methods Applied Sciences, 31 (2008), 501-528. Zbl1132.74038MR2394124DOI10.1002/mma.922
  15. KRANTZ, S. G. - PARKS, H. R., The Implicit Function Theorem. History, theory and applications. Birkhäuser, Boston, 2002. Zbl1012.58003MR1894435DOI10.1007/978-1-4612-0059-8
  16. MIELKE, A., Evolution of Rate-Independent Systems, Handbook of Differential Equations, Evolutionary Equations, v. 2, C.M. Dafermos, E. Feireisl (eds.) 461-559Elsevier, Amsterdam, 2005. Zbl1120.47062MR2549367
  17. ZANINI, C., Variational Techniques for Quasistatic Evolutionary Models, PhD Thesis, 2006, see http://digitallibrary.sissa.it/handle/1963/1874 

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