A Variational Model for Quasistatic Crack Growth in Nonlinear Elasticity: Some Qualitative Properties of the Solutions

Gianni Dal Maso; Alessandro Giacomini; Marcello Ponsiglione

Bollettino dell'Unione Matematica Italiana (2009)

  • Volume: 2, Issue: 2, page 371-390
  • ISSN: 0392-4041

Abstract

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We present the main existence result for quasistatic crack growth in the model proposed by Dal Maso, Francfort, and Toader, and prove some qualitative properties of the solutions.

How to cite

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Dal Maso, Gianni, Giacomini, Alessandro, and Ponsiglione, Marcello. "A Variational Model for Quasistatic Crack Growth in Nonlinear Elasticity: Some Qualitative Properties of the Solutions." Bollettino dell'Unione Matematica Italiana 2.2 (2009): 371-390. <http://eudml.org/doc/290560>.

@article{DalMaso2009,
abstract = {We present the main existence result for quasistatic crack growth in the model proposed by Dal Maso, Francfort, and Toader, and prove some qualitative properties of the solutions.},
author = {Dal Maso, Gianni, Giacomini, Alessandro, Ponsiglione, Marcello},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {371-390},
publisher = {Unione Matematica Italiana},
title = {A Variational Model for Quasistatic Crack Growth in Nonlinear Elasticity: Some Qualitative Properties of the Solutions},
url = {http://eudml.org/doc/290560},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Dal Maso, Gianni
AU - Giacomini, Alessandro
AU - Ponsiglione, Marcello
TI - A Variational Model for Quasistatic Crack Growth in Nonlinear Elasticity: Some Qualitative Properties of the Solutions
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/6//
PB - Unione Matematica Italiana
VL - 2
IS - 2
SP - 371
EP - 390
AB - We present the main existence result for quasistatic crack growth in the model proposed by Dal Maso, Francfort, and Toader, and prove some qualitative properties of the solutions.
LA - eng
UR - http://eudml.org/doc/290560
ER -

References

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  2. BREZIS, H., Convergence in 𝒟 ′ and in L 1 under strict convexity. Boundary value problems for partial differential equations and applications, 43-52, RMA Res. Notes Appl. Math., 29, Masson, Paris, 1993. Zbl0813.49016MR1260437
  3. CASTAING, C. - VALADIER, M., Convex analysis and measurable multifunctions. Lecture Notes in Mathematics, Vol. 580, Springer-Verlag, Berlin-New York, 1977. Zbl0346.46038MR467310
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  10. FRANCFORT, G. A. - LARSEN, C. J., Existence and convergence for quasistatic evolution in brittle fracture. Comm. Pure Appl. Math., 56 (2003), 1465-1500. Zbl1068.74056MR1988896DOI10.1002/cpa.3039
  11. FRANCFORT, G. A. - MARIGO, J.-J., Revisiting brittle fractures as an energy minimization problem. J. Mech. Phys. Solids, 46 (1998), 1319-1342. Zbl0966.74060MR1633984DOI10.1016/S0022-5096(98)00034-9
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