A Vanishing Viscosity Approach to a Quasistatic Evolution Problem With Nonconvex Energy
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1055-1080. 
@article{AIHPC_2009__26_4_1055_0,
     author = {Fiaschi, Alice},
     title = {A {Vanishing} {Viscosity} {Approach} to a {Quasistatic} {Evolution} {Problem} {With} {Nonconvex} {Energy}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1055--1080},
     publisher = {Elsevier},
     volume = {26},
     number = {4},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.02.003},
     mrnumber = {2542714},
     zbl = {1167.74005},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2008.02.003/}
}
TY  - JOUR
AU  - Fiaschi, Alice
TI  - A Vanishing Viscosity Approach to a Quasistatic Evolution Problem With Nonconvex Energy
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 1055
EP  - 1080
VL  - 26
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2008.02.003/
DO  - 10.1016/j.anihpc.2008.02.003
LA  - en
ID  - AIHPC_2009__26_4_1055_0
ER  - 
%0 Journal Article
%A Fiaschi, Alice
%T A Vanishing Viscosity Approach to a Quasistatic Evolution Problem With Nonconvex Energy
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 1055-1080
%V 26
%N 4
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2008.02.003/
%R 10.1016/j.anihpc.2008.02.003
%G en
%F AIHPC_2009__26_4_1055_0
Fiaschi, Alice. A Vanishing Viscosity Approach to a Quasistatic Evolution Problem With Nonconvex Energy. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1055-1080. doi : 10.1016/j.anihpc.2008.02.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2008.02.003/

[1] F. Cagnetti, A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path. Math., Models Methods Appl. Sci., in press. | MR | Zbl

[2] Dal Maso G., Desimone A., Mora M. G., Quasistatic Evolution Problems for Linearly Elastic - Perfectly Plastic Materials, Arch. Ration. Mech. Anal. 180 (2006) 237-291. | MR | Zbl

[3] G. Dal Maso, A. De Simone, M.G. Mora, M. Morini, A vanishing viscosity approach to quasistatic evolution in plasticity with softening, Arch. Ration. Mech. Anal., in press.

[4] Dal Maso G., Francfort G., Toader R., Quasistatic Crack Growth in Nonlinear Elasticity, Arch. Ration. Mech. Anal. 176 (2005) 165-225. | MR | Zbl

[5] Efendiev M. A., Mielke A., On the Rate-Independent Limit of Systems With Dry Friction and Small Viscosity, J. Convex Anal. 13 (2006) 151-167. | MR | Zbl

[6] Ekeland I., Temam R., Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976, Translation of I. Ekeland, R. Temam, Analyse convexe et problèmes variationnels, Dunod, Paris, 1972. | MR | Zbl

[7] A. Fiaschi, A Young measure approach to quasistatic evolution for a class of material models with nonconvex elastic energies, ESAIM-COCV, in press. Downloadable at http://cvgmt.sns.it/people/fiaschi/. | Numdam | Zbl

[8] Francfort G., Mielke A., Existence Results for a Class of Rate-Independent Material Models With Nonconvex Elastic Energy, J. Reine Angew. Math. 595 (2006) 55-91. | MR | Zbl

[9] D. Knees, A. Mielke, C. Zanini, On the inviscid limit of a model for crack propagation, Preprint, Wias 2007, n. 1268. | MR | Zbl

[10] Kočvara M., Mielke A., Roubíček T., A Rate-Independent Approach to the Delamination Problem, Math. Mech. Solids 11 (2006) 423-447. | MR | Zbl

[11] Mielke A., Evolution of Rate-Independent Systems, in: Dafermos C. M., Feireisl E. (Eds.), Evolutionary Equations. Vol. II, Handbook of Differential Equations, Elsevier/North-Holland, Amsterdam, 2005, pp. 461-559. | MR | Zbl

[12] Mielke A., Theil F., Levitas V. I., A Variational Formulation of Rate-Independent Phase Transformations Using an Extremum Principle, Arch. Ration. Mech. Anal. 162 (2002) 137-177. | MR | Zbl

[13] Ortiz M., Repetto E., Nonconvex Energy Minimization and Dislocation Structures in Ductile Single Crystals, J. Mech. Phys. Solids 47 (2) (1999) 397-462. | MR | Zbl

[14] Rockafellar R. T., Convex Analysis, Princeton University Press, Princeton, 1970. | MR | Zbl

[15] R. Toader, C. Zanini, An artificial viscosity approach to quasistatic crack growth, Preprint, SISSA 43/2006/M. | MR | Zbl

Cité par Sources :