A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy

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1. [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. Zbl1154.49005MR2435184
2. [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. Zbl1093.74007MR2210910
3. [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. Zbl1219.35305
4. [4] Dal Maso G., Francfort G., Toader R., Quasistatic crack growth in nonlinear elasticity, Arch. Ration. Mech. Anal.176 (2005) 165-225. Zbl1064.74150MR2186036
5. [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. Zbl1109.74040MR2211809
6. [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. Zbl0322.90046MR463994
7. [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/. Zbl1161.74010
8. [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. Zbl1101.74015MR2244798
9. [9] D. Knees, A. Mielke, C. Zanini, On the inviscid limit of a model for crack propagation, Preprint, Wias 2007, n. 1268. Zbl1151.49014MR2446401
10. [10] Kočvara M., Mielke A., Roubíček T., A rate-independent approach to the delamination problem, Math. Mech. Solids11 (2006) 423-447. Zbl1133.74038MR2245202
11. [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. Zbl1120.47062MR2182832
12. [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. Zbl1012.74054MR1897379
13. [13] Ortiz M., Repetto E., Nonconvex energy minimization and dislocation structures in ductile single crystals, J. Mech. Phys. Solids47 (2) (1999) 397-462. Zbl0964.74012MR1674064
14. [14] Rockafellar R.T., Convex Analysis, Princeton University Press, Princeton, 1970. Zbl0193.18401MR274683
15. [15] R. Toader, C. Zanini, An artificial viscosity approach to quasistatic crack growth, Preprint, SISSA 43/2006/M. Zbl1180.35521MR2493642

1. Alexander Mielke, Riccarda Rossi, Giuseppe Savaré, BV solutions and viscosity approximations of rate-independent systems
2. Alexander Mielke, Riccarda Rossi, Giuseppe Savaré, BV solutions and viscosity approximations of rate-independent systems