Geodesic
Irreversible Quasistatic Evolutions by Minimizing Movements
Journal of convex analysis, Tome 15 (2008) no. 3, pp. 523-534
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We present an abstract framework for irreversible rate independent evolution processes of quasi-static nature. The main tool relies on the minimizing movement theory. In particular situations, stability and energy inequality of Mielke's type are satisfied. Several examples are given, among which the obstacle erosion. 
@article{JCA_2008_15_3_JCA_2008_15_3_a5,
     author = {D. Bucur and G. Buttazzo},
     title = {Irreversible {Quasistatic} {Evolutions} by {Minimizing} {Movements}},
     journal = {Journal of convex analysis},
     pages = {523--534},
     year = {2008},
     volume = {15},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_3_JCA_2008_15_3_a5/}
}
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D. Bucur; G. Buttazzo. Irreversible Quasistatic Evolutions by Minimizing Movements. Journal of convex analysis, Tome 15 (2008) no. 3, pp. 523-534. http://geodesic.mathdoc.fr/item/JCA_2008_15_3_JCA_2008_15_3_a5/