Geodesic
Approximation and characterization of quasi-static $H^1$-evolutions for a cohesive interface with different loading-unloading regimes
Matteo Negri1 ; Enrico Vitali1
1Università di Pavia, Italy
Interfaces and free boundaries, Tome 20 (2018) no. 1, pp. 25-67

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DOI

We consider the quasi-static evolution of a prescribed cohesive interface: dissipative under loading and elastic under unloading. We provide existence in terms of parametrized BV-evolutions, employing a discrete scheme based on local minimization, with respect to the H1-norm, of a regularized energy. Technically, the evolution is fully characterized by: equilibrium, energy balance and Karush–Kuhn–Tucker conditions for the internal variable. Catastrophic regimes (discontinuities in time) are described by gradient flows of visco-elastic type.
DOI : 10.4171/ifb/396
Classification : 49-XX, 74-XX
Mots-clés : Cohesive fracture, quasi-static propagation, BV-evolution

Matteo Negri  1   ; Enrico Vitali  1

1 Università di Pavia, Italy 
Matteo Negri; Enrico Vitali. Approximation and characterization of quasi-static $H^1$-evolutions for a cohesive interface with different loading-unloading regimes. Interfaces and free boundaries, Tome 20 (2018) no. 1, pp. 25-67. doi: 10.4171/ifb/396
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     title = {Approximation and characterization of quasi-static $H^1$-evolutions for a cohesive interface with different loading-unloading regimes},
     journal = {Interfaces and free boundaries},
     pages = {25--67},
     year = {2018},
     volume = {20},
     number = {1},
     doi = {10.4171/ifb/396},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/396/}
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