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Cohesive fracture with irreversibility: quasistatic evolution for a model subject to fatigue

Show simple item record Crismale, Vito Lazzaroni, Giuliano Orlando, Gianluca 2016-07-27T14:16:10Z 2016-07-27T14:16:10Z 2016-07-19
dc.identifier.citation Preprint SISSA : 40/2016/MATE en_US
dc.description.abstract In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e., a complete fracture may be produced by oscillation of small jumps. The rst step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main di culty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries Preprint SISSA;40/2016/MATE
dc.subject Fatigue en_US
dc.subject Variational models en_US
dc.subject Young measures en_US
dc.subject Quasistatic evolution, en_US
dc.subject Cohesive fracture en_US
dc.title Cohesive fracture with irreversibility: quasistatic evolution for a model subject to fatigue en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.relation.firstpage 1 en_US
dc.relation.lastpage 26 en_US

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