Cohesive fracture with irreversibility: quasistatic evolution for a model subject to fatigue
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Date
2016-07-19
Journal Title
Journal ISSN
Volume Title
Publisher
SISSA
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
Description
Keywords
Fatigue, Variational models, Young measures, Quasistatic evolution,, Cohesive fracture
Citation
Preprint SISSA : 40/2016/MATE