Non UBC
DSpace
Giuliano Lazzaroni
2019-09-04T08:48:28Z
2019-03-07T16:08
In this talk we discuss 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 first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack 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 on a function and coincides with the variation of the jump of the displacement. Joint work with Vito Crismale and Gianluca Orlando.
https://circle.library.ubc.ca/rest/handle/2429/71595?expand=metadata
41.0 minutes
video/mp4
Author affiliation: University of Naples Federico II
Banff (Alta.)
10.14288/1.0380783
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Researcher
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Mechanics of deformable solids
Calculus of variations and optimal control; optimization
Applied mathematics
Globally stable quasistatic evolution for cohesive fracture with fatigue
Moving Image
http://hdl.handle.net/2429/71595