MENU

You are here

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

TitleCohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue
Publication TypeJournal Article
Year of Publication2018
AuthorsCrismale, V, Lazzaroni, G, Orlando, G
JournalMathematical Models and Methods in Applied Sciences
Volume28
Pagination1371-1412
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 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 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 on a function and coincides with the variation of the jump of the displacement.

URLhttps://doi.org/10.1142/S0218202518500379
DOI10.1142/S0218202518500379

Sign in