On the relation of Gamma-convergence parameters for pressure-driven quasi-static phase-field fracture

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Leon Kolditz
  • Katrin Mang

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OriginalspracheEnglisch
Aufsatznummer100047
Seiten (von - bis)100047
Seitenumfang1
FachzeitschriftExamples and Counterexamples
Jahrgang2
Frühes Online-Datum1 Feb. 2022
PublikationsstatusVeröffentlicht - Nov. 2022

Abstract

The proof of Γ-convergence builds the base of the well-known Ambrosio–Tortorelli functional leading to an energy functional for quasi-static phase-field fracture problems. Three parameters in a monolithic quasi-static phase-field fracture model are very relevant for the quality of the results: the length-scale ε, the regularization parameter κ to avoid ill-posedness of the system and the discretization parameter h. The work on hand presents numerical results considering a pressure-driven cavity in 2d with two quantities of interest, the crack opening displacement and the total crack volume. The focus will be to discuss the assumptions of Γ-convergence which demand: h=o(κ) and κ=o(ε) and ε→0. An error analysis of the chosen quantities of interest allows to identify a proper setting for the three mentioned model parameters.

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On the relation of Gamma-convergence parameters for pressure-driven quasi-static phase-field fracture. / Kolditz, Leon; Mang, Katrin.
in: Examples and Counterexamples, Jahrgang 2, 100047, 11.2022, S. 100047.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Kolditz L, Mang K. On the relation of Gamma-convergence parameters for pressure-driven quasi-static phase-field fracture. Examples and Counterexamples. 2022 Nov;2:100047. 100047. Epub 2022 Feb 1. doi: 10.1016/j.exco.2022.100047
Kolditz, Leon ; Mang, Katrin. / On the relation of Gamma-convergence parameters for pressure-driven quasi-static phase-field fracture. in: Examples and Counterexamples. 2022 ; Jahrgang 2. S. 100047.
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