Details
| Original language | English |
|---|---|
| Article number | 100047 |
| Pages (from-to) | 100047 |
| Number of pages | 1 |
| Journal | Examples and Counterexamples |
| Volume | 2 |
| Early online date | 1 Feb 2022 |
| Publication status | Published - 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.
Keywords
- Bulk regularization, Error analysis, Phase-field, Pressure-driven fracture, Γ-convergence
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Mathematics (miscellaneous)
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In: Examples and Counterexamples, Vol. 2, 100047, 11.2022, p. 100047.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the relation of Gamma-convergence parameters for pressure-driven quasi-static phase-field fracture
AU - Kolditz, Leon
AU - Mang, Katrin
PY - 2022/11
Y1 - 2022/11
N2 - 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.
AB - 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.
KW - Bulk regularization
KW - Error analysis
KW - Phase-field
KW - Pressure-driven fracture
KW - Γ-convergence
UR - http://www.scopus.com/inward/record.url?scp=85163998950&partnerID=8YFLogxK
U2 - 10.1016/j.exco.2022.100047
DO - 10.1016/j.exco.2022.100047
M3 - Article
VL - 2
SP - 100047
JO - Examples and Counterexamples
JF - Examples and Counterexamples
M1 - 100047
ER -