Details
| Original language | English |
|---|---|
| Title of host publication | Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference |
| Editors | Fred J. Vermolen, Cornelis Vuik |
| Publisher | Springer Science and Business Media Deutschland GmbH |
| Pages | 1185-1193 |
| Number of pages | 9 |
| ISBN (electronic) | 978-3-030-55874-1 |
| ISBN (print) | 9783030558734 |
| Publication status | Published - 22 Aug 2020 |
| Event | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Netherlands Duration: 30 Sept 2019 → 4 Oct 2019 |
Publication series
| Name | Lecture Notes in Computational Science and Engineering |
|---|---|
| Volume | 139 |
| ISSN (Print) | 1439-7358 |
| ISSN (electronic) | 2197-7100 |
Abstract
This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a hydro-static pressure as additional unknown besides the displacement field and the phase-field variable. To fulfill the fracture irreversibility constraint, we consider a formulation as a variational inequality in the phase-field variable. For adaptive mesh refinement, we use a recently developed residual-type a posteriori error estimator for the phase-field variational inequality which is efficient and reliable, and robust with respect to the phase-field regularization parameter. The proposed model and the adaptive error-based refinement strategy are demonstrated by means of numerical tests derived from the L-shaped panel test, originally developed for concrete. Here, the Poisson’s ratio is changed from the standard setting towards the incompressible limit ν → 0.5.
Keywords
- Adaptive refinement, Error estimation, Finite elements, Incompressible solids, Mixed system, Phase-field fracture
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Computational Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. ed. / Fred J. Vermolen; Cornelis Vuik. Springer Science and Business Media Deutschland GmbH, 2020. p. 1185-1193 (Lecture Notes in Computational Science and Engineering; Vol. 139).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Adaptive Numerical Simulation of a Phase-Field Fracture Model in Mixed Form Tested on an L-shaped Specimen with High Poisson Ratios
AU - Mang, Katrin
AU - Walloth, Mirjam
AU - Wick, Thomas
AU - Wollner, Winnifried
N1 - Funding Information: Acknowledgments This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—392587580. It is part of the Priority Program 1748 (DFG SPP 1748) Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis.
PY - 2020/8/22
Y1 - 2020/8/22
N2 - This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a hydro-static pressure as additional unknown besides the displacement field and the phase-field variable. To fulfill the fracture irreversibility constraint, we consider a formulation as a variational inequality in the phase-field variable. For adaptive mesh refinement, we use a recently developed residual-type a posteriori error estimator for the phase-field variational inequality which is efficient and reliable, and robust with respect to the phase-field regularization parameter. The proposed model and the adaptive error-based refinement strategy are demonstrated by means of numerical tests derived from the L-shaped panel test, originally developed for concrete. Here, the Poisson’s ratio is changed from the standard setting towards the incompressible limit ν → 0.5.
AB - This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a hydro-static pressure as additional unknown besides the displacement field and the phase-field variable. To fulfill the fracture irreversibility constraint, we consider a formulation as a variational inequality in the phase-field variable. For adaptive mesh refinement, we use a recently developed residual-type a posteriori error estimator for the phase-field variational inequality which is efficient and reliable, and robust with respect to the phase-field regularization parameter. The proposed model and the adaptive error-based refinement strategy are demonstrated by means of numerical tests derived from the L-shaped panel test, originally developed for concrete. Here, the Poisson’s ratio is changed from the standard setting towards the incompressible limit ν → 0.5.
KW - Adaptive refinement
KW - Error estimation
KW - Finite elements
KW - Incompressible solids
KW - Mixed system
KW - Phase-field fracture
UR - http://www.scopus.com/inward/record.url?scp=85106419052&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2003.09459
DO - 10.48550/arXiv.2003.09459
M3 - Conference contribution
AN - SCOPUS:85106419052
SN - 9783030558734
T3 - Lecture Notes in Computational Science and Engineering
SP - 1185
EP - 1193
BT - Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
A2 - Vermolen, Fred J.
A2 - Vuik, Cornelis
PB - Springer Science and Business Media Deutschland GmbH
T2 - European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019
Y2 - 30 September 2019 through 4 October 2019
ER -