Details
| Original language | English |
|---|---|
| Article number | 112752 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 361 |
| Early online date | 30 Dec 2019 |
| Publication status | Published - 1 Apr 2020 |
Abstract
This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a two-field variational inequality system, with the phase field function and the elastic displacements of the solid material as independent variables. Using a penalization strategy, this variational inequality system is transformed into a variational equality system, which is the formulation we take as the starting point for our algorithmic developments. The proposed scheme involves a partitioning of this model into two subproblems; phase field and mechanics, with added stabilization terms to both subproblems for improved efficiency and robustness. We analyze the convergence of the proposed scheme using a fixed point argument, and find that under a natural condition, the elastic mechanical energy remains bounded, and, if the diffusive zone around crack surfaces is sufficiently thick, monotonic convergence is achieved. Finally, the proposed scheme is validated numerically with several bench-mark problems.
Keywords
- Convergence analysis, Finite element, Fracture propagation, Iterative algorithm, Linearization, Phase field
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 361, 112752, 01.04.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters
AU - Kirkesæther Brun, Mats
AU - Wick, Thomas
AU - Berre, Inga
AU - Nordbotten, Jan Martin
AU - Radu, Florin Adrian
N1 - Funding Information: This work forms part of Research Council of Norway project 250223. The authors also acknowledges the support from the University of Bergen, Norway . The first author, MKB, thanks the group ‘Wissenschaftliches Rechnen’ of the Institute of Applied Mathematics of the Leibniz University Hannover for the hospitality during his research stay from Oct–Dec 2018. The second author, TW, has been supported by the German Research Foundation , Priority Program 1748 (DFG SPP 1748) named Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis. The subproject within the SPP1748 reads Structure Preserving Adaptive Enriched Galerkin Methods for Pressure-Driven 3D Fracture Phase-Field Models (WI 4367/2-1). Funding Information: This work forms part of Research Council of Norway project 250223. The authors also acknowledges the support from the University of Bergen, Norway. The first author, MKB, thanks the group ?Wissenschaftliches Rechnen? of the Institute of Applied Mathematics of the Leibniz University Hannover for the hospitality during his research stay from Oct?Dec 2018. The second author, TW, has been supported by the German Research Foundation, Priority Program 1748 (DFG SPP 1748) named Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis. The subproject within the SPP1748 reads Structure Preserving Adaptive Enriched Galerkin Methods for Pressure-Driven 3D Fracture Phase-Field Models (WI 4367/2-1).
PY - 2020/4/1
Y1 - 2020/4/1
N2 - This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a two-field variational inequality system, with the phase field function and the elastic displacements of the solid material as independent variables. Using a penalization strategy, this variational inequality system is transformed into a variational equality system, which is the formulation we take as the starting point for our algorithmic developments. The proposed scheme involves a partitioning of this model into two subproblems; phase field and mechanics, with added stabilization terms to both subproblems for improved efficiency and robustness. We analyze the convergence of the proposed scheme using a fixed point argument, and find that under a natural condition, the elastic mechanical energy remains bounded, and, if the diffusive zone around crack surfaces is sufficiently thick, monotonic convergence is achieved. Finally, the proposed scheme is validated numerically with several bench-mark problems.
AB - This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a two-field variational inequality system, with the phase field function and the elastic displacements of the solid material as independent variables. Using a penalization strategy, this variational inequality system is transformed into a variational equality system, which is the formulation we take as the starting point for our algorithmic developments. The proposed scheme involves a partitioning of this model into two subproblems; phase field and mechanics, with added stabilization terms to both subproblems for improved efficiency and robustness. We analyze the convergence of the proposed scheme using a fixed point argument, and find that under a natural condition, the elastic mechanical energy remains bounded, and, if the diffusive zone around crack surfaces is sufficiently thick, monotonic convergence is achieved. Finally, the proposed scheme is validated numerically with several bench-mark problems.
KW - Convergence analysis
KW - Finite element
KW - Fracture propagation
KW - Iterative algorithm
KW - Linearization
KW - Phase field
UR - http://www.scopus.com/inward/record.url?scp=85077029035&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2019.112752
DO - 10.1016/j.cma.2019.112752
M3 - Article
AN - SCOPUS:85077029035
VL - 361
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 112752
ER -