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 -