TY - JOUR

T1 - A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

AU - Heister, Timo

AU - Wheeler, Mary F.

AU - Wick, Thomas

N1 - Funding Information: The first author thanks the Center for Subsurface Modeling at ICES, UT Austin, for hosting his research stay in June 2014. Additionally, the first author is supported in part through the Computational Infrastructure in Geodynamics initiative (CIG) , through the National Science Foundation under Award No. EAR-0949446 and The University of California–Davis. The third author is grateful to the Alexander von Humboldt foundation and an ICES postdoctoral fellowship for supporting his work at ICES. This research was funded by ConocoPhillips grant UTA10-000444 , DOE grant ER25617 , Saudi Aramco grant UTA11-000320 and Statoil grant UTA13-000884 . The authors would like to express their sincere thanks for the funding. Finally, we would like to thank the reviewers for their excellent comments that allowed us to improve the paper. Publisher Copyright: © 2015 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2015/6/5

Y1 - 2015/6/5

N2 - In this paper, we consider phase-field based fracture propagation in elastic media. The main purpose is the development of a robust and efficient numerical scheme. To enforce crack irreversibility as a constraint, we use a primal-dual active set strategy, which can be identified as a semi-smooth Newton method. The active set iteration is merged with the Newton iteration for solving the fully-coupled nonlinear partial differential equation discretized using finite elements, resulting in a single, rapidly converging nonlinear scheme. It is well known that phase-field models require fine meshes to accurately capture the propagation dynamics of the crack. Because traditional estimators based on adaptive mesh refinement schemes are not appropriate, we develop a predictor-corrector scheme for local mesh adaptivity to reduce the computational cost. This method is both robust and efficient and allows us to treat temporal and spatial refinements and to study the influence of model regularization parameters. Finally, our proposed approach is substantiated with different numerical tests for crack propagation in elastic media and pressurized fracture propagation in homogeneous and heterogeneous media.

AB - In this paper, we consider phase-field based fracture propagation in elastic media. The main purpose is the development of a robust and efficient numerical scheme. To enforce crack irreversibility as a constraint, we use a primal-dual active set strategy, which can be identified as a semi-smooth Newton method. The active set iteration is merged with the Newton iteration for solving the fully-coupled nonlinear partial differential equation discretized using finite elements, resulting in a single, rapidly converging nonlinear scheme. It is well known that phase-field models require fine meshes to accurately capture the propagation dynamics of the crack. Because traditional estimators based on adaptive mesh refinement schemes are not appropriate, we develop a predictor-corrector scheme for local mesh adaptivity to reduce the computational cost. This method is both robust and efficient and allows us to treat temporal and spatial refinements and to study the influence of model regularization parameters. Finally, our proposed approach is substantiated with different numerical tests for crack propagation in elastic media and pressurized fracture propagation in homogeneous and heterogeneous media.

KW - Fracture mechanics

KW - Phase-field

KW - Predictor- corrector mesh adaptivity

KW - Primal-dual active set

UR - http://www.scopus.com/inward/record.url?scp=84927641743&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2015.03.009

DO - 10.1016/j.cma.2015.03.009

M3 - Article

AN - SCOPUS:84927641743

VL - 290

SP - 466

EP - 495

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -