Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme

Philip K. Kristensen, Emilio Martínez Pañeda*

*Corresponding author for this work

    Research output: Contribution to journalJournal articleResearchpeer-review

    179 Downloads (Pure)


    We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of quasi-static fracture, fatigue damage and dynamic cracking. The finite element results obtained reveal the robustness of quasi-Newton monolithic schemes, with convergence readily attained under both stable and unstable cracking conditions. Moreover, since the solution method is unconditionally stable, very significant computational gains are observed relative to the widely used staggered solution schemes. In addition, a new adaptive time increment scheme is presented to further reduce the computational cost while allowing to accurately resolve sudden changes in material behavior, such as unstable crack growth. Computation times can be reduced by several orders of magnitude, with the number of load increments required by the corresponding staggered solution being up to 3000 times higher. Quasi-Newton monolithic solution schemes can be a key enabler for large scale phase field fracture simulations. Implications are particularly relevant for the emerging field of phase field fatigue, as results show that staggered cycle-by-cycle calculations are prohibitive in mid or high cycle fatigue. The finite element codes are available to download from
    Original languageEnglish
    Article number102446
    JournalTheoretical and Applied Fracture Mechanics
    Number of pages13
    Publication statusPublished - 2020


    • Phase field fracture
    • Quasi-Newton
    • BFGS
    • Fractured carbonate reservoirs
    • Finite element analysis


    Dive into the research topics of 'Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme'. Together they form a unique fingerprint.

    Cite this