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

Emilio Martínez Pañeda's picture

Dear iMechanicians,

I hope this paper is of interest to you. We show that quasi-Newton methods make monolithic phase field fracture implementations very robust. Convergence and computations times orders of magnitude smaller than the usual staggered approaches are demonstrated in complex problems such as unstable cracking, fatigue or dynamic crack branching.

P.K. Kristensen, E. Martínez-Pañeda. Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme. Theoretical and Applied Fracture Mechanics 107: 102446 (2020).
https://www.sciencedirect.com/science/article/pii/S0167844219305580

 

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 www.empaneda.com/codes.

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