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

• Published in: Theoretical and applied fracture mechanics Vol. 107; p. 102446
• Main Authors: Kristensen, Philip K., Martínez-Pañeda, Emilio
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.06.2020; Elsevier BV
• Subjects: BFGS; Boundary value problems; Computer simulation; Computing costs; Convergence; Crack propagation; Fatigue cracking; Fatigue failure; Finite element analysis; Fracture; Fracture mechanics; High cycle fatigue; Phase field fracture; Quasi Newton methods; Quasi-Newton; Fracture; Finite element analysis; Quasi-Newton; Phase field fracture; BFGS
• ISSN: 0167-8442; 1872-7638
• DOI: 10.1016/j.tafmec.2019.102446

•The potential of monolithic quasi-Newton solution schemes for phase field fracture is demonstrated.•Convergence is achieved in complex problems across quasi-static fracture, phase field fatigue and dynamic cracking.•Computation times are reduced by orders of magnitude relative to staggered approaches.•Accurate phase field fatigue calculations can be obtained with only 4 increments per cycle, as opposed to the +1000 increments needed with staggered schemes.•The results could have important implications in the phase field and non-local damage communities. 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.