  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 reduces 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.
