Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation

Prof. Thomas Wick

Oct. 10, 2017, 3:30 p.m. S2 416-1

In this presentation, the purpose is on
the development of a fully monolithic solution
algorithm for quasi-static phase-field fracture propagation. Phase-field
fracture
is a variational approach to fracture and
consists of two coupled partial differential equations and it is well known
that the underlying energy functional is non-convex and
sophisticated algorithms are required.
The incremental, spatially-discretized problem is treated with adaptive
finite elements and predictor-corrector mesh adaptivity that
allows for a very small regularization parameter in the crack region.
The nonlinear problem is solved with adaptive modified Newton algorithms,
which work as inner loop within an inexact augmented
Lagrangian iteration for relaxing
the crack irreversibility
constraint.
Specifically, the fully monolithic approach is compared to a
quasi-monolithic
approach in which phase-field is approximated through extrapolation
in the displacement equation. These comparisons are done in terms of
certain quantities of interest and computational cost.
Moreover, features such as crack nucleation,
joining, branching and fracture networks are addressed.
All findings are critically commented pointing to open questions
and future improvements.