An assessment of the phase field formulation for crack growth

Markus Klinsmann*, Daniele Rosato, Marc Kamlah, Robert M. McMeeking

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

81 Citations (Scopus)


The phase field description for crack growth and fracture is an attractive alternative to numerical methods based on discrete representations of cracks, since the phase field methodology avoids the numerically challenging monitoring of the discontinuities introduced by the crack. In particular, for the simulation of complex crack growth topologies and application to coupled systems, e.g. with thermal or electrical fields, the phase field method has shown promise. However, an accurate prediction of the crack growth initiation is mandatory for a reliable simulation of crack trajectories both in terms of load history and the path followed through the material. In this work, we therefore investigate predictions of crack growth derived from the phase field method and compare them with established relations from fracture mechanics. To implement the phase field method for crack growth, a parallelized finite element method computer code using adaptive mesh refinement is developed and implemented. Results from it are presented. For these results, pre-existing cracks are introduced into the finite element model in two ways, including their representation as discrete discontinuities and as heterogeneities in the phase field order parameter.

Original languageEnglish
Pages (from-to)313-330
Number of pages18
JournalComputer Methods in Applied Mechanics and Engineering
Early online date25 Jun 2015
Publication statusPublished - 1 Sept 2015

Bibliographical note

Date of Acceptance: 15/06/2015

The presented results were mainly achieved during a visit of four months in the group of Prof. Robert McMeeking at the University of California, Santa Barbara. This stay was financially supported by a scholarship of the Karlsruhe House of Young Scientists (KHYS).


  • Energy release rate
  • Fracture
  • Initial crack modeling
  • Phase field


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