Computational Mechanics

, Volume 63, Issue 5, pp 1019–1046 | Cite as

A phase-field crack model based on directional stress decomposition

  • Christian Steinke
  • Michael KaliskeEmail author
Original Paper


Phase-field crack approximation relies on the proper definition of the crack driving strain energy density to govern the crack evolution and a realistic model for the modified stresses on the crack surface. A novel approach, the directional split, is introduced, analyzed and compared to the two commonly used formulations, which are the spectral split and the volumetric–deviatoric split. The directional split is based on the decomposition of the stress tensor with respect to the crack orientation, specified by a local crack coordinate system, into crack driving and persistent components. Accordingly, a modified stress strain relation is proposed to model fundamental crack characteristics properly, and a thermodynamically consistent crack driving strain energy density is postulated. The split is applied to numerical examples of initially cracked specimens and compared to results obtained by the two standard approaches.


Numerical crack approximation Brittle fracture mechanics Phase-field method Dynamic fracture 



The authors would like to acknowledge the financial support of “German Research Foundation“ under Grant KA 1163/19 and as well the technical support of the centre for information services and high performance computing of TU Dresden for providing access to the Bull HPC-Cluster.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Structural AnalysisTechnische Universität DresdenDresdenGermany

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