A phase-field crack model based on directional stress decomposition

Research paper by Christian Steinke, Michael Kaliske

Indexed on: 06 Apr '19Published on: 19 Sep '18Published in: Computational Mechanics


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.