A numerical implementation of the length-scale independent phase field method


The phase field method for fracture integrates the Griffith theory and damage mechanics approach to predict crack initiation and propagation within one framework. It replaced the discrete representation of crack by diffusive damage and solved it based on a minimization of the global energy storage functional. As a result, no crack tracking topology is needed, and complex crack shapes can be captures without user intervention. However, it is also reported to have an inconsistency between the predicted fracture toughness and the material strength. Recently, a novel energetic degradation function was proposed in literature to handle this issue. This research does some further modifications to the global energy storage functional so that Newton's method can be directly used to solve the energy minimization. With the new energy form, direct implementation of the length-scale independent phase field method into finite element packages like LS-DYNA becomes possible. This paper presents the framework and details of implementing the length-scale independent phase field method into LS-DYNA through a user-defined element and material subroutine. Several numerical examples are presented to compare with the experiment crack shape. Most importantly, this paper is one of the first ones to quantitatively predict accurate force response compared to experiments. These examples verify the accuracy of the new energy form and implementation.

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Correspondence to Wenlong Zhang.

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Zhang, W., Tabiei, A. & French, D. A numerical implementation of the length-scale independent phase field method. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-020-01027-1

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  • Phase field method
  • Length-scale independency
  • Newton’s method