On the use of a fourth-order degradation tensor for fracture phase-field models
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Perhaps the main hurdle of fracture phase-field models is to properly account for material degradation in multiple directions at the same time and choosing appropriate degradation functions to evolve the damage variables. We present a novel phase-field model with the introduction of a fourth-order degradation tensor that does not require a choice of degradation functions. Its components are evolved according to the strain state of the material making possible to properly account for the degradation in any direction, independently of the loading or boundary conditions. A particular irreversibility criterion is used based on the geometric average of the eigenvalues from the degraded elasticity tensor. The energy split for tension-compression asymmetry is also considered and derived considering the fourth-order degradation tensor. Consequently, it is possible to consider an anisotropic degradation both during the crack propagation or as an initial condition.
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