ABSTRACT
In this paper, we review and implement the phase field model for dynamic brittle fracture at finite strains. This model approximates sharp crack discontinuities using a continuous scalar field, the so-called phase field, which represents the smooth transition between the intact and broken material phases. Furthermore, an original length-scale parameter governs the diffusive approximation of sharp cracks, while the evolution of the phase field describes the fracture process. We account for the loss of material stiffness during fracture by linking the phase field to the body’s bulk energy using a quadratic degradation function. We further apply the volumetric-deviatoric split of Amor, Marigo, & Maurini (2009) to distinguish the fracture behavior in tension, shear, and compression. The phase field model is implemented within the in-house finite element software SESKA. Herein, the phase field and displacement are computed simultaneously using the Newmark time integration. The capabilities of the model are demonstrated by solving a single-edge notched block under tension and shear. Additionally, the effect of the length-scale parameter and mesh-size dependency on the solutions is investigated. The obtained results show that the model can reproduce the propagation of cracks without any additional algorithmic treatment. They further reveal that smaller values of the length-scale converge to the sharp crack topology and yield larger failure stresses. In contrast, a large length-scale combined with a too coarse mesh-size can produce unrealistic results.
