Speaker
Description
During the last years, the phase-field method for fracture has gained a lot of attention. It has become the most frequently used method for the simulation of quasi-static and dynamic fracture processes for brittle and ductile materials. Its biggest advantages are the simplicity of the implementation and the fact that it can capture crack propagation, branching, coalescence and initiation without the evaluation of additional criteria in a post-processing step. Despite its great success, the classical phase-field method has one severe disadvantage if standard Lagrange finite elements are employed. Due to the necessity of very fine meshes in the vicinity of an existing crack and its front, the computational effort is very high. This computational effort is further amplified by the highly nonlinear behaviour even for the simulation of linear elastic fracture mechanics processes. The extended phase-field method (XPFM) combines the phase-field method for fracture with concepts from the extended/generalized finite element method. The concept aims at a significant reduction of computational effort in comparison to the standard phase-field method while keeping the advantages of not having to explicitly track the crack geometry and introduce additional crack propagation criteria. The XPFM is based on a transformed phase-field ansatz in combination with an enriched displacement field ansatz which depends on the phase-field. In the current approach, the enrichment function of the displacement field is formulated in a discrete way which avoids the potentially difficult calculation of the crack geometry. The enrichment function is calculated by solving phase-field dependent Laplacian equations on the element level which can be done in an efficient way. In this contribution, the XPFM, its algorithmic treatment as well as its application to common academic examples is presented.
[1] Loehnert, S.; Krüger, C.; Klempt, V.; Munk, L.: An enriched phase-field method for the efficient simulation of fracture processes. Computational Mechanics, vol. 71(5), pp. 1015-1039 (2023)
[2] Krüger, C.; Curosu, V.; Loehnert, S.: An Extended Phase-Field Approach for the Efficient Simulation of Fatigue Fracture Processes. International Journal for Numerical Methods in Engineering, vol. 125, e7422
