The numerical modeling of fracture phenomena is of high relevance with respect to safety and durability of engineering structures. In this context, the phase field method (PFM) is a prominent approach for brittle fracture modeling. Due to its variational nature [1], it facilitates the simulation of complex fracture phenomena, such as crack branching and coalescence. As a regularized approach to crack propagation modeling, however, it is based on the use of a small length scale parameter which in turn leads to the requirement of very fine meshes. Particularly in 3D, the numerical effort associated with phase field modeling can be prohibitive. Therefore, adaptive solution schemes for phase field modeling of fracture have recently received attention.
In this contribution, an image-based scaled boundary finite element approach to three-dimensional phase field modeling will be presented, that has recently been proposed in Ref. [2]. The scaled boundary finite element method (SBFEM) is a semi-analytical technique that can be used on polyhedral elements with an arbitrary number of faces and thus facilitates numerical analyses on octree meshes. These hierarchical meshes stimulate rapid mesh size transition and lend themselves to adaptive refinement. Octree meshes can be generated and refined automatically from digital images, which is particularly advantageous for highly heterogeneous geometries [3]. In a balanced octree mesh, a limited number of unique cell configurations exist. This is exploited in the design of efficient numerical simulation techniques based on SBFEM. In addition, the SBFEM provides an energy-based error estimator, which is obtained as a result of the semi-analytical solution procedure without additional effort. In the context of phase field modeling, the latter is combined with a threshold value for the phase field variable. Following the derivation of a staggered solution scheme based on the scaled boundary finite element solutions of both the phase field equation and the balance of momentum, various examples are presented to illustrate the procedure.
References
1. C. Miehe, F. Welschinger, M. Hofacker, Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, Int J Numer Methods Eng, 83 (2010), 1273-1311.
2. R. Assaf, C. Birk, S. Natarajan, H. Gravenkamp, Three-dimensional phase-field modeling of brittle fracture using an adaptive octree-based scaled boundary finite element approach, Comput Methods Appl Mech Engrg, 399 (2022), 115364.
3. A. Saputra, H. Talebi, D. Tran, C. Birk, C. Song, Automatic image-based stress analysis by the scaled boundary finite element method, Int J Numer Methods Eng, 109 (2017), 697-738
