Efficient phase-field fracture simulations for fracture analysis in heterogeneous materials

Abstract:

(from [1])

Fracture in heterogeneous materials with complex microstructures poses significant challenges due to the intricate interactions between material heterogeneities and crack propagation. The phase-field method for brittle fracture has emerged as a particularly suitable and powerful simulation technique for addressing these challenges, offering a robust framework for capturing complex crack paths, branching, and coalescence of multiple cracks. The method, however, has notable drawbacks that can hinder its application to real-world simulations. Key limitations include its computationally intensive nature, driven by the need for fine spatial discretizations to resolve the smeared crack phase-field, small time step sizes for accurate crack detection, and slow convergence of staggered solution schemes during critical load steps. These challenges are addressed by proposing a combination of three complementary techniques to enhance both the performance and robustness of the phase-field fracture simulations: adaptive spatial refinement to focus computational effort near fractures, physically motivated convergence criterion to improve solver efficiency, and adaptive temporal refinement and coarsening to optimize time step sizes dynamically. The goal is to achieve efficient simulations without compromising physical accuracy, enabling reliable fracture modeling in heterogeneous microstructures. This study investigates the elastic and fracture responses of materials with varying microscopic properties, such as filler volume fraction and inclusion sizes.

Contact:

Maurice Rohracker

Institute of Applied Mechanics

Friedrich-Alexander-Universität Erlangen-Nürnberg

Egerlandstr. 5

91058 Erlangen

Software:

All phase-field fracture simulations were performed with deal.II [2], version 9.2.0, on the HPC cluster Fritz of NHR@FAU. The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU). The hardware is funded by the German Research Foundation (DFG).

License:

Creative Commons Attribution 4.0 International

Context:

Dataset supplementing published article:

[1] M.Rohracker, P.Kumar, P.Steinmann, J.Mergheim, "Efficient phase-field fracture simulations for fracture analysis in heterogeneous materials", Computational Mechanics, 2025, 10.1007/s00466-025-02685-3

This dataset contains the complete results presented in [1], which include global variables, field variables, and meshes.

File structure:

The file structure is explained in more detail in the shipped README.md in the dataset folder.

References:

[1] M.Rohracker, P.Kumar, P.Steinmann, J.Mergheim, "Efficient phase-field fracture simulations for fracture analysis in heterogeneous materials", Computational Mechanics, 2025, 10.1007/s00466-025-02685-3

[2] D. Arndt, W. Bangerth, B. Blais, T. C. Clevenger, M. Fehling, A. V. Grayver, T. Heister, L. Heltai, M. Kronbichler, M. Maier, P. Munch, J.-P. Pelteret, R. Rastak, I. Thomas, B. Turcksin, Z. Wang, D. Wells, The deal.II Library, Version 9.2 Journal of Numerical Mathematics, vol. 28, p. 131-146, 2020.