A 3D benchmark problem for crack propagation in brittle fracture

L. Hug*, S. Kollmannsberger, Z. Yosibash, E. Rank

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We propose a full 3D benchmark problem for brittle fracture based on experiments as well as a validation in the context of phase-field models. The example consists of a series of four-point bending tests on graphite specimens with sharp V-notches at different inclination angles. This simple setup leads to a mixed mode (I + II + III) loading which results in complex yet stably reproducible crack surfaces. The proposed problem is well suited for benchmarking numerical methods for brittle fracture and allows for a quantitative comparison of failure loads and propagation paths as well as initiation angles and the fracture surface. For evaluation of the crack surfaces image-based 3D models of the fractured specimen are provided along with experimental and numerical results. In addition, measured failure loads and computed load–displacement curves are given. To demonstrate the applicability of the benchmark problem, we show that for a phase-field model based on the Finite Cell Method and multi-level hp-refinement the complex crack surface as well as the failure loads can be well reproduced.

Original languageEnglish
Article number112905
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - 1 Jun 2020


FundersFunder number
Israel Science Foundation319 No. 964/18
Technische Universität München12.03
International Graduate School of Science and Engineering


    • Benchmark
    • Brittle fracture
    • Finite cell method
    • Multi-level hp-adaptivity
    • Phase-field modeling
    • Verification and validation


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