Implementation aspects of a phase-field approach for brittle fracture

Abstract

This paper provides a comprehensive overview of a phase-field model of fracture in solid mechanics setting. We start reviewing the potential energy governing the whole process of fracture including crack initiation, branching or merging. Then, a discretization of system of equation is derived, in which the key aspect is that for the correctness of fracture phenomena, a split into tensile and compressive terms of the strain energy is performed, which allows crack to occur in tension, not in compression. For numerical analysis, standard finite element shape functions are used for both primary fields including displacements and phase field. A staggered scheme which solves the two fields of the problem separately is utilized for solution step and illustrated with a segment of Python code.

Keywords

phase-field modeling / FEM / staggered scheme / fracture

References

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Acknowledgement

The authors would like to thank M.Sc Hoang-Giang Bui from Institute for Structural Mechanics, Ruhr University Bochum for his support on the implementation based on the open source software—Kratos and for helpful discussions on aspects of fracture mechanics.

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2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature