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Advanced Methods of Continuum Mechanics for Materials and Structures pp 307–324Cite as

Phase-Field Modelling of Damage and Fracture—Convergence and Local Mesh Refinement

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 60))

Abstract

In this contribution, we outline the combination of a phase-field model of brittle fracture with adaptive spline-based approximations. The phase-field method provides a convenient way to model crack propagation without topological updates of the used discretisation as the crack is represented implicitly in terms of an order parameter field that can be interpreted as damage variable. For the accurate approximation of the order parameter field that may exhibit steep gradients, we utilise locally refined hierarchical B-splines in conjunction with Bézier extraction. The latter allows for the implementation of the approach in any standard finite element code. Moreover, standard procedures of adaptive finite element analysis for error estimation and marking of elements are directly applicable due to the strict use of an element viewpoint. Two different demonstration problems are considered. At first we examine the convergence properties of the phase-field approach and explain the influence of the domain size and the discretisation for the one-dimensional problem of a bar. Afterwards, results of the adaptive local refinement are compared with uniformly refined Lagrangian and spline-based discretisations. In the second example, the developed algorithms are applied to simulate crack propagation in a two-dimensional single-edge notched, shear loaded plate.

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Acknowledgments

The authors gratefully acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) in the Priority Programme 1748 “Reliable simulation techniques in solid mechanics. Development of non-standard discretization methods, mechanical and mathematical analysis” under the project KA3309/3-1.

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Authors and Affiliations

  1. Institute of Solid Mechanics, Technische Universität Dresden, 01062, Dresden, Germany

    Markus Kästner, Paul Hennig, Thomas Linse & Volker Ulbricht

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  1. Markus Kästner
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  2. Paul Hennig
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  3. Thomas Linse
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  4. Volker Ulbricht
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Correspondence to Markus Kästner .

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Editors and Affiliations

  1. Institute of Mechanics IFME, Otto von Guericke University, Magdeburg, Sachsen-Anhalt, Germany

    Konstantin Naumenko

  2. Otto von Guericke University, Institute of Mechanics, Magdeburg, Germany

    Marcus Aßmus

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Kästner, M., Hennig, P., Linse, T., Ulbricht, V. (2016). Phase-Field Modelling of Damage and Fracture—Convergence and Local Mesh Refinement. In: Naumenko, K., Aßmus, M. (eds) Advanced Methods of Continuum Mechanics for Materials and Structures. Advanced Structured Materials, vol 60. Springer, Singapore. https://doi.org/10.1007/978-981-10-0959-4_17

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  • DOI: https://doi.org/10.1007/978-981-10-0959-4_17

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-0958-7

  • Online ISBN: 978-981-10-0959-4

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