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On the relation between phase-field crack approximation and gradient damage modelling

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Abstract

The finite element implementation of a gradient enhanced microplane damage model is compared to a phase-field model for brittle fracture. Phase-field models and implicit gradient damage models share many similarities despite being conceived from very different standpoints. In both approaches, an additional differential equation and a length scale are introduced. However, while the phase-field method is formulated starting from the description of a crack in fracture mechanics, the gradient method starts from a continuum mechanics point of view. At first, the scope of application for both models is discussed to point out intersections. Then, the analysis of the employed mathematical methods and their rigorous comparison are presented. Finally, numerical examples are introduced to illustrate the findings of the comparison which are summarized in a conclusion at the end of the paper.

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Acknowledgements

The authors would like to acknowledge the financial support of German Research Foundation under grant KA 1163/19 and of ANSYS, Inc, Canonsburg, USA. Furthermore, we thank the Center for Information Services and High Performance Computing (ZIH) at TU Dresden for generous allocations of computer time.

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  1. Institute for Structural Analysis, Technische Universität Dresden, Dresden, Germany

    Christian Steinke, Imadeddin Zreid & Michael Kaliske

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  1. Christian Steinke
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  2. Imadeddin Zreid
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  3. Michael Kaliske
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Correspondence to Michael Kaliske.

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Steinke, C., Zreid, I. & Kaliske, M. On the relation between phase-field crack approximation and gradient damage modelling. Comput Mech 59, 717–735 (2017). https://doi.org/10.1007/s00466-016-1369-9

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