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Multiphase-field model of small strain elasto-plasticity according to the mechanical jump conditions

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Abstract

We introduce a small strain elasto-plastic multiphase-field model according to the mechanical jump conditions. A rate-independent \(J_2\)-plasticity model with linear isotropic hardening and without kinematic hardening is applied exemplary. Generally, any physically nonlinear mechanical model is compatible with the subsequently presented procedure. In contrast to models with interpolated material parameters, the proposed model is able to apply different nonlinear mechanical constitutive equations for each phase separately. The Hadamard compatibility condition and the static force balance are employed as homogenization approaches to calculate the phase-inherent stresses and strains. Several verification cases are discussed. The applicability of the proposed model is demonstrated by simulations of the martensitic transformation and quantitative parameters.

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Acknowledgements

We thank the Daimler AG for funding our investigations. Additionally the authors thank the German Research Foundation for funding through the graduate schools GRK 1483 and GRK 2078. Furthermore, support by the Helmholtz program RE is acknowledged. The authors gratefully acknowledge the editorial support by Leon Geisen.

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Authors and Affiliations

  1. Institute of Materials and Processes (IMP), Karlsruhe University of Applied Science, Moltkestrasse 30, 76133, Karlsruhe, Germany

    Christoph Herrmann, Ephraim Schoof, Daniel Schneider, Andreas Reiter & Britta Nestler

  2. Institute of Applied Materials (IAM-CMS), Karlsruhe Institute of Technology (KIT), Kaiserstrasse 12, 76131, Karlsruhe, Germany

    Daniel Schneider, Felix Schwab, Michael Selzer & Britta Nestler

Authors
  1. Christoph Herrmann
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  2. Ephraim Schoof
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  3. Daniel Schneider
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  4. Felix Schwab
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  5. Andreas Reiter
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  6. Michael Selzer
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  7. Britta Nestler
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Correspondence to Christoph Herrmann.

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Herrmann, C., Schoof, E., Schneider, D. et al. Multiphase-field model of small strain elasto-plasticity according to the mechanical jump conditions. Comput Mech 62, 1399–1412 (2018). https://doi.org/10.1007/s00466-018-1570-0

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  • DOI: https://doi.org/10.1007/s00466-018-1570-0

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