Computational Mechanics

, Volume 62, Issue 6, pp 1399–1412 | Cite as

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

  • Christoph HerrmannEmail author
  • Ephraim Schoof
  • Daniel Schneider
  • Felix Schwab
  • Andreas Reiter
  • Michael Selzer
  • Britta Nestler
Original Paper


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.


Phase-field model Mechanical jump conditions Plasticity 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Christoph Herrmann
    • 1
    Email author
  • Ephraim Schoof
    • 1
  • Daniel Schneider
    • 1
    • 2
  • Felix Schwab
    • 2
  • Andreas Reiter
    • 1
  • Michael Selzer
    • 2
  • Britta Nestler
    • 1
    • 2
  1. 1.Institute of Materials and Processes (IMP)Karlsruhe University of Applied ScienceKarlsruheGermany
  2. 2.Institute of Applied Materials (IAM-CMS)Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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