Computational Mechanics

, Volume 55, Issue 1, pp 27–35 | Cite as

Small strain elasto-plastic multiphase-field model

  • Daniel SchneiderEmail author
  • Stefan Schmid
  • Michael Selzer
  • Thomas Böhlke
  • Britta Nestler
Original Paper


A small strain plasticity model, based on the principles of continuum mechanics, is incorporated into a phase-field model for heterogeneous microstructures in polycrystalline and multiphase material systems (Nestler et al., Phys Rev 71:1–6, 2005). Thereby, the displacement field is computed by solving the local momentum balance dynamically (Spatschek et al., Phys Rev 75:1–14, 2007) using the finite difference method on a staggered grid. The elastic contribution is expressed as the linear approximation according to the Cauchy stress tensor. In order to calculate the plastic strain, the Prandtl–Reuss model is implemented consisting of an associated flow rule in combination with the von Mises yield criterion and a linear isotropic hardening approximation. Simulations are performed illustrating the evolution of the stress and plastic strain using a radial return mapping algorithm for single phase system and two phase microstructures. As an example for interface evolution coupling with elasto-plastic effects, we present crack propagation simulations in ductile material.


Phase-field Multiphase-field  Elasto-plasticity Crack propagation 



We thank the DFG for funding our investigations in the framework of the Research Training Group 1483. The work was further supported by the state Baden-Wuerttemberg and European Fonds for regional development with a center of excellence in Computational Materials Science and Engineering and by Helmholtz Portfolio topic ”Materials Science for Energy and its Applications in Thin Film Photovoltaics and in Energy Efficiency”.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Daniel Schneider
    • 1
    Email author
  • Stefan Schmid
    • 1
  • Michael Selzer
    • 1
    • 2
  • Thomas Böhlke
    • 3
  • Britta Nestler
    • 1
    • 2
  1. 1.Institute of Materials and ProcessesKarlsruhe University of Applied ScienceKarlsruheGermany
  2. 2.Institute of Applied Materials (IAM)Karlsruhe Institute of TechnologyKarlsruheGermany
  3. 3.Institute of Engineering Mechanics, Chair for Continuum MechanicsKarlsruhe Institute of TechnologyKarlsruheGermany

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