Spectral Solvers for Crystal Plasticity and Multi-physics Simulations

  • Pratheek ShanthrajEmail author
  • Martin Diehl
  • Philip Eisenlohr
  • Franz Roters
  • Dierk Raabe
Living reference work entry

Later version available View entry history


The local and global behavior of materials with internal microstructures is often investigated on a (representative) volume element. Typically, periodic boundary conditions are applied on such “virtual specimens” to mimic the situation in the bulk of the material. While, in general, different types of boundary value solvers can be used to solve for mechanical equilibrium, spectral methods have been established as a powerful numerical tool especially suited for this task [for application examples see 1–7]. Starting from the pioneering work of Moulinec and Suquet [8], several improvements in performance and stability have been achieved for solving mechanical boundary value problems [9–13]. Recent advancements of using the spectral approach to solve coupled field equations enable the modeling of multiphysical phenomena such as fracture propagation, temperature evolution, chemical diffusion, and phase transformation in conjunction with the mechanical boundary value problem. The fundamentals of such a multi-physics framework, which is implemented in the Düsseldorf Advanced Materials Simulation Kit (DAMASK) [14, 57] are presented in the following together with implementation details and illustrative examples.



PS and FR acknowledge funding through SFB 761 Steel – ab initio by the Deutsche Forschungsgemeinschaft (DFG). MD acknowledges the funding of the TCMPrecipSteel project in the framework of the SPP 1713 Strong coupling of thermo-chemical and thermo-mechanical states in applied materials by the DFG.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Pratheek Shanthraj
    • 1
    • 3
    Email author
  • Martin Diehl
    • 1
  • Philip Eisenlohr
    • 2
  • Franz Roters
    • 1
  • Dierk Raabe
    • 1
  1. 1.Max-Planck-Institut für Eisenforschung GmbHDüsseldorfGermany
  2. 2.Chemical Engineering and Materials ScienceMichigan State UniversityEast LansingUSA
  3. 3.The School of MaterialsThe University of ManchesterManchesterUK

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