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Elastic interactions in phase-field crystal models: numerics and postprocessing

  • Francisco Bernal , Rainer Backofen and Axel Voigt
Published/Copyright: June 11, 2013
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 101 Issue 4

Abstract

In this paper, numerical and implementation aspects of the phase-field crystal model with elastic interactions are addressed. This model leads to a time-dependent, sixth-order system of differential equations which yields a continuous density field, from which individual atom positions can be extracted and tracked in time. We solve the system using high-order finite elements, and reconstruct the elastic properties of the crystal from the atomic displacements with a meshless interpolation scheme. Numerical simulations are performed of benchmark experiments, which include deformation and dislocation dynamics.

Keywords: PFC; Dislocations; Finite elements
* Correspondence address, Prof. Dr. Axel Voigt, TU-Dresden, Fachrichtung Mathematik, Institut für Wissenschaftliches Rechnen, D-01062 Dresden, Germany. Tel.: +49 351 463 3 41 87, Fax: +49 351 463 3 70 96. E-mail:

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Received: 2009-12-18
Accepted: 2010-1-19
Published Online: 2013-06-11
Published in Print: 2010-04-01

© 2010, Carl Hanser Verlag, München

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. Second Symposium on Phase-Field Modelling in Materials Science
  5. Basic
  6. Phase-field modeling of surface diffusion
  7. Elastic and plastic effects on solid-state transformations: A phase field study
  8. Elastic interactions in phase-field crystal models: numerics and postprocessing
  9. Phase-field modeling of solute trapping: comparative analysis of parabolic and hyperbolic models
  10. Multi-phase field study of the equilibrium state of multi-junctions
  11. Numerical study on the evolution of stress distribution in cellular microstructures
  12. Effect of surface charges on the polarization distribution in ferroelectric nanotubes
  13. Efficient and reliable finite element techniques for phase field models
  14. Applied
  15. Phase-field simulation of microstructure formation in technical magnesium alloys
  16. Phase-field modelling of gas porosity formation during the solidification of aluminium
  17. Application of the phase-field method in predicting gas bubble microstructure evolution in nuclear fuels
  18. Simulation of reaction-diffusion phenomena occurring between Ir coating and Ni–Al alloy substrate using phase-field model
  19. Phase-field simulation of γ(A1) + γ′(L12) + γ′′(D022) three-phase microstructure formation in Ni-base superalloys
  20. Phase field modelling of austenite formation from ultrafine ferrite–carbide aggregates in Fe–C
  21. Phase field simulation of austenite grain growth in the HAZ of microalloyed linepipe steel
  22. Dual-scale phase-field simulation of grain growth upon reheating of a microalloyed line pipe steel
  23. Phase field simulation of grain growth with grain boundary segregation
  24. Notification
  25. DGM News
https://doi.org/10.3139/146.110296
Keywords for this article
PFC; Dislocations; Finite elements

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. Second Symposium on Phase-Field Modelling in Materials Science
  5. Basic
  6. Phase-field modeling of surface diffusion
  7. Elastic and plastic effects on solid-state transformations: A phase field study
  8. Elastic interactions in phase-field crystal models: numerics and postprocessing
  9. Phase-field modeling of solute trapping: comparative analysis of parabolic and hyperbolic models
  10. Multi-phase field study of the equilibrium state of multi-junctions
  11. Numerical study on the evolution of stress distribution in cellular microstructures
  12. Effect of surface charges on the polarization distribution in ferroelectric nanotubes
  13. Efficient and reliable finite element techniques for phase field models
  14. Applied
  15. Phase-field simulation of microstructure formation in technical magnesium alloys
  16. Phase-field modelling of gas porosity formation during the solidification of aluminium
  17. Application of the phase-field method in predicting gas bubble microstructure evolution in nuclear fuels
  18. Simulation of reaction-diffusion phenomena occurring between Ir coating and Ni–Al alloy substrate using phase-field model
  19. Phase-field simulation of γ(A1) + γ′(L12) + γ′′(D022) three-phase microstructure formation in Ni-base superalloys
  20. Phase field modelling of austenite formation from ultrafine ferrite–carbide aggregates in Fe–C
  21. Phase field simulation of austenite grain growth in the HAZ of microalloyed linepipe steel
  22. Dual-scale phase-field simulation of grain growth upon reheating of a microalloyed line pipe steel
  23. Phase field simulation of grain growth with grain boundary segregation
  24. Notification
  25. DGM News
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