![13th World Congress on Computational Mechanics (WCCM XIII)
2nd Pan American Congress on Computational Mechanics (PANACM II)
July 22-27, 2018, New York, NY, USA
The Strong Form Collocation Method for the Prediction of Polycrystalline
Solidification with the Diffuse-interface Approach
Ashkan Almasi*, Jeong-Hoon Song**
*University of Colorado Boulder, **University of Colorado Boulder
ABSTRACT
Application of a diffuse-interface, or phase field, approach to modelling polycrystalline solidification has become a
significant topic of interest in science and engineering research. Such modelling requires suitable computational
methods to solve the relevant differential equations. In this study, we use the particle difference method (PDM)
[1-2], a strong-form point collocation method, to model solidification of polycrystalline materials and perform a
subsequent stress analysis. The PDM is a meshfree method based on Taylor polynomial expansion and the
moving least square approach. One of its distinct features is that the PDM can directly discretize the strong form of
governing partial differential equations. Consequently, the PDM neither performs domain integration nor constructs
a mesh, thus saving computational time. After describing the formulation of the PDM and some techniques used in
the subsequent analysis, this study takes advantage of these benefits of the PDM to predict the solidification
process in two cases, one with 5 grains and the other with 36 grains, using grain growth kinetics [3]. Afterward,
stress analysis is performed with the predicted polycrystalline morphology, yielding results for displacement, strain,
stress, and Von Mises stress in the polycrystalline solid for various levels of discretization. Finally, these results are
compared to results from the finite element method for verification, demonstrating that the PDM successfully
predicts polycrystalline solidification and computes stress in the predicted morphology. References [1] Young-Cheol
Yoon and Jeong-Hoon Song. Extended particle difference method for weak and strong discontinuity problems: part
i. derivation of the extended particle derivative approximation for the representation of weak and strong
discontinuities. Computational Mechanics, 53(6):1087–1103, 2014. [2] Young-Cheol Yoon and Jeong-Hoon Song.
Extended particle difference method for moving boundary problems. Computational Mechanics, 54(3):723–743,
2014. [3] Danan Fan and L-Q Chen. Computer simulation of grain growth using a continuum field model. Acta
Materialia, 45(2):611–622, 1997.](https://image.slidesharecdn.com/wccm2018aalmasi-181011203909/85/The-Strong-Form-Collocation-Method-for-the-Prediction-of-Polycrystalline-Solidification-with-the-Diffuse-interface-Approach-1-320.jpg)
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The Strong Form Collocation Method for the Prediction of Polycrystalline Solidification with the Diffuse-interface Approach
- 1. 13th World Congress on Computational Mechanics (WCCM XIII) 2nd Pan American Congress on Computational Mechanics (PANACM II) July 22-27, 2018, New York, NY, USA The Strong Form Collocation Method for the Prediction of Polycrystalline Solidification with the Diffuse-interface Approach Ashkan Almasi*, Jeong-Hoon Song** *University of Colorado Boulder, **University of Colorado Boulder ABSTRACT Application of a diffuse-interface, or phase field, approach to modelling polycrystalline solidification has become a significant topic of interest in science and engineering research. Such modelling requires suitable computational methods to solve the relevant differential equations. In this study, we use the particle difference method (PDM) [1-2], a strong-form point collocation method, to model solidification of polycrystalline materials and perform a subsequent stress analysis. The PDM is a meshfree method based on Taylor polynomial expansion and the moving least square approach. One of its distinct features is that the PDM can directly discretize the strong form of governing partial differential equations. Consequently, the PDM neither performs domain integration nor constructs a mesh, thus saving computational time. After describing the formulation of the PDM and some techniques used in the subsequent analysis, this study takes advantage of these benefits of the PDM to predict the solidification process in two cases, one with 5 grains and the other with 36 grains, using grain growth kinetics [3]. Afterward, stress analysis is performed with the predicted polycrystalline morphology, yielding results for displacement, strain, stress, and Von Mises stress in the polycrystalline solid for various levels of discretization. Finally, these results are compared to results from the finite element method for verification, demonstrating that the PDM successfully predicts polycrystalline solidification and computes stress in the predicted morphology. References [1] Young-Cheol Yoon and Jeong-Hoon Song. Extended particle difference method for weak and strong discontinuity problems: part i. derivation of the extended particle derivative approximation for the representation of weak and strong discontinuities. Computational Mechanics, 53(6):1087–1103, 2014. [2] Young-Cheol Yoon and Jeong-Hoon Song. Extended particle difference method for moving boundary problems. Computational Mechanics, 54(3):723–743, 2014. [3] Danan Fan and L-Q Chen. Computer simulation of grain growth using a continuum field model. Acta Materialia, 45(2):611–622, 1997.