A simple phase-field model for interface tracking in three dimensions

2019 ◽  
Vol 78 (4) ◽  
pp. 1154-1165 ◽  
Author(s):  
Abbas Fakhari ◽  
Martin Geier ◽  
Diogo Bolster
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Three Dimensions ◽  
Interface Tracking ◽  
Simple Phase

Non-axisymmetric growth of dendrite with arbitrary symmetry in two and three dimensions: sharp interface model vs phase-field model

2020 ◽  
Vol 229 (19-20) ◽  
pp. 2899-2909
Author(s):  
L. V. Toropova ◽  
P. K. Galenko ◽  
D. V. Alexandrov ◽  
M. Rettenmayr ◽  
A. Kao ◽  
...  
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Three Dimensions ◽  
Interface Model ◽  
Sharp Interface Model

Computer Simulation of Grain Growth in Three Dimensions by the Phase Field Model with Anisotropic Grain-Boundary Mobilities

2007 ◽  
Vol 539-543 ◽  
pp. 2437-2442
Author(s):  
Yoshihiro Suwa ◽  
Yoshiyuki Saito ◽  
Hidehiro Onodera
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Large Scale ◽  
Field Model ◽  
Phase Field Model ◽  
High Mobility ◽  
Minor Component ◽  
Three Dimensions ◽  
A Minor

The kinetics and topology of grain growth in three dimensions were simulated using a phase-field model with anisotropic grain-boundary mobilities. In order to perform large scale calculations we applied both modifications of algorithms and parallel coding techniques to the Fan and Chen's phase-field algorithm. Kinetics of abnormal grain growth is presented. It is observed that the grains of a minor component which are at the beginning surrounded preferentially by boundaries of high mobility grow faster than the grains of a major component until the texture reverses completely. Additionally, topological results of grain structures, such as grain size distributions and grain face distributions, are discussed

Phase field model for electrically induced damage using microforce theory

2021 ◽  
pp. 108128652110520
Author(s):  
Elizaveta Zipunova ◽  
Evgeny Savenkov
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Order Term ◽  
Phase Field Model ◽  
Special Problem ◽  
Three Dimensions ◽  
Electric Permittivity ◽  
One Dimensional ◽  
Codimension Two ◽  
Problem Setting

In this paper, we present a consistent derivation of the phase field model for electrically induced damage. The derivation is based on Gurtin’s microstress and microforce theory and the Coleman–Noll procedure. The resulting model accounts for Ohmic currents, includes charge conservation law and allows for finite electric permittivity and conductivity distribution in the medium. Special attention is devoted to the case when the damaged region is a codimension-two object, i.e., a curve in three dimensions. It is shown that in this case the free energy of the model necessarily includes a high-order term, which ensures the well-posedness of the problem. A special problem setting is proposed to account for the prescribed charge distribution. Local features of the phase field distribution are illustrated with one-dimensional axisymmetric numerical experiments.

Phase Field Model Simulation of Grain Growth in Three Dimensions under Isotropic and Anisotropic Grain Boundary Energy Conditions

2007 ◽  
Vol 558-559 ◽  
pp. 1101-1106 ◽  
Author(s):  
Kyung Jun Ko ◽  
Pil Ryung Cha ◽  
Jong Tae Park ◽  
Jae Kwan Kim ◽  
Nong Moon Hwang
Keyword(s):  
Solid State ◽  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Field Model ◽  
Boundary Energy ◽  
Phase Field Model ◽  
Three Dimensions ◽  
Energy Conditions ◽  
Grain Boundary Energy

Phase-field model (PFM) in multiple orientation fields was used to simulate the grain growth in three-dimensions (3-D) for isotropic and anisotropic grain boundary energy. In the simulation, the polycrystalline microstructure was described by a set of non-conserved order parameters and each order parameter describes each orientation of grains. For isotropic grain boundary energy, the simulation showed the microstructure evolution of normal grain growth. For anisotropic grain boundary energy, however, the simulation showed that certain grains which share a high fraction of low energy grain boundaries with other grains have a high probability to grow by wetting along triple junctions and can grow abnormally with a growth advantage of solid-state wetting. The PFM simulation shows the realistic microstructural evolution of island and peninsular grains during abnormal grain growth by solid-state wetting.

scholarly journals A phase field model for snow crystal growth in three dimensions

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Gilles Demange ◽  
Helena Zapolsky ◽  
Renaud Patte ◽  
Marc Brunel
Keyword(s):  
Crystal Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Three Dimensions ◽  
Snow Crystal

On the Fully Implicit Solution of a Phase-Field Model for Binary Alloy Solidification in Three Dimensions

2012 ◽  
Vol 4 (06) ◽  
pp. 665-684 ◽  
Author(s):  
Christopher E. Goodyer ◽  
Peter K. Jimack ◽  
Andrew M. Mullis ◽  
Hongbiao Dong ◽  
Yu Xie
Keyword(s):  
Binary Alloy ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Second Order ◽  
Three Dimensions ◽  
Computational Techniques ◽  
Time Step ◽  
Alloy Solidification ◽  
Fully Implicit

AbstractA fully implicit numerical method, based upon a combination of adaptively refined hierarchical meshes and geometric multigrid, is presented for the simulation of binary alloy solidification in three space dimensions. The computational techniques are presented for a particular mathematical model, based upon the phase-field approach, however their applicability is of greater generality than for the specific phase-field model used here. In particular, an implicit second order time discretization is combined with the use of second order spatial differences to yield a large nonlinear system of algebraic equations as each time step. It is demonstrated that these equations may be solved reliably and efficiently through the use of a nonlinear multigrid scheme for locally refined grids. In effect this paper presents an extension of earlier research in two space dimensions (J. Comput. Phys., 225 (2007), pp. 1271-1287) to fully three-dimensional problems. This extension is validated against earlier two-dimensional results and against some of the limited results available in three dimensions, obtained using an explicit scheme. The efficiency of the implicit approach and the multigrid solver are then demonstrated and some sample computational results for the simulation of the growth of dendrite structures are presented.

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