Interface Conditions for a Phase Field Model with Anisotropic and Non-Local Interactions

2011 ◽  
Vol 202 (2) ◽  
pp. 349-372 ◽  
Author(s):  
Xinfu Chen ◽  
Gunduz Caginalp ◽  
Emre Esenturk
Author(s):  
Xinfu Chen ◽  
Gunduz Caginalp ◽  
Emre Esenturk

2019 ◽  
Vol 53 (3) ◽  
pp. 805-832
Author(s):  
Élie Bretin ◽  
Roland Denis ◽  
Jacques-Olivier Lachaud ◽  
Édouard Oudet

We propose a framework to represent a partition that evolves under mean curvature flows and volume constraints. Its principle follows a phase-field representation for each region of the partition, as well as classical Allen–Cahn equations for its evolution. We focus on the evolution and on the optimization of problems involving high resolution data with many regions in the partition. In this context, standard phase-field approaches require a lot of memory (one image per region) and computation timings increase at least as fast as the number of regions. We propose a more efficient storage strategy with a dedicated multi-image representation that retains only significant phase field values at each discretization point. We show that this strategy alone is unfortunately inefficient with classical phase field models. This is due to non local terms and low convergence rate. We therefore introduce and analyze an improved phase field model that localizes each phase field around its associated region, and which fully benefits of our storage strategy. To demonstrate the efficiency of the new multiphase field framework, we apply it to the famous 3D honeycomb problem and the conjecture of Weaire–Phelan’s tiling.


2016 ◽  
Author(s):  
Larry Kenneth Aagesen ◽  
Daniel Schwen

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Min Yang ◽  
Lu Wang ◽  
Wentao Yan

AbstractA three-dimensional phase-field model is developed to simulate grain evolutions during powder-bed-fusion (PBF) additive manufacturing, while the physically-informed temperature profile is implemented from a thermal-fluid flow model. The phase-field model incorporates a nucleation model based on classical nucleation theory, as well as the initial grain structures of powder particles and substrate. The grain evolutions during the three-layer three-track PBF process are comprehensively reproduced, including grain nucleation and growth in molten pools, epitaxial growth from powder particles, substrate and previous tracks, grain re-melting and re-growth in overlapping zones, and grain coarsening in heat-affected zones. A validation experiment has been carried out, showing that the simulation results are consistent with the experimental results in the molten pool and grain morphologies. Furthermore, the grain refinement by adding nanoparticles is preliminarily reproduced and compared against the experimental result in literature.


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