Attaining regularization length insensitivity in phase-field models of ductile failure

2021 ◽  
Vol 384 ◽  
pp. 113936
Author(s):  
Brandon Talamini ◽  
Michael R. Tupek ◽  
Andrew J. Stershic ◽  
Tianchen Hu ◽  
James W. Foulk ◽  
...  
Keyword(s):  
Phase Field ◽  
Ductile Failure ◽  
Phase Field Models

scholarly journals Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling

2017 ◽  
Vol 17 (4) ◽  
pp. 661-678 ◽  
Author(s):  
Harbir Antil ◽  
Sören Bartels
Keyword(s):  
Image Processing ◽  
Phase Field ◽  
Differential Operators ◽  
Mathematical Tool ◽  
Phase Field Models ◽  
Field Modeling ◽  
Regularity Properties ◽  
Fractional Pdes ◽  
Fractional Differential ◽  
Fractional Differential Operators

AbstractFractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.

scholarly journals Minimization and Eulerian Formulation of Differential Geormetry Based Nonpolar Multiscale Solvation Models

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Zhan Chen
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Lagrangian Formulation ◽  
Global Minimizer ◽  
Solvation Model ◽  
Phase Field Models ◽  
Eulerian Formulation ◽  
Solvation Models ◽  
Similarity And Difference ◽  
Nonpolar Solvation

AbstractIn this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while their decompositions of attractive and repulsive parts are different. That indicates a distinction between phase field models of solvation and our Eulerian formulation.

scholarly journals Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains

2012 ◽  
Vol 468 (2147) ◽  
pp. 3705-3724 ◽  
Author(s):  
Markus Schmuck ◽  
Marc Pradas ◽  
Grigorios A. Pavliotis ◽  
Serafim Kalliadasis
Keyword(s):  
Porous Media ◽  
Free Energy ◽  
Phase Field ◽  
Single Channel ◽  
Confined Geometries ◽  
Science And Engineering ◽  
Hilliard Equation ◽  
Phase Field Models ◽  
Cahn Hilliard Equation ◽  
Double Well Potential

We derive a new, effective macroscopic Cahn–Hilliard equation whose homogeneous free energy is represented by fourth-order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly heterogeneous domains. To the best knowledge of the authors, this seems to be the first attempt of upscaling the Cahn–Hilliard equation in such domains. The new homogenized equation should have a broad range of applicability owing to the well-known versatility of phase-field models. The additionally introduced feature of systematically and reliably accounting for confined geometries by homogenization allows for new modelling and numerical perspectives in both science and engineering. Our results are applied to wetting dynamics in porous media and to a single channel with strongly heterogeneous walls.

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