Isogeometric Analysis of the Cahn-Hilliard Phase-Field Model

2007 ◽  
Author(s):  
Hector Gomez ◽  
Victor M. Calo ◽  
Yuri Bazilevs ◽  
Thomas J. Hughes
Keyword(s):  
Phase Field ◽  
Isogeometric Analysis ◽  
Field Model ◽  
Phase Field Model

Triangulation Based Isogeometric Analysis of the Cahn-Hilliard Phase-Field Model

2018 ◽  
Author(s):  
Ruochun Zhang ◽  
Xiaoping Qian
Keyword(s):  
Convergence Analysis ◽  
Phase Field ◽  
Isogeometric Analysis ◽  
Field Model ◽  
Complex Geometry ◽  
Phase Field Model ◽  
Initial Condition ◽  
Isoperimetric Problems ◽  
Time Step ◽  
System Evolution

This paper presents the triangulation based isogeometric analysis of the Cahn–Hilliard phase-field model. We validate our method by convergence analysis, show detailed system evolution from a randomly perturbed initial condition and then discuss related isoperimetric problems. Lastly an example highlighting its efficacy in complex geometry is provided. Triangulation based isogeometric analysis shows time step stability and complex geometry adaptability in our experiments.

Phase Field Dynamic Modelling of Shape Memory Alloys Based on Isogeometric Analysis

2012 ◽  
Vol 78 ◽  
pp. 63-68 ◽  
Author(s):  
Rakesh Dhote ◽  
Hector Gomez ◽  
Roderick Melnik ◽  
Jean Zu
Keyword(s):  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Microstructure Evolution ◽  
Phase Field ◽  
Isogeometric Analysis ◽  
Field Model ◽  
Phase Field Model ◽  
Higher Order ◽  
Martensitic Phase Transformations

Shape Memory Alloys (SMAs) exhibit complex behaviors as a result of their constituent phases and microstructure evolution. In this paper, we focus on the numerical simulations of microstructure evolution in SMAs using a phase-field model for the two dimensional square-to-rectangular martensitic phase transformations. The phase-field model, based on the Ginzburg-Landau theory, has strong non-linearity, thermo-mechanical coupling, and higher-order differential terms and presents substantial challenges for numerical simulations. The isogeometric analysis, developed in this paper using the rich NURBS basis functions, offers several advantages in solving such complex problems with higher-order partial differential equations as the problem at hand. To our best knowledge, we report here for the first time the use of the new method in the study of microstructure evolution in SMAs. The numerical experiments of microstructure evolution have been carried out on the FePd SMA specimen. The results are in good agreement with those previously reported in the literature.

Isogeometric analysis of the Cahn–Hilliard phase-field model

2008 ◽  
Vol 197 (49-50) ◽  
pp. 4333-4352 ◽  
Author(s):  
Héctor Gómez ◽  
Victor M. Calo ◽  
Yuri Bazilevs ◽  
Thomas J.R. Hughes
Keyword(s):  
Phase Field ◽  
Isogeometric Analysis ◽  
Field Model ◽  
Phase Field Model
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