scholarly journals Asymptotic Behaviour for a Phase-Field Model with Hysteresis in One-Dimensional Thermo-Visco-Plasticity

2004 ◽  
Vol 49 (4) ◽  
pp. 309-341 ◽  
Author(s):  
Olaf Klein
Keyword(s):  
Asymptotic Behaviour ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
One Dimensional

One-dimensional phase-field model for binary alloys

2000 ◽  
Vol 212 (3-4) ◽  
pp. 574-583 ◽  
Author(s):  
D.I. Popov ◽  
L.L. Regel ◽  
W.R. Wilcox
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Binary Alloys ◽  
Phase Field Model ◽  
One Dimensional

Linear stability analysis and metastable solutions for a phase-field model

1999 ◽  
Vol 129 (3) ◽  
pp. 571-600 ◽  
Author(s):  
A. Jiménez-Casas ◽  
A. Rodríguez-Bernal
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Phase Field ◽  
Field Model ◽  
Equilibrium Points ◽  
Phase Field Model ◽  
One Dimensional ◽  
Stability And Instability ◽  
The One

We study the linear stability of equilibrium points of a semilinear phase-field model, giving criteria for stability and instability. In the one-dimensional case, we study the distribution of equilibria and also prove the existence of metastable solutions that evolve very slowly in time.

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.

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