A phenomenological approach to fatigue with a variational phase-field model: The one-dimensional case

2018 ◽  
Vol 190 ◽  
pp. 53-73 ◽  
Author(s):  
Roberto Alessi ◽  
Stefano Vidoli ◽  
Laura De Lorenzis
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Phenomenological Approach ◽  
Dimensional Case ◽  
One Dimensional ◽  
The One

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.

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

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.

scholarly journals Thermodynamics and Analysis of Predicted Responses of a Phase Field Model for Ductile Fracture

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5842
Author(s):  
Aris Tsakmakis ◽  
Michael Vormwald
Keyword(s):  
Fracture Mechanics ◽  
Ductile Fracture ◽  
Phase Field ◽  
Damage Mechanics ◽  
Field Model ◽  
Phase Field Model ◽  
Isotropic Hardening ◽  
Linear Elastic ◽  
Isotropic Damage ◽  
The One

The fundamental idea in phase field theories is to assume the presence of an additional state variable, the so-called phase field, and its gradient in the general functional used for the description of the behaviour of materials. In linear elastic fracture mechanics the phase field is employed to capture the surface energy of the crack, while in damage mechanics it represents the variable of isotropic damage. The present paper is concerned, in the context of plasticity and ductile fracture, with a commonly used phase field model in fracture mechanics. On the one hand, an appropriate framework for thermodynamical consistency is outlined. On the other hand, an analysis of the model responses for cyclic loading conditions and pure kinematic or pure isotropic hardening are shown.

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