TY - JOUR

T1 - Mathematical concepts for the micromechanical modelling of dislocation dynamics with a phase-field approach

AU - Kundin, J

AU - Emmerich, H

AU - Zimmer, J

PY - 2011/1

Y1 - 2011/1

N2 - This contribution reviews the mathematical concepts of micromechanical modelling in the phase-field approach applied to dislocation dynamics. The intention is two-fold. On the one hand, modelling of dislocation dynamics is a very recent field of development in phase-field theory, in comparison to the simulation of diffusional phase transformation and related microstructure evolution problems in materials science. The reason is that modelling dislocation dynamics poses several challenges for phase-field concepts which go beyond purely diffusional problems in materials science such as, e.g. dendritic solidification, as we point out in Section 3. On the other hand, the modelling of dislocations has triggered further wide-ranging developments of phase-field based models for deformation problems. This is an important development, since a comprehensive model for deformation problems should include displacive as well as diffusional degrees of freedom from the atomic scale to the microscale. This is something phase-field theory is capable of, as discussed in this review article. We aim to give an overview of relevant mathematical concepts, and to stimulate further steps in this direction.

AB - This contribution reviews the mathematical concepts of micromechanical modelling in the phase-field approach applied to dislocation dynamics. The intention is two-fold. On the one hand, modelling of dislocation dynamics is a very recent field of development in phase-field theory, in comparison to the simulation of diffusional phase transformation and related microstructure evolution problems in materials science. The reason is that modelling dislocation dynamics poses several challenges for phase-field concepts which go beyond purely diffusional problems in materials science such as, e.g. dendritic solidification, as we point out in Section 3. On the other hand, the modelling of dislocations has triggered further wide-ranging developments of phase-field based models for deformation problems. This is an important development, since a comprehensive model for deformation problems should include displacive as well as diffusional degrees of freedom from the atomic scale to the microscale. This is something phase-field theory is capable of, as discussed in this review article. We aim to give an overview of relevant mathematical concepts, and to stimulate further steps in this direction.

KW - dislocation dynamics

KW - phase-field approach

KW - micromechanics

KW - modelling

UR - http://www.scopus.com/inward/record.url?scp=78249265039&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1080/14786435.2010.485587

U2 - 10.1080/14786435.2010.485587

DO - 10.1080/14786435.2010.485587

M3 - Article

SN - 1478-6435

VL - 91

SP - 97

EP - 121

JO - Philosophical Magazine

JF - Philosophical Magazine

IS - 1

ER -