The effect of the diffusion on the bifurcation behavior of dislocation patterns in the one-dimensional finite domain
Document Type
Conference Proceeding
Publication Date
6-8-2016
Abstract
© 2016 Author(s). We study the pattern formation in dislocation dynamics of solid materials through bifurcation analysis. The model under study is the celebrated Walgraef-Aifantis (W-A) model of dislocation patterning in one dimensional finite domain. The model describes the evolution of the patterns along the domain and it consists of a couple of partial diffusion equations. The system is a reaction diffusion type with two different diffusion coefficients, one for the mobile (free to move due to stress in the slip plane) dislocations and the second for the immobile dislocations (slow movement or trapped ones). We analytically study the onset of instabilities as the diffusion coefficients are varied. We finally construct the bifurcation diagram with respect to the diffusion coefficients.
Publication Title
AIP Conference Proceedings
Recommended Citation
Spiliotis, K.,
Russo, L.,
&
Aifantis, E.
(2016).
The effect of the diffusion on the bifurcation behavior of dislocation patterns in the one-dimensional finite domain.
AIP Conference Proceedings,
1738.
http://doi.org/10.1063/1.4951931
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/9004