[P2-21] Parametric model of discrete dislocation dynamics based on mathematical theory of moving curves
In this contribution we present the comprehensive model of discrete dislocation dynamics based on the mathematical theory of moving curves. The purpose of our model is the precise and mathematically rigorous description of the dynamics of dislocations, which are represented as smooth curves evolving in their respective slip planes.
Dislocations are described by parametric curves and their motion is governed by the curvature driven flow.
The parametric model is coupled with the model of tagential velocity for increased stability, and with algorithms for topological changes which allow modeling of complex effects as merging, splitting, self-replication or interaction with obstacles.
The numerical algorithm is based on the flowing finite volume method.
We present qualitative and quantitative results of our numerical simulations. We demonstrate the capabilities of our model in the predicting of dipole formation and consequent estimation of the endurance limit, in the modeling of several interacting dislocations, and in the application of our method on complex scenarios involving moving dislocations interactiong with several obstacles.
Dislocations are described by parametric curves and their motion is governed by the curvature driven flow.
The parametric model is coupled with the model of tagential velocity for increased stability, and with algorithms for topological changes which allow modeling of complex effects as merging, splitting, self-replication or interaction with obstacles.
The numerical algorithm is based on the flowing finite volume method.
We present qualitative and quantitative results of our numerical simulations. We demonstrate the capabilities of our model in the predicting of dipole formation and consequent estimation of the endurance limit, in the modeling of several interacting dislocations, and in the application of our method on complex scenarios involving moving dislocations interactiong with several obstacles.