An Improved Collocation Method to Treat Traction-Free Surfaces in Dislocation Dynamics Simulations

Abstract

Dislocation dynamics simulations is an inherently multi-scale computational methodology in materials deformation modeling. The authors address an important topic in such modeling which is the treatment of boundary conditions on the computational domain. Specifically, the effect of traction-free surfaces on the plasticity, i.e. the motion of dislocations and ensuing plastic flow, is treated here. To solve this numerical problem, the surface in question is meshed with elements each representing a dislocation loop. The boundary condition is enforced by solving a system of equations at each time step for the Burgers vectors of such loops. This is a collocation method with collocation points on the surface, and therefore, the higher the areal density of the points, the better the numerical outcome. Modeling results have been verified and are presented herein.