Sylvie Aubry

A multiply parallel implementation of finite element-based discrete dislocation dynamics for arbitrary geometries

Discrete dislocation dynamics (DD) approaches have proven useful in modeling the dynamics of large ensembles of dislocations. Continuing interest in finite body effects via image stresses has extended DD numerical approaches to improve the handling of surfaces. However, a physically accurate, yet computationally scalable, implementation has been elusive. This paper presents a new framework and implementation of a finite element-based discrete DD code that (1) treats arbitrarily shaped non-convex surfaces through image tractions, (2) allows for systematic refinement of the finite element mesh both in the bulk and on the surface and (3) provides a platform to scale to relatively larger and lengthier simulations. The approach is based on the capabilities of the Parallel Dislocation Simulator coupled through a distributed shared memory implementation for the calculation of large numbers of dislocation segments interacting with an independently large number of surface finite elements. Surface tracking approaches enable topological features at surfaces to be modeled. We verify the computed results via comparisons with analytical solutions for an infinite screw dislocation and prismatic loop near a surface and examine surface effects on a Frank–Read source. Convergence of the image force error with h- and p-refinement is shown to indicate the computational robustness. Additionally, through larger numerical experiments, we demonstrate the new capabilities in a three-dimensional elastic body of finite extent.

Implicit integration methods for dislocation dynamics

In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. This paper investigates the viability of high-order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge–Kutta time integrators are explored as a way of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newtons method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newtons method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.