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Plastic deformation of most crystalline materials is due to the motion of lattice dislocations. Therefore, the simulation of the interaction and dynamics of these defects has become state-of-the-art method to study work hardening, size effects, creep and many other mechanical properties of metallic specimens. Lot of efforts have been made to make the simulations realistic by including specific dislocation mechanisms and the effect of free surfaces. However, less attention has been devoted to the numerical scheme that is used to solve the equations of motion. In this paper we propose a scheme that speeds up simulations by several orders of magnitude. The scheme is implicit because this type is the most efficient one for solving stiff equations that arise due to the long-range nature of dislocation interactions. The numerical results show that the method is not only faster than other approaches at the same numerical precision, but it can also be efficiently applied even without dislocation annihilation. The suggested method significantly increases the achievable volume and/or duration of discrete dislocation dynamics simulations and can be generalized for complex 2D and 3D simulations as well. [ABSTRACT FROM AUTHOR]

A numerical method is developed to efficiently calculate the stress (and displacement) field in finite 2D rectangular media. The solution is expanded on a function basis with elements that satisfy the Navier–Cauchy equation. The obtained solution approximates the boundary conditions with their finite Fourier series. The method is capable to handle Dirichlet, Neumann and mixed boundary value problems as well and it was found to converge exponentially fast to the analytical solution with respect to the size of the basis. Possible application in discrete dislocation dynamics simulations is discussed and compared to the widely used finite element methods: it was found that the new method is superior in terms of computational complexity. [ABSTRACT FROM AUTHOR]