The dynamic organization of dislocation structures: A simulation

Recent Progress in Discrete Dislocation Dynamics and Its Applications to Micro Plasticity

“…The particular choice of H and q is intentionally left unspecified, so that the current formulation is suitable for Hermite interpolation schemes of arbitrary degree (linear, cubic,…). Substituting (15) in (14) and using the analogous discretization k 2 ¼ MðuÞ m ab ðtÞ for the Lagrange multipliers, the following discrete problem is obtained X…”

“…[10][11][12][13][14] Only during the late-1980s, however, the term discrete dislocation dynamics (DDD) was coined in relationship to two-dimensional computer simulations aimed to shed light on the physical origins and the conditions for dislocation pattern evolution. [15][16][17] More recently, these computational tools have developed into sophisticated three-dimensional codes, [18][19][20][21][22][23][24] which are now used in massive DDD simulations for investigating the fundamental mechanisms of dislocation plasticity. Such computer simulations are now directly and successfully compared to experiments on nano-and micro-scale materials, such as thin films, 25,26 nano-indentation, 27,28 and the deformation of micro-pillars.…”

Dynamic Discrete Dislocation Plasticity

“…computationally cheap and robust methodology able to tackle large systems with flexible boundary conditions. DDP was introduced by Van der Giessen and Needleman in 1995 (Van der Giessen & Needleman, 1995) as a departure from previous two-dimensional dislocation models (Amodeo & Ghoniem, 1990a, 1990bBacon, 1967;Foreman, 1967;Gulluoglu & Hartley, 1992Gulluoglu, Srolovitz, David, LeSar, & Lomdahl, 1989;Lépinoux & Kubin, 1987). The key feature of DDP is its handling of the boundary conditions using linear superposition following the original proposal by Lubarda, Blume, and Needleman (1993).…”

Ambiguities in the calculation of dislocation self energies

“…The first such simulations involved systems of parallel dislocations and thus were effectively two-dimensional [1][2][3]. More recently, simulations involving fully three-dimensional dislocation loops and microstructures have begun to be performed [4 -8].…”