Computer Simulaltion of Dislocation Pattern Formation

Yield stress strengthening in ultrafine-grained metals: A two-dimensional simulation of dislocation dynamics

“…However, for numerical reasons, it is practically impossible to compare in 3D dislocation mechanisms occurring at different length scales (e.g., for different grain sizes) without rescaling the dislocation densities. To by-pass this problem, 2D simulations of DD may be of interest (Le´pinoux and Kubin, 1987;Ghoniem and Amodeo, 1988;Van der Giessen and Needleman, 1995). The price to pay for the reduction of the dimensionality of dislocations from lines to points is often an oversimplification of the dislocation mechanisms and of the slip geometry.…”

“…The procedure used to simulate DD (Ghoniem and Amodeo, 1988;Van der Giessen and Needleman, 1995;Benzerga et al, 2004;Go´mez-Garcı´a et al, 2006) can be summarized as follows. At every time step, (i) a load increment is applied, (ii) the dislocation stress fields and the Peach-Koeler forces are computed at the coordinates of the point-like dislocations, (iii) the displacement of the dislocations is predicted using a stress vs. velocity law and (iv) the possible occurrence of dislocation reactions is examined with the help of local rules.…”

Adaptive generalized mathematical homogenization framework for nanostructured materials

“…An alternative approach, which embeds dislocations directly in the continuum representation using discrete dislocation dynamics [34] or partition of unity approach [35] is preferable for large grains such as those of polycrystals.…”

“…We believe that the proposed adaptive strategy that converts continuum representation of the entire nanograin where dislocation has been detected into an atomistic representation is a nearly optimal strategy since soon thereafter subsequent piling up and interactions of the defects at the grain boundaries take place [33]. An alternative approach, which embeds dislocations directly in the continuum representation using discrete dislocation dynamics [34] or partition of unity approach [35] is preferable for large grains such as those of polycrystals.…”

Multiscale Discrete Dislocation Dynamics Plasticity

“…The DD analysis and its computer simulation modeling devised by many researchers (Ghoniem and Amodeo 1988;Canova, Brechet et al 1992;Kubin 1993;Schwarz and Tersoff 1996;Zbib, Rhee et al 1996;Zbib, Rhee et al 1998) has been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association with computational algorithms such as finite elements.…”