Zbib, H. M., Shehadeh, M., Khan, S. M. A., and Karami, G., “Multiscale Dislocation Dynamics Plasticity”, Int. J. Multiscale Comp. Eng., vol. 1(1), pp. 73-89, 2003.

Abstract

A discrete Dislocation Dynamics (DD) model for crystalline materials coupled with finite elements (FE) analysis developed recently by Zbib and co-workers is reviewed. The three-dimensional continuum-based FE formulation for elastoviscoplasticity incorporates the DD simulation replacing the usual plasticity constitutive relations, leading to what is called a Multiscale Dislocation Dynamics Plasticity (MDDP). The coupling involves a non-trivial homogenization to obtain local plastic strains from the contributions of discrete plastic events captured in DD. The superposition principle is utilized in order to find the effects of the boundaries (free, rigid or interfaces) on the dislocation movement. The developed computer code can efficiently handle size-dependent small-scale plasticity phenomena and related material instabilities at various length scales ranging from the nano-microscale to the mesoscale. The DD modeling is based on the fundamental physical laws governing dislocation motions and their interactions with various defects, interfaces, and external loadings. The multi-scale frame of consideration merges the two scales of nano-microscale, where plasticity is determined, and the continuum scale, where the energy transport is based. In order to illustrate the usefulness of this approach in investigating a wide range of plasticity phenomena, results for a set of case studies are presented. This includes, the deformation and dislocation structure during nanoindentation in bcc and fcc single crystals, analyses pertaining to the formation of dislocation boundaries during heavy deformation, dislocations interaction with shock-waves during impact loading conditions, and dislocation-defect interaction.

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