Mechanical Engineering ETDs

Publication Date

Spring 5-14-2022


Dislocation theory is the fundamental tool for explaining plasticity in the material. The elastic field of a material is always influenced by the presence of dislocations and other defects independent of the loading configurations. Scientists and researchers have minimal success in solving plasticity problems analytically. And for this reason, the capturing of dislocation dynamics is highly dependent on numerical modeling, which is always a challenge for its inherent multi-scale nature. Current research investigates and develops self-consistent numerical models for different plasticity problems based on the distributed-dislocation technique and the collocation-point method. Numerical methods are developed for different boundary conditions in the presence of crystal dislocations and discontinuities in the material. Boundary conditions due to the discontinuity in the material are satisfied by placing image or fictitious dislocations or dislocations of unknown Burgers vectors at predefined places. On the free surfaces, some designated points are selected (termed as “collocation points”) to enforce the boundary conditions there only. Numerical models are developed to satisfy the boundary conditions at those collocation points, assuming that satisfying the boundary conditions at those collocation points is sufficient to capture the field solution of the problem. Burgers vectors of those fictitious dislocations are solved for using a system of linear equations that ensures the tractions on the collocation points are zero. It is evident from the assumption that the numerical solution improves as the number of collocation points on the free surfaces increases. The developed numerical scheme is implemented in one of the existing Dislocation Dynamics (DD) codes by Zbib et al. to show the free surface effect in a constant strain-rate simulation. The applications extend to free surfaces with complex geometry and can thus capture the interaction of multiple voids of any geometry. Other studies tackled the singular behavior near the dislocation core, the effect of multiple dislocations or multipoles on the plasticity of the material as well as the effect of solute atoms on both the elastic and plastic behavior of metallic crystalline materials.


Dislocation Dynamics, Plasticity, Multiscale Modeling, Boundary Conditions

Degree Name

Mechanical Engineering

Level of Degree


Department Name

Mechanical Engineering

First Committee Member (Chair)

Tariq A. Khraishi

Second Committee Member

Yu-Lin Shen

Third Committee Member

Rafiqul Tarefdar

Fourth Committee Member

Hojun Lim

Document Type