Dislocations are line defects in crystals. Discrete dislocation dynamics is a powerful simulation tool for crystalline materials. The climb motion of dislocations, which couples with vacancy diffusion, plays important roles for materials properties. We have developed dislocation climb formulations based on the Green’s functions for multiple, curved dislocations. The dislocation climb velocity is determined from the Peach-Koehler force on dislocations through vacancy diffusion in a nonlocal manner. We have also designed efficient numerical discretization methods for this new formulation. We have validated the dislocation climb model by upscalings from a stochastic model on atomistic scale. The obtained new self-climb formulation due to vacancy pipe diffusion is able to quantitatively describe the experimental observations of conservative motions of prismatic dislocation loops. Efficient simulation model based on phase field approach has been developed. The obtained formulations and numerical methods provide a tool for more accurate dislocation dynamics simulations and deeper understandings of dislocation climb and related materials properties.

Yang Xiang is a professor and PG programs coordinator of mathematics department at the Hong Kong University of Science and Technology (HKUST). He received his PhD degree in mathematics from Courant Institute (New York University) in 2001. He was a postdoctoral fellow at Princeton University from 2001 to 2003 before he came to HKUST. He is a plenary speaker at the SIAM Conference on Mathematical Aspects of Materials Science (2021).Prof. Xiang's current research interests include modeling and simulations in materials science, numerical analysis and scientific computation in multiscale problems, data science and image science.