Multiscale crystal defect dynamics: a dual-lattice process zone model

Abstract

In this work, we present the theoretical and computational formulations of a multiscale crystal defect dynamics (MCDD) for the simulation of crystal defects at small scales. The main novelties of the proposed MCDD are: (1) We use the dual-lattice tessellation to construct a dual-lattice process zone model that can represent different types of crystal defects in a single crystal; (2) We adopt a fourth-order (four scales) hierarchical strain gradient theory to model constitutive behaviours of various defect process zones, in which the atomistic-informed higher order Cauchy–Born rule is employed, and (3) We employ the Barycentric finite element technique to construct finite element shape functions for polygonal and polyhedral process zone elements. The proposed MCDD method provides an efficient and viable alternative for both molecular dynamics and dislocation dynamics in simulations of defect evolutions such as void growth, dislocation nucleation, and fracture. In particular, MCDD offers a mesoscale description for dynamic lattice microstructure, defect microstructure, and their interactions. The method offers a possible solution for studying nanoscale and mesoscale crystalline plasticity.

Keywords:

• defect mechanics
• dislocation dynamics
• embedded atom method
• finite element method
• mesoscale plasticity
• multiscale simulation

Acknowledgments

Dr. Lisheng Liu of Wuhan University of Science and Technology (China) had participated in the early phase of this research, and we benefited from many discussions with him. We would like to thank an anonymous reviewer for his comments and suggestions.