A Multiscale Modeling Method for Deformations on Atomic Lattice Defects and Application to Plasticity
Abstract
Computing the displacements of atoms undergoing deformation in a perfect lattice requires the use of the so-called Cauchy-Born approximation. Near defects such as at vacancies or dislocations, this approximation does not hold and a computationally costly energy minimization over a large number of atoms is unavoidable. Presented is a self-consistent multiscale methodology enabling an approximation to the displacements near defects without requiring full energy minimization over successive load increments. It enables description of the fundamental mechanical behavior of crystalline materials at the length scale of a macroscopic continuum (i.e., millimeter resolution) given discrete atomic interactions at the nanoscale (i.e., angstrom resolution). The basic formulation is derived from mathematical homogenization which requires the definition of a representative crystalline volume element containing periodic defects. Numerical simulations demonstrate the utility of the framework for the particular case of tungsten. Elastic stiffness and energetic properties of periodic unit cells containing vacancies, screw dislocations, and low-angle twist boundaries are computed followed by demonstrative calculations of the extension to atomistic plastic flow.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 2006
- Accession Number
- ADA481240
Entities
People
- John D. Clayton
- Peter W. Chung
Organizations
- United States Army Research Laboratory