Multiscale Methodology: From Atoms to Continuum
Abstract
Research in multiscale methods has recently flourished with the help of ever-improving computer technology. These developments enable computational physics methods to challenge many of the fundamental limitations of continuum mechanics with larger atomistic simulations and sophisticated hybrid atomistic-continuum methods. The foundation of most hybrid methods presently lies in the judicious application of kinematic constraints between regions of atoms and regions of continuum finite elements. This juxtaposes atomic and continuum force fields and introduces an interface along which atoms and nodes are unnaturally constrained. This report is divided into three sections. Section 1 reports on an investigation of finding sources of numerical error due to this unphysical constraint. A heuristic upper bound is derived for a specific example of graphene. In section 2, a literature review of a technique that can potentially eliminate this error is presented. The review covers efforts in engineering for composite materials rooted in a firm mathematical basis for the so-called asymptotic expansion homogenization method (AEH). In section 3, AEH is used as a framework for developing analytical multiscale formulations for frozen atoms at the small scale and continuum mechanics at the large-scale. Analytical solutions for simple systems are used to illustrate the method and its features.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2002
- Accession Number
- ADA398023
Entities
People
- Peter W. Chung
- Raju R. Namburu
Organizations
- United States Army Research Laboratory