Lecture Series during Fall 2005 and Spring 2006

From nano to macro: Introduction to atomistic modeling techniques: Supplementary materials

Lecture 3: Concurrent scale coupling techniques: From nano to macro

Copy of slides

A long-standing research question in modeling the mechanical behavior of materials is the development methods to couple atomistic, discrete models with continuum theories of deformation, such as the finite element (FE) method. In this third lecture of the series entitled “From nano to ma cro: Introduction to atomistic modeling techniques”, we present an overview over various scale coupling techniques, with a focus on concurrent coupling of atomistic and continuum scales. These new methods represent a significant step towards achieving a concurrent integration of the nanoscale to the macroscopic scale. The new techniques enable seamless integration of atomistic approaches such as Density Functional Theory (DFT), Tight binding (TB), or empirical potentials such as the embedded atom method (EAM) with continuum theories of deformation (e.g. FE method). We review various approaches, including the MAAD method coupling TB with FE, the quasicontinuum (QC) method coupling EAM potentials with FE, as well as the bridging scale theory providing theoretical concepts to couple the atomistic scale with continuum theories. Unlike classical FE formulations, atomistic based descriptions do not require empirical parameters that define constitutive laws, but are instead completely based on fundamental, often quantum mechanical calculations. We review examples associated with each of these techniques, and discuss the drawbacks, potentials, and future developments associated with each of these methods. We discuss how atomistic-continuum coupling can be extended to describe finite temperature systems, currently still representing a major research topic. We briefly discuss alternative applications in the area of representing complex molecules such as beads, and coupling such mesoscopic regions with fully atomistic descriptions. In the final part of this lecture, we discuss how such new methods enable describing the deformation and fracture behavior of materials based on a fundamental, atomistic perspective, and thus potentially provide a new tool for the next generation of engineers, which may be utilized to design and understand the behavior of materials and structures.

Literature and further reading

Figure: Concurrent scale coupling simulation of Si-SiO systems. Hybrid models as shown here coupling ReaxFF-Tersoff (Buehler et al., 2005) enable a thorough description of chemistry coupled with mechanics of materials.

Copyright (c) 1999-2005 Markus J. Buehler. All rights reserved.