Mixed Atomistic-Continuum Models of Material Behavior: The Art of Transcending Atomistics and Informing Continua

The recent development of microscopes that allow for the examination of defects at the atomic scale has made possible a more direct connection between the defects and the macroscopic response they engender (see, e. g., MRS Bulletin, December 1999). Techniques ranging from high-resolution electron microscopy, which make possible the determination of the atomic-level structure of dislocation cores and grain boundaries, to the atomic force microscopes that bring new meaning to experiments such as those based on nanoindentation, all pose deep challenges as regards the modeling of the mechanics of materials. Each of these experiments calls for renewed efforts to cement the connection between defect mechanics and macroscopic constitutive descriptions. However, the link between the defects themselves and the observed macroscopic behavior is often a difficult one to forge theoretically and remains an active area of research.