Many properties of real materials need to be described at various length scales, from the atomistic to continuum, in order to
capture in a convincing manner the link between the microscopic processes and the macroscopic behavior. A typical example is the mechanical response of metals to external loads, which is
characterized as ductile or brittle at the macroscopic scale, depending on the ability of the material to absorb the load by plastic deformation. This response can be drastically altered by the presence of impurities and their influence on bonding between the atoms in crucial regions like the tip of a crack.
The delocalized nature of electronic states in a metal makes the desciption of such effects particularly challenging. We have been pursuing methodologies for coupling the quantum mechanical
atomistic scale to the classical atomistic, which is the first step in a multiscale approach to this problem, and to the continuum.
In this talk, I will present the essential features of these methodologies and their limitations and potential for realistic applications.p>
This work was performed in collaboration with Nick Choly, Weinan E,Gang Lu and Ellad Tadmor.
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