The Theory and Implementation of the Quasicontinuum Method

While atomistic simulations have provided great insight into the basic mechanisms of processes like plasticity, diffusion and phase transformations in solids, there is an important limitation to these methods. Specifically, the large number of atoms in any realistic macroscopic structure is typically much too large for direct simulation. Consider that the current benchmark for largescale fully atomistic simulations is on the order of 109 atoms, using massively paralleled computer facilities with hundreds or thousands of CPUs. This represents 1/10 000 of the number of atoms in a typical grain of aluminum, and 1/1 000 000 of the atoms in a typical micro-electro-mechanical systems (MEMS) device. Further, it is apparent that with such a large number of atoms, substantial regions of a problem of interest are essentially behaving like a continuum. Clearly, while fully atomistic calculations are essential to our understanding of the basic “unit” mechanisms of deformation, they will never replace continuum models altogether.