A Quasicontinuum Approach to Modeling Discrete Microstructures

The quasicontinuum method, which was developed for atomic lattices, is extended to a more general class of microstructural models in which discrete points interact via discrete interactions. Such models allow one to study the influence of small-scale features (e.g. defects) in large-scale problems in a natural fashion, but may be prohibitively expensive. The quasicontinuum method allows one to reduce the resolution of the description where appropriate, so that realistic simulations become feasible. The conventional, energy based method is reformulated in terms of a virtual power balance. The summation rules used to account for the influence of discarded lattice points are also revisited. The performance of the resulting method is illustrated by an example