Monte Carlo simulation of dynamic uniaxial strain in two-dimensional Lennard-Jones lattices

Abstract

We describe an extension of conventional Monte Carlo techniques which allows stimulation of a system of atoms subjected to a dynamic physical process consisting of a sequence of time-variable external conditions. The simulation is based on the approximation of a continuous evolutionary process by the finite concatenation of differentially varying static constraints each of which is treated by Monte Carlo techniques. Such a method can only be used to treat rates which are fast or slow relative to the appropriate characteristic time of the system, but allows modeling of atomic systems too complex to treat with the use of molecular-dynamics techniques. This method is particularly useful on atomistic models of mechanical stress and material yielding, and is used herein to simulate the response of atomic lattices to dynamic uniaxial strain. The results of the simulation are then discussed in the context of shock-wave loading.