Coarse Graining of Atomistic Description at Finite Temperature Using Formal Asymptotics

In this paper, we propose a computational method for coarse graining the atomistic description at finite temperature using formal asymptotics. The method is based on the ansatz that there exists a separation of scales between the time scale of the atomic fluctuations and that of the thermodynamic processes, such as thermal expansion. We use the WKBmethod to propose an averaging scheme for treating the thermal degrees of freedom and deriving an effective Hamiltonian for the atomistic system. This energy functional is incorporated into the quasicontinuum framework to achieve a seamless coarse graining on the spatial scale. Numerical validation is performed by computing the thermal equilibrium properties of selected materials. The scope of the method based on the use of perturbation theory is discussed, and its capability is illustrated by way of simulating dislocation nucleation under a nanoindenter.