A robust, coupled approach for atomistic-continuum simulation.

Abstract

This report is a collection of documents written by the group members of the Engineering Sciences Research Foundation (ESRF), Laboratory Directed Research and Development (LDRD) project titled "A Robust, Coupled Approach to Atomistic-Continuum Simulation". Presented in this document is the development of a formulation for performing quasistatic, coupled, atomistic-continuum simulation that includes cross terms in the equilibrium equations that arise due to kinematic coupling and corrections used for the calculation of system potential energy to account for continuum elements that overlap regions containing atomic bonds, evaluations of thermo-mechanical continuum quantities calculated within atomistic simulations including measures of stress, temperature and heat flux, calculation used to determine the appropriate spatial and time averaging necessary to enable these atomisticallydefined expressions to have the same physical meaning as their continuum counterparts, and a formulation to quantify a continuum "temperature field", the first step towards constructing a coupled atomistic-continuum approach capable of finite temperature and dynamic analyses.

An enhanced version of the heat exchange algorithm with excellent energy conservation properties

“…We note that the above formulation of the velocity update as presented by Aubry et al 13 is simpler than the one which was originally proposed by Ikeshoji and Hafskjold 6 . In the latter case, is a more complex function of the velocities, but it is easy to see that both formulations are equivalent.…”

“…Since there is no net energy flux into the system according to our assumptions, this also implies that the total system energy 𝐸 remains constant. We note that the above formulation of the velocity update as presented by Aubry et al 13 is simpler than the one which was originally proposed by Ikeshoji and Hafskjold 6 . In the latter case, 𝜉 𝑘 is a more complex function of the velocities, but it is easy to see that both formulations are equivalent.…”

“…Particles outside any thermostatted region are not affected by this procedure. For the individual region , the velocity update can be formulated as 6,13 ↦ →¯=…”

Effect of Rotational Degrees of Freedom on Molecular Mobility

“…Based on the MD technique used in the current work, all degrees of freedom of the system, including the C 60 rotational DOFs, were explicitly taken into account. In order to study the effect of rotational DOFs on the dynamics of surface diffusion and mobility of C 60 , a second series of simulations were also performed at the same temperature range, in which, however, the rotational DOFs of the C 60 were frozen based on the energy separation technique and routines provided by the LAMMPS package. ,− It is noteworthy that in these simulations only the rotational DOFs of C 60 were frozen while all its other DOFs were remained untouched. The results of two different sets of simulations (in the presence and absence of C 60 rotation) were analyzed and compared with each other to examine the effect of rotational DOFs on the surface diffusion of the C 60 admolecule.…”