Fast and accurate quasi-atom method for simultaneous atomistic and continuum simulation of solids

TL;DR

A novel hybrid method of simultaneous atomistic simulation of solids in critical regions (contacts surfaces, cracks areas, etc.), along with continuum modeling of other parts, which demonstrates a significant superiority of the approach in computational speed and implementation convenience.

Abstract

We report a novel hybrid method of simultaneous atomistic simulation of solids in critical regions (contacts surfaces, cracks areas, etc.), along with continuum modeling of other parts. The continuum is treated in terms of quasi-atoms of different size, comprising composite medium. The parameters of interaction potential between the quasi-atoms are optimized to match elastic properties of the composite medium to those of the atomic one. The optimization method coincides conceptually with the online Machine Learning (ML) methods, making it computationally very efficient. Such an approach allows a straightforward application of standard software packages for molecular dynamics (MD), supplemented by the ML-based optimizer. The new method is applied to model systems with a simple, pairwise Lennard-Jones potential, as well with multi-body Tersoff potential, describing covalent bonds. Using LAMMPS software we simulate collision of particles of different size. Comparing simulation results, obtained by the novel method, with full-atomic simulations, we demonstrate its accuracy, validity and overwhelming superiority in computational speed. Furthermore, we compare our method with other hybrid methods, specifically, with the closest one -- AtC (Atomic to Continuum) method. We demonstrate a significant superiority of our approach in computational speed and implementation convenience. Finally, we discuss a possible extension of the method for modeling other phenomena.

Figures (6)

• Figure 1: Illustration of two colliding multi-scale particles comprised of real atoms (black) in the critical region - the area of their contact and three different types of quasi-atoms, blue, yellow and rose, which are twice, four and eight times larger than the real atoms.
• Figure 2: Main panel: The computation time dependence for inter-particle collisions, on the particle size for the original atomistic particles (blue line) and multi-scale particles: with $N=2$ types of atoms/quasi-atoms (lilac line), $N=3$ types (orange line) and $N=4$ types (green line). The original atomistic particles interact via standard Lennard-Jones potential corresponding to copper, while the potential parameters for the quasi-atoms are found by the optimization procedure. Inset: The dependence of the relative error for the target parameters, associated with the elastic constants of copper, on the iteration step of the optimization procedure for $N=4$ (see the main text).
• Figure 3: Comparative analysis of the collision dynamics of composite particles, comprised of atoms and quasi-atoms of three types and completely atomistic particles (full-scale MD simulations). The inter-particle force is plotted as the function of the overlap, $\xi=R_1+R_2-r_{12}$. The radii of the particles are $R_1=R_2=75\, \text{\AA}$, the impact velocity is $V=100\,m/s.$ The simulation time step is $\Delta t = 0.1\,\mathrm{fs}$ and cutoff distance for LJ potential is $r_{cut}=2.5\,\sigma$.
• Figure 4: Comparison of the collision dynamics of mesoscopic composite particles of radius $R=0.1\ \mu m$ with four types of atoms/quasi-atoms, with the prediction of theoretical models -- the Hertz theory for non-adhesive contact (left) and JKR theory for the adhesive contact (right). Two types of the inter-atomic potentials are demonstrated -- the pairwise Lennard-Jones potential (upper panels) and multi-atomic Tersoff potential (bottom panels). The inter-particle force is plotted as the function of the overlap (see the text for detail).
• Figure 5: Computation time for equilibrium copper system at T=300 K, as a function of the system size. See the text for details.