# zbMATH — the first resource for mathematics

Coupling a reactive potential with a harmonic approximation for atomistic simulations of material failure. (English) Zbl 1425.74030
Summary: Molecular dynamics (MD) simulations involving reactive potentials can be used to model material failure. The empirical potentials which are used in such simulations are able to adapt to the atomic environment, at the expense of a significantly higher computational cost than non-reactive potentials. However, during a simulation of failure, the reactive ability is needed only in some limited parts of the system, where bonds break or form and the atomic environment changes. Therefore, simpler non-reactive potentials can be used in the remainder of the system, provided that such potentials reproduce correctly the behavior of the reactive potentials in this region, and that seamless coupling is ensured at the interface between the reactive and non-reactive regions. In this article, we propose a methodology to combine a reactive potential with a non-reactive approximation thereof, made of a set of harmonic pair and angle interactions and whose parameters are adjusted to predict the same energy, geometry and Hessian in the ground state of the potential. We present a methodology to construct the non-reactive approximation of the reactive potential, and a way to couple these two potentials. We also propose a criterion for on-the-fly substitution of the reactive potential by its non-reactive approximation during a simulation. We illustrate the correctness of this hybrid technique for the case of MD simulation of failure in two-dimensional graphene originally modeled with REBO potential.
##### MSC:
 74A25 Molecular, statistical, and kinetic theories in solid mechanics 74A45 Theories of fracture and damage
ReaxFF
Full Text:
##### References:
 [1] Ashurst, W. T.; Hoover, W. G., Microscopic fracture studies in the two-dimensional triangular lattice, Phys. Rev. B, 14, 1465-1473, (1976) [2] Abraham, F. F.; Brodbeck, D.; Rafey, R. A.; Rudge, W. E., Instability dynamics of fracture: A computer simulation investigation, Phys. Rev. Lett., 73, 272-275, (1994) [3] Abraham, F. F.; Brodbeck, D.; Rudge, W. E.; Xu, X., A molecular dynamics investigation of rapid fracture mechanics, J. Mech. Phys. Solids, 45, 9, 1595-1619, (1997) · Zbl 0974.74558 [4] Abell, G. C., Empirical chemical pseudopotential theory of molecular and metallic bonding, Phys. Rev. B, 31, 6184-6196, (1985) [5] Brenner, D. W., Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Phys. Rev. B, 42, 9458-9471, (1990) [6] Tersoff, J., New empirical model for the structural properties of silicon, Phys. Rev. Lett., 56, 632-635, (1986) [7] Stuart, S. J.; Tutein, A. B.; Harrison, J. A., A reactive potential for hydrocarbons with intermolecular interactions, J. Chem. Phys., 112, 14, 6472-6486, (2000) [8] van Duin, A. C.T.; Dasgupta, S.; Lorant, F.; Goddard, W. A., Reaxff: A reactive force field for hydrocarbons, J. Phys. Chem. A, 105, 41, 9396-9409, (2001) [9] Brenner, D. W.; Shenderova, O. A.; Harrison, J. A.; Stuart, S. J.; Ni, B.; Sinnott, S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, J. Phys.: Condens. Matter, 14, 783, (2002) [10] Tersoff, J., New empirical approach for the structure and energy of covalent systems, Phys. Rev. B, 37, 6991-7000, (1988) [11] Plimpton, S. J., Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys., 117, 1-19, (1995) · Zbl 0830.65120 [12] Pastewka, L.; Pou, P.; Pérez, R.; Gumbsch, P.; Moseler, M., Describing bond-breaking processes by reactive potentials: importance of an environment-dependent interaction range, Phys. Rev. B, 78, (2008) [13] Pastewka, L.; Klemenz, A.; Gumbsch, P.; Moseler, M., Screened empirical bond-order potentials for si-C, Phys. Rev. B, 87, (2013) [14] Buehler, M. J.; van Duin, A. C.T.; Goddard, W. A., Multiparadigm modeling of dynamical crack propagation in silicon using a reactive force field, Phys. Rev. Lett., 96, (2006) [15] Bernstein, N.; Kermode, J. R.; Csányi, G., Hybrid atomistic simulation methods for materials systems, Rep. Progr. Phys., 72, 2, (2009) [16] Gao, W.; Huang, R., Thermomechanics of monolayer graphene: rippling, thermal expansion and elasticity, J. Mech. Phys. Solids, 66, 42-58, (2014) [17] Tewary, V. K.; Yang, B., Parametric interatomic potential for graphene, Phys. Rev. B, 79, (2009) [18] Atrash, F.; Hashibon, A.; Gumbsch, P.; Sherman, D., Phonon emission induced dynamic fracture phenomena, Phys. Rev. Lett., 106, (2011) [19] Dove, M. T., Introduction to lattice dynamics, (1993), Cambridge University Press [20] Shell, M. S., The relative entropy is fundamental to multiscale and inverse thermodynamic problems, J. Chem. Phys., 129, 14, (2008) [21] Rudzinski, J. F.; Noid, W. G., Coarse-graining entropy, forces, and structures, J. Chem. Phys., 135, 21, (2011) [22] Tejada, I. G.; Brochard, L.; Stoltz, G.; Legoll, F.; Lelièvre, T.; Cancès, E., Combining a reactive potential with a harmonic approximation for molecular dynamics simulation of failure: construction of a reduced potential, J. Phys.: Conf. Ser., 574, 1, (2015) [23] Mounet, N., Structural, vibrational and thermodynamic properties of carbon allotropes from first-principles: diamond, graphite, and nanotubes, (2005), Massachusetts Institute of Technology, (Master’s thesis) [24] Tadmor, E. B.; Ortiz, M.; Phillips, R., Quasicontinuum analysis of defects in solids, Phil. Mag. A, 73, 6, 1529-1563, (1996) [25] Tadmor, E. B.; Legoll, F.; Kim, W. K.; Dupuy, L. M.; Miller, R. E., Finite-temperature quasi-continuum, Appl. Mech. Rev., 65, 1, (2013) [26] Luskin, M.; Ortner, C., Atomistic-to-continuum coupling, Acta Numer., 22, 397-508, (2013) · Zbl 06302681 [27] Miller, R. E.; Tadmor, E. B., A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods, Model. Simul. Mater. Sci. Eng., 17, 5, (2009) [28] Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E., Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 6, 1087-1092, (1953) [29] Vanderbilt, D.; Taole, S. H.; Narasimhan, S., Anharmonic elastic and phonon properties of si, Phys. Rev. B, 40, 5657-5668, (1989) [30] Bou-Rabee, N.; Owhadi, H., Long-run accuracy of variational integrators in the stochastic context, SIAM J. Numer. Anal., 48, 1, 278-297, (2010) · Zbl 1215.65012 [31] Allen, M. P.; Tildesley, D. J., Computer simulation of liquids, (1987), Oxford University Press · Zbl 0703.68099
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.