Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T01:06:48.583Z Has data issue: false hasContentIssue false

Dynamical Coupling Atomistic and Continuum Simulations

Published online by Cambridge University Press:  20 August 2015

Guowu Ren*
Affiliation:
Key Laboratory for Computational Physical Sciences (MOE), Fudan University, Shanghai 200433, China
Dier Zhang*
Affiliation:
Key Laboratory for Computational Physical Sciences (MOE), Fudan University, Shanghai 200433, China
Xin-Gao Gong*
Affiliation:
Key Laboratory for Computational Physical Sciences (MOE), Fudan University, Shanghai 200433, China
*
Corresponding author.Email:[email protected]
Get access

Abstract

We propose a new multiscale method that couples molecular dynamics simulations (MD) at the atomic scale and finite element simulations (FE) at the continuum regime. By constructing the mass matrix and stiffness matrix dependent on coarsening of grids, we find a general form of the equations of motion for the atomic and continuum regions. In order to improve the simulation at finite temperatures, we propose a low-pass phonon filter near the interface between the atomic and continuum regions, which is transparent for low frequency phonons, but dampens the high frequency phonons.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Kohlhoff, S., Gumbsch, P. and Fischmeister, H. F., Crack propagation in b.c.c crystals studied with a combined finite-element and atomistic model, Phil. Mag. A, 64 (1991), 851–878.Google Scholar
[2]Broughton, J. Q., Abraham, F. F., Bernstein, N. and Kaxiras, E., Concurrent coupling of length scales: methodology and application, Phys. Rev. B, 60 (1999), 2391–1403.Google Scholar
[3]Tadmor, E. B., Ortiz, M. and Phillips, R., Quasicontinuum analysis of defects in solids, Phil. Mag. A, 73 (1996), 1529–1563.Google Scholar
[4]Rudd, R. E. and Broughton, J. Q., Coarse-grained molecular dynamics and the atomic limit of finite elements, Phys. Rev. B, 58 (1998), R5893–R5896.Google Scholar
[5]Wanger, G. J. and Liu, W. K., Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys., 190 (2003), 249–274.Google Scholar
[6]Xiao, S. P. and Belytschko, T., A bridging domain method for coupling continua with molecular dynamics, Comput. Methods Appl. Mech. Eng., 193 (2004), 1645–1669.Google Scholar
[7]Read, D. T. and Tewary, V. K., Multiscale model of near-spherical germanium quantum dots in silicon, Nanotechnology, 18 (2007), 105402.Google Scholar
[8]Knap, J. and Ortiz, M., Effect of indenter-radius size on Au (001) nanoindentation, Phys. Rev. Lett., 90 (2003), 226102.Google Scholar
[9]Peng, Q., Zhang, X., Hung, L., Carter, E. A. and Lu, G., Quantum simulation of materials at micron scales and beyond, Phys. Rev. B, 78 (2008), 054118.Google Scholar
[10]Shilkrot, L. E., Miller, R. E. and Curtin, W. A., Coupled atomistic and discrete dislocation plasticity, Phys. Rev. Lett., 89 (2002), 025501.Google Scholar
[11]Lidorikis, E., Bachlechner, M. E., Kalia, R. K., Nakano, A. and Vashishta, P., Coupling length scales for multiscale atomistics-continuum simulations: atomistically induced stress distributions in Si/Si 3N 4 nanopixels, Phys. Rev. Lett., 87 (2001), 086104.Google Scholar
[12]Luan, B. Q., Hyun, S., Molinari, J. F., Bernstein, N. and Mark Robbins, O., Multiscale modeling of two-dimensional contacts, Phys. Rev. B, 74 (2006), 046710.CrossRefGoogle ScholarPubMed
[13]Bažant, Z. P., Spurious reflection of elastic waves in nonuniform finite element grids, Comput. Methods Appl. Mech. Eng., 16 (1978), 91–100.Google Scholar
[14]Rudd, R. E. and Broughton, J. Q., Coarse-grained molecular dynamics: nonlinear finite elements and finite temperature, Phys. Rev. B, 72 (2005), 144104.Google Scholar
[15]Liu, W. K., Park, H. S., Qian, D., Karpov, E. G., Kadowaki, H. and Wagner, G. J., Bridging scale methods for nanomechanics and materials, Comput. Methods Appl. Mech. Eng., 195 (2006), 1407–1421.Google Scholar
[16]Zhou, S. J., Lomdahl, P. S., Thomson, R. and Holian, B. L., Dynamic crack processes via molecular dynamics, Phys. Rev. Lett., 76 (1996), 2318–2321.Google Scholar
[17]Qu, S., Shastry, V., Curtin, W. A. and Miller, R. E., A finite-temperature dynamic coupled atomistic/discrete dislocation method, Model. Simul. Mater. Sci. Eng., 13 (2005), 1101–1118.Google Scholar
[18]Cai, W., Koning, M. de, Bulatov, V. V. and Yip, S., Minimizing boundary reflections in coupleddomain simulations, Phys. Rev. Lett., 85 (2000), 3213–3216.Google Scholar
[19] W. E and Huang, Z., Matching conditions in atomistic-continuum modeling of materials, Phys. Rev. Lett., 87 (2001), 135501.Google Scholar
[20]Yang, J. Z. and Li, X., Comparative study of boundary conditions for molecular dynamics simulations of solids at low temperature, Phys. Rev. B, 73 (2006), 224111.Google Scholar
[21]Namilae, S., Nicholson, D. M., Nukala, P. K. V. V., Gao, C. Y., Osetsky, Y. N. and Keffer, D. J., Absorbing boundary conditions for molecular dynamics and multiscale modeling, Phys. Rev. B, 76 (2007), 144111.Google Scholar
[22]Li, S., Liu, X., Agrawal, A. and To, A. C., Perfectly matched multiscale simulations for discrete lattice systems: extension to multiple dimensions, Phys. Rev. B, 74 (2006), 045418.Google Scholar
[23]Jones, R. E. and Kimmer, C. J., Efficient non-reflecting boundary condition constructed via optimization of damped layers, Phys. Rev. B, 81 (2010), 094301.Google Scholar
[24]Kraczek, B., Miller, S. T., Haber, R. B. and Johnson, D. D., Adaptive spacetime method using Riemann jump conditions for coupled atomistic-continuum dynamics, J. Comput. Phys., 229 (2010), 2061–2092.Google Scholar
[25]Born, M. and Huang, K., Dynamical Theories of Crystal Lattices, Clarendo Press, Oxford, 1954.Google Scholar
[26]Hughes, T. J. R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987.Google Scholar
[27]Mitra, S. K., Digital Signal Processing: A Computer-Based Approach, McGraw-Hill, 2004.Google Scholar