Research Papers

A Hybrid Molecular Dynamics/Atomic-Scale Finite Element Method for Quasi-Static Atomistic Simulations at Finite Temperature

[+] Author and Article Information
Ran Xu

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Bin Liu

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: liubin@tsinghua.edu.cn

1Corresponding author.

Manuscript received September 29, 2013; final manuscript received October 22, 2013; accepted manuscript posted October 25, 2013; published online December 10, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(5), 051005 (Dec 10, 2013) (7 pages) Paper No: JAM-13-1410; doi: 10.1115/1.4025807 History: Received September 29, 2013; Revised October 22, 2013; Accepted October 25, 2013

In this paper, a hybrid quasi-static atomistic simulation method at finite temperature is developed, which combines the advantages of MD for thermal equilibrium and atomic-scale finite element method (AFEM) for efficient equilibration. Some temperature effects are embedded in static AFEM simulation by applying the virtual and equivalent thermal disturbance forces extracted from MD. Alternatively performing MD and AFEM can quickly obtain a series of thermodynamic equilibrium configurations such that a quasi-static process is modeled. Moreover, a stirring-accelerated MD/AFEM fast relaxation approach is proposed in which the atomic forces and velocities are randomly exchanged to artificially accelerate the “slow processes” such as mechanical wave propagation and thermal diffusion. The efficiency of the proposed methods is demonstrated by numerical examples on single wall carbon nanotubes.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Sanchez-Portal, D., Artacho, E., Soler, J. M., Rubio, A., and Ordejon, P., 1999, “Ab Initio Structural, Elastic, and Vibrational Properties of Carbon Nanotubes,” Phys. Rev. B, 59(19), pp. 12678–12688. [CrossRef]
Demczyk, B. G., Wang, Y. M., Cumings, J., Hetman, M., Han, W., Zettl, A., and Ritchie, R. O., 2002, “Direct Mechanical Measurement of the Tensile Strength and Elastic Modulus of Multiwalled Carbon Nanotubes,” Mat. Sci. Eng. A Struct. Mat. Prop. Microstruct. Process., 334(1–2), pp. 173–178. [CrossRef]
Zheng, Q. S., and Jiang, Q., 2002, “Multiwalled Carbon Nanotubes as Gigahertz Oscillators,” Phys. Ref. Lett., 88(4), p. 045503. [CrossRef]
Boland, J. J., Wu, B., and Heidelberg, A., 2005, “Mechanical Properties of Ultrahigh-Strength Gold Nanowires,” Nature Mater., 4(7), pp. 525–529. [CrossRef]
Huang, J. Y., Chen, S., Wang, Z. Q., Kempa, K., Wang, Y. M., Jo, S. H., Chen, G., Dresselhaus, M. S., and Ren, Z. F., 2006, “Superplastic Carbon Nanotubes—Conditions Have Been Discovered That Allow Extensive Deformation of Rigid Single-Walled Nanotubes.,” Nature, 439(7074), pp. 281–281. [CrossRef] [PubMed]
Ma, W., Liu, L., Zhang, Z., Yang, R., Liu, G., Zhang, T., An, X., Yi, X., Ren, Y., Niu, Z., Li, J., Dong, H., Zhou, W., Ajayan, P. M., and Xie, S., 2009, “High-Strength Composite Fibers: Realizing True Potential of Carbon Nanotubes in Polymer Matrix Through Continuous Reticulate Architecture and Molecular Level Couplings,” Nano Lett., 9(8), pp. 2855–2861. [CrossRef] [PubMed]
Alder, B. J., and Wainwright, T. E., 1957, “Phase Transition for a Hard Sphere System,” J. Chem. Phys., 27(5), pp. 1208–1209. [CrossRef]
Alder, B. J., and Wainwright, T. E., 1959, “Studies in Molecular Dynamics. 1. General Method,” J. Chem. Phys., 31(2), pp. 459–466. [CrossRef]
Branício, P. S., and Rino, J.-P., 2000, “Large Deformation and Amorphization of Ni Nanowires Under Uniaxial Strain: A Molecular Dynamics Study,” Phys. Rev. B, 62(24), pp. 16950–16955. [CrossRef]
Wei, C. Y., Cho, K. J., and Srivastava, D., 2003, “Tensile Strength of Carbon Nanotubes Under Realistic Temperature and Strain Rate,” Phys. Rev. B, 67(11), p. 115407. [CrossRef]
Koh, S. J. A., Lee, H. P., Lu, C., and Cheng, Q. H., 2005, “Molecular Dynamics Simulation of a Solid Platinum Nanowire Under Uniaxial Tensile Strain: Temperature and Strain-Rate Effects,” Phys. Rev. B, 72(8), p. 085414. [CrossRef]
Chen, Y. L., Liu, B., Huang, Y., and Hwang, K. C., 2011, “Fracture Toughness of Carbon Nanotube-Reinforced Metal- and Ceramic-Matrix Composites,” J. Nanomater., 2011(1), p. 746029. [CrossRef]
Jennings, A. T., Li, J., and Greer, J. R., 2011, “Emergence of Strain-Rate Sensitivity in Cu Nanopillars: Transition From Dislocation Multiplication to Dislocation Nucleation,” Acta Materialia, 59(14), pp. 5627–5637. [CrossRef]
Al-Lafi, W., Jin, J., Xu, S. X., and Song, M., 2010, “Performance of MWCNT/HDPE Nanocomposites at High Strain Rates,” Macromol. Mat. Eng., 295(6), pp. 519–522. [CrossRef]
Lim, A. S., An, Q., Chou, T. W., and Thostenson, E. T., 2011, “Mechanical and Electrical Response of Carbon Nanotube-Based Fabric Composites to Hopkinson Bar Loading,” Compos. Sci. Tech., 71(5), pp. 616–621. [CrossRef]
E. W. N., Engquist, B., and Huang, Z. Y., 2003, “Heterogeneous Multiscale Method: A General Methodology for Multiscale Modeling,” Phys. Rev. B, 67(9), pp. 92101. [CrossRef]
Iannuzzi, M., Laio, A., and Parrinello, M., 2003, “Efficient Exploration of Reactive Potential Energy Surfaces Using Car-Parrinello Molecular Dynamics,” Phys. Rev. Lett., 90(23), p. 238302. [CrossRef] [PubMed]
Dupuy, L. M., Tadmor, E. B., Miller, R. E., and Phillips, R., 2005, “Finite-Temperature Quasicontinuum: Molecular Dynamics Without All the Atoms,” Phys. Rev. Lett., 95(6), p. 060202. [CrossRef] [PubMed]
Zhou, M., 2005, “Thermomechanical Continuum Representation of Atomistic Deformation at Arbitrary Size Scales,” Proc. R. Soc. Math. Phys. Eng. Sci., 461(2063), pp. 3437–3472. [CrossRef]
Kulkarni, Y., Knap, J., and Ortiz, M., 2008, “A Variational Approach to Coarse Graining of Equilibrium and Non-Equilibrium Atomistic Description at Finite Temperature,” J. Mech. Phys. Solid., 56(4), pp. 1417–1449. [CrossRef]
Branduardi, D., Bussi, G., and Parrinello, M., 2012, “Metadynamics With Adaptive Gaussians,” J. Chem. Theory Comp., 8(7), pp. 2247–2254. [CrossRef]
Parrinello, M., and Rahman, A., 1981, “Polymorphic Transitions in Single-Crystals—A New Molecular-Dynamics Method,” J. Appl. Phys., 52(12), pp. 7182–7190. [CrossRef]
Wang, J. H., Li, J., Yip, S., Phillpot, S., and Wolf, D., 1995, “Mechanical Instabilities of Homogeneous Crystals,” Phys. Rev. B, 52(17), pp. 12627–12635. [CrossRef]
Falk, M. L., and Langer, J. S., 1998, “Dynamics of Viscoplastic Deformation in Amorphous Solids,” Phys. Rev. E, 57(6), pp. 7192–7205. [CrossRef]
Liu, B., Huang, Y., Jiang, H., Qu, S., and Hwang, K. C., 2004, “The Atomic-Scale Finite Element Method,” Comp. Meth. Appl. Mech. Eng., 193(17–20), pp. 1849–1864. [CrossRef]
Liu, B., Jiang, H., Huang, Y., Qu, S., Yu, M. F., and Hwang, K. C., 2005, “Atomic-Scale Finite Element Method in Multiscale Computation With Applications to Carbon Nanotubes,” Phys. Rev. B, 72(3), p. 035435. [CrossRef]
Lesar, R., Najafabadi, R., and Srolovitz, D. J., 1989, “Finite-Temperature Defect Properties From Free-Energy Minimization,” Phys. Rev. Lett., 63(6), pp. 624–627. [CrossRef] [PubMed]
Najafabadi, R., and Srolovitz, D. J., 1995, “Evaluation of the Accuracy of the Free-Energy-Minimization Method,” Phys. Rev. B, 52(13), pp. 9229–9233. [CrossRef]
Wang, H. Y., Hu, M., Xia, M. F., Ke, F. J., and Bai, Y. L., 2008, “Molecular/Cluster Statistical Thermodynamics Methods to Simulate Quasi-Static Deformations at Finite Temperature,” Int. J. Solid. Struct., 45(13), pp. 3918–3933. [CrossRef]
Jiang, H., Huang, Y., and Hwang, K. C., 2005, “A Finite-Temperature Continuum Theory Based on Interatomic Potentials,” J. Eng. Mat. Tech., 127(4), pp. 408–416. [CrossRef]
Iacobellis, V., and Behdinan, K., 2012, “Multiscale Coupling Using a Finite Element Framework at Finite Temperature,” Int. J. Num. Meth. Eng., 92(7), pp. 652–670. [CrossRef]
Guo, W., and ChangT. Z., 2002, “Freezing Atom Method in Molecular Dynamics Simulation,” Int. J. Nonlin. Sci. Num. Sim., 3(3–4), pp. 717–720. [CrossRef]
Verlet, L., 1967, “Computer Experiments on Classical Fluids. I. Thermodynamical Properties of Lennard–Jones Molecules,” Phys. Rev., 159(1), pp. 98–103. [CrossRef]
Verlet, L., 1968, “Computer Experiments on Classical Fluids. 2. Equilibrium Correlation Functions,” Phys. Rev., 165(1), pp. 201–214. [CrossRef]
Hockney, R. W., and Eastwood, J. W., 1981, Computer Simulation Using Particles, McGraw-Hill, New York.
Yakobson, B. I., Dumitrica, T., and Hua, M., 2006, “Symmetry-, Time-, and Temperature-Dependent Strength of Carbon Nanotubes,” Proc. Natl. Acad. Sci. USA, 103(16), pp. 6105–6109. [CrossRef]
Wang, X., Li, Q., Xie, J., Jin, Z., Wang, J., Li, Y., Jiang, K., and Fan, S., 2009, “Fabrication of Ultralong and Electrically Uniform Single-Walled Carbon Nanotubes on Clean Substrates,” Nano Lett., 9(9), pp. 3137–3141. [CrossRef] [PubMed]
Yakobson, B. I., Campbell, M. P., Brabec, C. J., and Bernholc, J., 1997, “High Strain Rate Fracture and C-Chain Unraveling in Carbon Nanotubes,” Computat. Mater. Sci., 8(4), pp. 341–348. [CrossRef]
Ruoff, R. S., Yu, M. F., Files, B. S., and Arepalli, S., 2000, “Tensile Loading of Ropes of Single Wall Carbon Nanotubes and Their Mechanical Properties,” Phys. Rev. Lett., 84(24), pp. 5552–5555. [CrossRef] [PubMed]
Jose-Yacaman, M., Troiani, H. E., Miki-Yoshida, M., Camacho-Bragado, G. A., Marques, M.A.L., Rubio, A., and Ascencio, J. A., 2003, “Direct Observation of the Mechanical Properties of Single-Walled Carbon Nanotubes and Their Junctions at the Atomic Level,” Nano Lett., 3(6), pp. 751–755. [CrossRef]
Brenner, D. W., Shenderova, O. A., Harrison, J. A., Stuart, S. J., Ni, B., and Sinnott, S. B., 2002, “A Second-Generation Reactive Empirical Bond Order (Rebo) Potential Energy Expression for Hydrocarbons,” J. Phys. Conden. Matt., 14(4), pp. 783–802. [CrossRef]
Nose, S., 1984, “A Molecular-Dynamics Method for Simulations in the Canonical Ensemble,” Molecular Phys., 52(2), pp. 255–268. [CrossRef]
Hoover, W. G., 1985, “Canonical Dynamics—Equilibrium Phase-Space Distributions,” Phys. Rev. A, 31(3), pp. 1695–1697. [CrossRef] [PubMed]
Hone, J., Lee, C., Wei, X. D., and Kysar, J. W., 2008, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene,” Science, 321(5887), pp. 385–388. [CrossRef] [PubMed]
Xu, R., Liu, B., and Dong, Y., 2013, “Scalable Hierarchical Parallel Algorithm for the Solution of Super Large-Scale Sparse Linear Equations,” ASME J. Appl. Mech., 80(2), pp. 020901–8. [CrossRef]
Andersen, H. C., 1980, “Molecular-Dynamics Simulations at Constant Pressure and/or Temperature,” J. Chem. Phys., 72(4), pp. 2384–2393. [CrossRef]
Jiang, H., Yu, M. F., Liu, B., and Huang, Y., 2004, “Intrinsic Energy Loss Mechanisms in a Cantilevered Carbon Nanotube Beam Oscillator,” Phys. Rev. Lett., 93(18), p 185501. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Schematic flow chart of hybrid molecular dynamics/atomic-scale finite element method for quasi-static atomistic simulations at finite temperature

Grahic Jump Location
Fig. 2

The potential energy variation of (8,8) CNT in step-by-step tensile test simulated by the hybrid MD/AFEM atomic quasi-static algorithm at T = 150 K and T = 300 K

Grahic Jump Location
Fig. 3

(a) The static 2D axial tensile stress as function of tensile strain for (8,8) CNT at different temperatures; (b) the temperature dependence of the tensile modulus of (8,8) single-wall CNT

Grahic Jump Location
Fig. 4

The required CPU time of the hybrid AFEM/MD method and the pure MD to acquire the steady deformed configurations of initially straight (5,5) armchair carbon nanotubes subject to the lateral force

Grahic Jump Location
Fig. 5

Schematic flow chart of stirring-accelerated MD/AFEM relaxation method for nonequilibrium molecular systems

Grahic Jump Location
Fig. 6

(a) Schematic diagram of an (8,8) single wall CNT subject to a axial displacement loading in the middle, and the displacement loading is suddenly released at 0 ps. (b) The variation of potential energy of CNT versus time of three relaxation simulations: MD without any interference (i.e., free vibration). (c) MD with Nose–Hoover thermostat at 300 K and (d) stirring-accelerated MD/AFEM relaxation.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In