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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

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

Bin Liu

AML
CNMM
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.

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Fig. 1

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

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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

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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

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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

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Fig. 5

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

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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.

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