The study of deformation and stress—strain distribution of nano-scale thin sheet copper under the biaxial tensile loads by using molecular dynamics and finite-element method

Abstract

This paper investigates the strain and stress distributions in a nano-scale copper thin sheet under the biaxial tensile action, within the range of elasticity, by employing the molecular dynamics (MD) and finite-element method (FEM). Each atom is regarded as a node and the lattice as an element. The nano-scale copper thin sheet model, established in this study, is based on the face centered cubic lattice structure, and divides the lattice into 24 constant strain tetrahedron elements. After MD simulation, the biaxial force is found to be almost the same during the biaxial tensile action. Simulation results reveal that the stress and strain are highly closer at the edge of the sheet. The presence of strain around the upper and lower surfaces in the central region of the thin sheet indicates that after exhibiting biaxial tensile activity, contraction occurs in the region. The FEM/MD model, constructed in this paper directly melts the FEM spirit in MD computation. This facilitates the analysis of stress and strain in the entire nano-scale range for the nano-scale copper thin sheet.

Keywords

copper molecular dynamics finite-element method nano-scale thin sheet biaxial tension

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References

Drexler

K. E.

Nanosystems: molecular machinery, manufacturing, and computation 1992 (John Wiley & Sons, Inc. USA).

Alder

B. J.

Wainwright

T. E.

Phase transition for a hard sphere system. J. Chem. Phys. 1957 27 1208–1209.

Alder

B. J.

Wainwright

T. E.

Studies in molecular dynamics. I. General method. J. Chem. Phys. 1959 31 459–466.

Lutsko

J. F.

Stress and elastic constants in anisotropic solids: Molecular dynamics techniques. J. Appl. Phys. 1988 64(3)1152–1154.

Schotz

Rasmussen

Jacobsen

K. W.

Nielsen

O. H.

Mechanical deformation of nanocrystalline materials. Philos. Mag. Lett. 1996 74(5)339–344.

Iwaki

Molecular dynamics study on stress-strain in very thin film (size and location of region for defining stress and strain). JSMEInt.J. Ser. A 1996 39(3)346–353.

Miyazaki

Shiozaki

Calculation of mechanical properties of solids using molecular dynamics method. JSME Int.J. Ser. A 1996 39(4)606–612.

Satoshi

Takashi

Shinsuke

Study of a combined FEM-MD method for silicon. JSME Ser. A 2001 44(1)152–159.

Julia

A. S.

Leonid

V. Z.

Barbara

J. G.

A combined molecular dynamics and finite element method technique applied to laser induced press wave propagation. Comput. Phys. Commun. 1999 118 11–16.

10.

Liu

Zhang

Y. W.

A three-dimensional concurrent atomistic/continuum analysis of an eptiaxially strained island. J. Appl. Phys. 2003 94(10)6350–6353.

11.

Rudd

R. E.

Broughton

J. Q.

Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperatures. Phys. Rev. B 2005 72 144104–32.

12.

Lidorikis

Bachlechner

M. E.

Kalia

R. K.

Nakano

Vashishta

Coupling atomistic and continuum length scales in heteroepitaxial systems: Multi-scale molecular-dynamics/finite-element simulations of strain relaxation in Si/Si₃N₄ nanopixels. Phys. Rev. B 2005 72 115338–16.

13.

Lin

Z. C.

Huang

J. C.

A nano-orthogonal cutting model based on a modified molecular dynamics technique. Nanotechnology 2004 15 510–519.

14.

Gwo

Scanning probe oxidation of silicon nitride masks for nanoscale lithography, micromachining, and selective epitaxial growth on silicon. J. Phys. Chem. Solids 2001 62 1673–1687.

15.

Girifalco

L. A.

Weizer

V. G.

Application of the Morse potential function to cubic metals. Phys. Rev. 1959 31 459–466.

16.

Haile

J. M.

Molecular dynamic simulation: elementary methods 1992 (JohnWiely & Sons, Inc. USA).

17.

Verlet

Computer ‘experiments’ on classical fluids. II. Equilibrium correlation function. Phys. Rev. 1968 165 201–214.

18.

Huebner

K. H.

Thornton

E. A.

The finite element method for engineers 1995 (John Wiley & Sons New York).

19.

Benito

D. C.

Argon

A. S.

Yip

Molecular dynamics simulation of creak tip process in alapa-iron and copper. J. Appl. Phys. 1983 54(9)4864–4878.

20.

Lin

Z. C.

Huang

J. C.

A study on rigid body boundary layer interface force model for stress calculation and stress-strain behavior of nanoscale uniaxial tension. Nanotechnology 2004 15 1509–1518.