Abstract

Motivated by the need for a more efficient simulation of material behavior at both larger length scale and longer time scale than direct molecular dynamics simulation, an atomistic field theory (AFT) for modeling and simulation of multiphase material systems has been developed. Atomistic formulation of the multiscale field theory and its corresponding finite element implementation are briefly introduced. By virtue of finite element analysis of classical continuum mechanics, we show the existing phenomena of spurious wave reflections at the interfaces between regions with different mesh sizes. AFT is employed to investigate the wave propagation in magnesium oxide from the atomistic region to the continuum region without any special numerical treatment. Unlike some other atomistic/continuum computational methods, AFT has demonstrated the capability to display both acoustic and optic types of wave motion. Numerical results show that AFT has the capability to significantly reduce the wave reflections at the interface. This work provides a more fundamental understanding of wave reflections at the atomistic/continuum interface.

1.
Li
,
S.
,
Liu
,
X.
,
Agrawal
,
A.
, and
To
,
A. C.
, 2006, “
Perfectly Matched Multiscale Simulations for Discrete Systems: Extension to Multiple Dimensions
,”
Phys. Rev. B
0556-2805,
74
, p.
045418
.
2.
Abraham
,
F. F.
,
Broughton
,
J. Q.
,
Bernstein
,
N.
, and
Kaxiras
,
E.
, 1998, “
Spanning the Continuum to Quantum Length Scales in a Dynamic Simulation of Brittle Fracture
,”
Europhys. Lett.
0295-5075,
44
(
6
), pp.
783
787
.
3.
Broughton
,
J. Q.
,
Abraham
,
F. F.
,
Bernstein
,
N.
, and
Kaxiras
,
E.
, 1999, “
Concurrent Coupling of Length Scales: Methodology and Applications
,”
Phys. Rev. B
0556-2805,
60
, pp.
2391
2403
.
4.
Rudd
,
R. E.
, 2001, “
Concurrent Multiscale Modeling of Embedded Nanomechanics
,”
Mater. Res. Soc. Symp. Proc.
0272-9172,
677
, pp.
1.6.1
1.6.12
.
5.
Rudd
,
R. E.
, and
Broughton
,
J. Q.
, 2000, “
Concurrent Coupling of Length Scales in Solid State Systems
,”
Phys. Status Solidi B
0370-1972,
217
, pp.
251
291
.
6.
Rudd
,
R. E.
, and
Broughton
,
J. Q.
, 1998, “
Coarse-Grained Molecular Dynamics and the Atomic Limit of Finite Element
,”
Phys. Rev. B
0556-2805,
58
, pp.
R5893
R5896
.
7.
Cai
,
W.
,
de Koning
,
M.
,
Bulatov
,
V. V.
, and
Yip
,
S.
, 2000, “
Minimizing Boundary Reflections in Coupled-Domain Simulations
,”
Phys. Rev. Lett.
0031-9007,
85
(
15
), pp.
3213
3216
.
8.
Wagner
,
G. J.
, and
Liu
,
W. K.
, 2003, “
Coupling of Atomistic and Continuum Simulations Using a Bridging Scale Decomposition
,”
J. Comput. Phys.
0021-9991,
190
, pp.
249
274
.
9.
To
,
A. C.
, and
Li
,
S.
, 2005, “
Perfectly Matched Multiscale Simulations
,”
Phys. Rev. B
0556-2805,
72
(
3
), p.
035414
.
10.
E
,
W.
, and
Huang
,
Z.
, 2001, “
Matching Conditions in Atomistic-Continuum Modeling of Materials
,”
Phys. Rev. Lett.
0031-9007,
87
, p.
135501
.
11.
E
,
W.
, and
Huang
,
Z.
, 2002, “
A Dynamic Atomistic-Continuum Method for the Simulation of Crystalline Materials
,”
J. Comput. Phys.
0021-9991,
182
, pp.
234
261
.
12.
Li
,
X.
and
E
,
W.
, 2005, “
Multiscale Modeling of Dynamics of Solids at Finite Temperature
,”
J. Mech. Phys. Solids
0022-5096,
53
, pp.
1650
1685
.
13.
E
,
W.
,
Engquist
,
B.
,
Li
,
X.
,
Ren
,
W.
, and
Vanden-Eijnden
,
E.
, 2007, “
The Heterogeneous Multiscale Method: A Review
,”
Comm. Comp. Phys.
1815-2406,
2
(
3
), pp.
367
450
.
14.
Belytschko
,
T.
, and
Xiao
,
S. P.
, 2003, “
Coupling Methods for Continuum Model With Molecular Model
,”
Int. J. Multiscale Comp. Eng.
1543-1649,
1
, pp.
115
126
.
15.
Xiao
,
S. P.
, and
Belytsckko
,
T.
, 2004, “
A Bridging Domain Method for Coupling Continua With Molecular Dynamics
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
, pp.
1645
1669
.
16.
Tadmor
,
E. B.
,
Ortiz
,
M.
, and
Phillips
,
R.
, 1996, “
Quasicontinuum Analysis of Defects in Solids
,”
Philos. Mag.
1478-6435,
73
, pp.
1529
1563
.
17.
Curtin
,
W. A.
, and
Miller
,
R. E.
, 2003, “
Atomistic/Continuum Coupling in Computational Materials Science
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
11
, pp.
R33
R68
.
18.
Eringen
,
A. C.
, and
Suhubi
,
E. S.
, 1964, “
Nonlinear Theory of Simple Micro-Elastic Solids I
,”
Int. J. Eng. Sci.
0020-7225,
2
, pp.
189
203
.
19.
Eringen
,
A. C.
, 1999,
Microcontinuum Field Theories—I: Foundations and Solids
,
Springer
,
New York
.
20.
Eringen
,
A. C.
, 2001,
Microcontinuum Field Theories–II: Fluent Media
,
Springer
,
New York
.
21.
Chen
,
Y.
,
Lee
,
J. D.
, and
Eskandarian
,
A.
, 2003, “
Examining Physical Foundation of Continuum Theories From Viewpoint of Phonon Dispersion Relations
,”
Int. J. Eng. Sci.
0020-7225,
41
, pp.
61
83
.
22.
Irving
,
J. H.
, and
Kirkwood
,
J. G.
, 1950, “
The Statistical Theory of Transport Processes. IV. The Equations of Hydrodynamics
,”
J. Chem. Phys.
0021-9606,
18
, pp.
817
829
.
23.
Hardy
,
R. J.
, 1982, “
Formulas for Determining Local Properties in Molecular-Dynamics Simulations: Shock Waves
,”
J. Chem. Phys.
0021-9606,
76
(
1
), pp.
622
628
.
24.
Chen
,
Y.
, and
Lee
,
J. D.
, 2003, “
Connecting Molecular Dynamics to Micromorphic Theory. Part I: Instantaneous Mechanical Variables
,”
Physica A
0378-4371,
322
, pp.
359
376
.
25.
Chen
,
Y.
, and
Lee
,
J. D.
, 2003, “
Connecting Molecular Dynamics to Micromorphic Theory. Part II: Balance Laws
,”
Physica A
0378-4371,
322
, pp.
377
392
.
26.
Chen
,
Y.
, and
Lee
,
J. D.
, 2005, “
Atomistic Formulation of a Multiscale Theory for Nano/Micro Physics
,”
Philos. Mag.
1478-6435,
85
, pp.
4095
4126
.
27.
Chen
,
Y.
, and
Lee
,
J. D.
, 2006, “
Conservation Laws at Nano/Micro Scales
,”
J. Mech. Mater. Struct.
1559-3959,
1
, pp.
681
704
.
28.
Chen
,
Y.
,
Lee
,
J. D.
, and
Xiong
,
L.
, 2006, “
Stresses and Strains at Nano/Micro Scales
,”
J. Mech. Mater. Struct.
1559-3959,
1
, pp.
705
723
.
29.
Chen
,
Y.
,
Lee
,
J. D.
,
Lei
,
Y.
, and
Xiong
,
L.
, 2006, “
A Multiscale Field Theory: Nano/Micro Materials
,”
Multiscaling in Molecular and Continuum Mechanics: Interaction of Time and Size From Macro to Nano
,
Springer
,
New York
, pp.
23
65
.
30.
Chen
,
Y.
,
Lee
,
J. D.
, and
Xiong
,
L.
, 2009, “
A Generalized Continuum Theory for Modeling of Multiscale Material Behavior
,”
J. Eng. Mech.
0733-9399,
135
(
3
), pp.
149
155
.
31.
Lee
,
J. D.
,
Wang
,
X.
, and
Chen
,
Y.
, 2009, “
Multiscale Material Modeling and Its Application to a Dynamic Crack Propagation Problem
,”
Theor. Appl. Fract. Mech.
0167-8442,
51
(
1
), pp.
33
40
.
32.
Chen
,
Y.
, 2009, “
Reformulation of Microscopic Balance Equations for Multiscale Materials Modeling
,”
J. Chem. Phys.
0021-9606,
130
(
13
), p.
134706
.
33.
Grimes
,
R. W.
, 1994, “
Solution of MgO, CaO, and TiO2 in α-Al2O3
,”
J. Am. Ceram. Soc.
0002-7820,
77
, pp.
378
384
.
34.
Holmes
,
N.
, and
Belytschko
,
T.
, 1976, “
Postprocessing of Finite Element Transient Response Calculations by Digital Filters
,”
Comput. Struc.
,
6
, pp.
211
216
.
You do not currently have access to this content.