Los Alamos National Laboratory/LANL_CD.ISO/stills/mat_mod.txt

Text File | 1992-12-01 | 7KB | 189 lines

MATERIALS MODEL-
ING VIA MASSIVELY
PARALLEL MOLECU-
LAR DYNAMICS

At Los Alamos, we have embarked
upon a program to study the behavior
of materials under the influence of
external stresses and heat flow, using
the method of molecular dynamics
(MD), where the motion of millions of
strongly interacting atoms or molecules
is followed on a computer. Because the
complex flow phenomena occur on
much larger distance scales than do
molecular sizes and spacings, and
because the time scales of interest are
much longer than are vibrational peri-
ods or mean collision times, we are
using the massively parallel CM-5 at
the ACL for these simulations. On the
earlier version of this machine (CM-2),
we were able to carry out preliminary
simulations of 106 atoms for over 1000
vibrational periods, using some 50
hours of cpu time. For these 2D calcula-
tions, the linear dimension is 0.3
micrometers, and the physical time
duration is a nanosecond. In fact, we
have shown that 8 x 106 atoms are feasi-
ble on the CM-2, and 3 x 107 atoms can
be simulated on the CM-5, which is
estimated to be capable of 10 times the
clock speed of the CM-2 by the end of
1992. This order of magnitude increase
in both size and speed of the CM-5 rela-
tive to the CM-2 is comparable to the
relative advantages of the CM-2 over
the single-processor Cray Y-MP. On the
CM-5, we may be able to extend the
physical time simulated to 0.1 ms, for
cpu times of less than 200 hours.

 The Fortran 90 MD code on the Con-
nection Machines has been written in
such a way that a variety of geometries
(initial conditions) and external driving
forces (boundary conditions) are easily
implemented. For bulk materials,
where periodic boundary conditions
are appropriate, three distinct kinds of
dynamics are available: (1) the usual
Newtonian equations of motion (micro-
canonical ensemble - NVE - constant
number of particles N, constant volume
V, constant total energy E, as well as
constant total linear momentum); (2)
isothermal Nose'-Hoover MD (canoni-
cal ensemble - NVT - where T is the
temperature of the heat bath); and (3)
isothermal-isobaric Nose'-Hoover MD
(NPT - where P is the diagonal of the
pressure tensor). In addition to these
special ensemble dynamics, the peri-
odic boundaries under Newtonian
mechanics can be moved at constant
independent velocities. If correspond-
ing velocity gradients are imposed
upon the peculiar momenta of the
atoms, homogeneous adiabatic expan-
sion can be simulated; otherwise, inho-
mogeneous shock waves can be
generated. Moreover, boundary-driven
flows, such as either Couette shear flow
or heat flow between hot and cold
walls, can be simulated. Simple geo-
metric objects (e.g., free surfaces,
spheres, and plates) can be generated
and given body velocities. Input to the
code at setup time and for restarts is
uncomplicated, and modifications of
the MD code to do more complicated
initial and boundary conditions is not
difficult.

 The particle positions and momenta
are updated by integrating the equa-
tions of motion via the Stoermer (or
Verlet) method of finite central differ-
ences. In the case of Nose'-Hoover
dynamics, the handful of global control
variables for coupling of the thermostat
and barostat are also easily handled by
the Stoermer method. In addition to
being time-reversible and very robust
(e.g., energy and linear momentum are
well conserved over long trajectory
times), Stoermer integration minimizes
memory requirements to arrays for the
phase (particle coordinates and
momenta) and forces, plus the few sca-
lars for the Nose'-Hoover coupling
variables.

 We have applied this parallel MD code
to shock-wave propagation, annealing
of polycrystalline materials, and spalla-
tion phenomena (fracture). Shock-wave
simulations revealed similar induced
plasticity for ductile materials, whose
atoms interact via a many-body embed-
ded-atom method (EAM) potential
appropriate for metals, compared with
brittle pair-potential materials - at least
in 2D, where dislocations are more eas-
ily formed than in 3D. The annealing
calculations demonstrate that coarsen-
ing of grains proceeds by the motion of
grain boundaries in the direction of
concavity (big grains gobble up little
ones), so that the average linear dimen-
sion grows with time t like t0.3. Spalla-
tion occurs when a thin plate of
material hits a thicker target at suffi-
cient velocity. The shock waves gener-
ated on impact are relieved by
rarefaction waves at the free surfaces
opposite the impact plane. When the
rarefactions meet at the spall plane, the
material is put into tension; if the
impact is hard enough, the material
expands until it breaks. Our MD simu-
lations showed that homogeneous
uniaxial adiabatic expansion (linear
velocity profile about the spall plane) is
an excellent approximation. Moreover,
a simple dislocation-motion model
accounts well for the stress at failure, as
a function of the imposed strain rate.

 We are planning to apply this versatile
MD code (in both 2D and 3D) to a wide
variety of interesting phenomena,
including fracture under various exter-
nal driving forces, dislocation genera-
tion at crack tips, shock-wave-induced
plasticity in granular (polycrystalline)
solids, ablation of surfaces by radiation
(in collaboration with 3M), chemically
reactive flow (as in detonation waves,
in collaboration with the Naval
Research Laboratory), and polymer
dynamics problems, including simula-
tion of the flow of colloidal suspensions
(in collaboration with du Pont). Many
of these applications directly impact the
development and manufacturing of
novel materials by American industry.

The first sequence (TXY) shows a MD simula-
tion of shock wave in a 2D Lennard-
Jones solid. Particle velocities are col-
ored by a rainbow ranging from -up
(deep blue) to 0 (blue-green) to +up
(bright red), where up is the piston
velocity. The shock front moves to the
right at the shock velocity (us) which
is greater than the speed of sound; the
piston is at the far left. An elastic pre-
cursor has almost reached the right-
hand edge of the window, which
includes about 1/3 of the total number
of atoms (65K). The plastic wave is
near the midpoint of the window.

The second sequence (V) shows a MD shock-
wave simulation. Local crystal orienta-
tion for each particle (hexagonal sym-
metry is assumed) is colored by a
rainbow ranging from -30 deg. relative to
the horizontal (deep blue) to 0 deg. (blue-
green) to + 30 deg. (bright red). Shock-
induced dislocation generation is
apparent near the midpoint of the
window (plastic wave front); disloca-
tion cores appear as localized spots.

Acknowledgement: Brad Holian, LANL, T-12