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1
Wave Propagation Prediction in
Homogeneous Materials Using
Hybrid Lattice Particle Modeling
Investigators: Ge Wang, Ahmed. Al

Ostaz,
Alexander H.

D. Cheng and P. Raju Mantena
Civil Engineering Department
University of Mississippi
Research Background
Dynamic
deformation
often
involves
wave
propagation,
i
.
e
.
,
stress
has
to
travel
through
the
material
body
.
Dynamic
fracture
and
fragmentation
under
high
strain
rate
loads
(impact,
blasting,
crush,
collapse,
high
speed
puncture/penetration,
comminution,
.
etc
.
)
has
broad
civilian/military
applications
.
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2
Hopkinson Bar Test
(by M.A. Kaiser, 1998)
Shock on a sharp

nosed
supersonic body
Spallation as a result of impact without
penetration of the impacting object
(
http://en.wikipedia.org/wiki
)
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3
Outline
Brief
review
of
major
macroscopic
dynamic
fracture
approaches
Hybrid
lattice
particle
modeling
(HLPM)
HLPM
of
wave
propagation
and
applications
Conclusions
10/30/2013
4
Outline
Brief
review
of
major
dynamic
fracture
approaches
Hybrid
lattice
particle
modeling
(HLPM)
HLPM
of
wave
propagation
and
applications
Conclusions
1. Brief review of major dynamic
fracture approaches
Continuum
Mechanics
Based
Approaches
(CMBA)
:
FEM
Discrete
Element
Based
Approaches
(DEBA)
:
PFC,
SPH,
PM,
etc
.
Combinations
of
CMBA

DEBA
:
PFEM,
MPM
(material
point
method),
etc
.
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5
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Simulations with meshing techniques
Meshless (SPH)
Lagrange
Euler
ALE
(Arbitrary Lagrange Euler)
FEM
(AUTODYN course materials)
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Outline
Brief
review
of
major
dynamic
fracture
approaches
Hybrid
lattice
particle
modeling
(HLPM)
HLPM
of
wave
propagation
and
applications
Conclusions
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Hybrid Lattice Particle Modeling (HLPM) of Dynamic Fragmentation of Solids
Ge Wang, Ahmed Al

Ostaz, Alexander H.

D. Cheng and P. Raju Mantena
Department of Civil Engineering, the University of Mississippi, MS 38655, http://www.olemiss.edu/~gewang
Motivations
Mechanical
behavior
of
a
solid
material
is
controlled
by
its
microstructure
.
Complex
macroscopic
behaviors,
such
as
fracture
and
failure,
arise
from
microstructure
interactions
.
Thus,
if
the
microstructure
and
the
microstructural
interactions
within
a
numerical
model
could
be
correctly
and
accurately
replicated,
then
that
model
should
precisely
reproduce
the
macroscopic
behaviors
.
However,
current
computing
power
limits
the
size
of
the
atomic
ensemble
to
numbers
of
atoms
that
are
too
small
to
be
useful
for
most
engineering

scale
systems
.
Hybrid
Lattice
Particle
Modeling
(HLPM)
is
developed
to
directly
mi mic
microstructural
features
and
can
be
executed
in
reasonable
times
on
standard
computers
.
Model Introduction
H
LPM
is
a
dynamic
simulation
that
uses
small
discrete
solid
physical
particle
(or
quasi

molecular
particles)
as
a
representation
of
a
given
fluid
or
solid
.
Different
particle
interaction
schemes
and
mesh
structures
can
be
adopted
.
It
combines
the
knowledge
of
both
lattice
modeling
and
particle
modeling
.
Interactions of HLPM
Linear:
Non

linear:
(a) Polynomial
(b) Lennard
–
Jones
Validations of HLPM
(a) Epoxy in tension (b) Indentation of polymeric materials
Meshing structures
Applications of HLPM
High strain rate loading:
Thermally induced fracture:
(a) Temperature
(b) Fracture
Mixture
of
calcite
and
pyrite
subject
to
a
microwave
Blasting:
Crack propagation:
Spallation of plate impact:
Wave propagation:
3

D puncture/penetration:
Numerical discretization scheme in PFC (particle
flow code), PFEM (particle finite element method)
and HLPM
PFC
HLPM
PFEM
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critical time increment:
k
: the stiffness
m
: a point mass
x
:
displacement
critical time increment:
k
: the stiffness
m
: a point mass
u
:
displacement
critical time increment:
k
: the stiffness
m
: a point mass
r
:
displacement
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10
Outline
Brief
review
of
major
dynamic
fracture
approaches
Hybrid
lattice
particle
modeling
(HLPM)
HLPM
of
wave
propagation
and
applications
Conclusions
HLPM simulations of Wave Propagation
Prediction in Homogeneous Materials
Problem descriptions:
Material properties:
Theoretical wave propagation speeds:
1

D:
2

D:
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1

D: L=12.7
cm
2

D: A=12.7x1.21
(cont.)
Using dynamic BC
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Dynamics BC:
. Duration=
Wave propagation speed: (i)
1D
: 2000.0 m/s; (ii)
2D
: 2133.0 m/s
Horizontal amplitude
(cont.)
Using dynamic BC
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Vertical amplitude
(cont.)
Using Kinematic BC
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Kinematic BC:
constantly
Wave propagation speed: 2133.0 m/s
Horizontal amplitude
(cont.)
Using Kinematic BC
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Vertical amplitude
Applications
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(a) HLPM simulations
(b) MD simulations
(A. M. Krivtsov, 2004)
Spall Crack Formation
(cont.)
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HLPM simulations
(a) weak interface interaction
(b) strong interface interaction
(cont.)
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Cavity Blasting
HLPM simulations
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Outline
Brief
review
of
major
dynamic
fracture
approaches
Hybrid
lattice
particle
modeling
(HLPM)
HLPM
of
wave
propagation
and
applications
Conclusions
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Conclusions
Hybrid
lattice
particle
modeling
(HLPM)
can
be
an
alternative
tool
to
explore
wave
propagation
in
materials
.
HLPM
is
being
developed
ultimately
for
investigating
shock
wave
related
problems
.
Validations
are
required
in
the
coming
stage
.
October 30, 2013
21
Grant Acknowledgement
Department of Homeland Security

through Southeast Region Research
Initiative (SERRI), USA.
ONR, Office of Naval Research, Solid Mechanics Program, USA.
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