Homogeneous Materials Using

10/30/2013

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
)

10/30/2013

3

Outline



Brief

review

of

major

macroscopic

dynamic

fracture

approaches


Hybrid

lattice

particle

modeling

(HLPM)



HLPM

of

wave

propagation

and

applications


Conclusions

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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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6

Simulations with meshing techniques

Meshless (SPH)

Lagrange

Euler

ALE

(Arbitrary Lagrange Euler)

FEM

(AUTODYN course materials)

10/30/2013

7

Outline



Brief

review

of

major

dynamic

fracture

approaches


Hybrid

lattice

particle

modeling

(HLPM)



HLPM

of

wave

propagation

and

applications


Conclusions


10/30/2013

8

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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9

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

10/30/2013

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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11

1
-
D: L=12.7
cm

2
-
D: A=12.7x1.21

(cont.)

Using dynamic BC



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12


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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13

Vertical amplitude

(cont.)

Using Kinematic BC

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14


Kinematic BC:

constantly

Wave propagation speed: 2133.0 m/s

Horizontal amplitude

(cont.)

Using Kinematic BC

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15

Vertical amplitude

Applications

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16

(a) HLPM simulations

(b) MD simulations

(A. M. Krivtsov, 2004)

Spall Crack Formation

(cont.)

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17

HLPM simulations

(a) weak interface interaction

(b) strong interface interaction

(cont.)

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18

Cavity Blasting

HLPM simulations

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19

Outline



Brief

review

of

major

dynamic

fracture

approaches


Hybrid

lattice

particle

modeling

(HLPM)



HLPM

of

wave

propagation

and

applications


Conclusions

10/30/2013

20

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.