Multiscale Considerations in Modeling of Nonlinear Elastomers H.T. ...

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1. REPORT DATE

3. DATES COVERED 2. REPORT TYPE

2003

00-00-2003 to 00-00-2003

4. TITLE AND SUBTITLE

5a. CONTRACT NUMBER

Multiscale Considerations in Modeling of Nonlinear Elastomers

5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

North Carolina State University,Center for Research in Scientific Computation,Raleigh,NC,27695-8205 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

8. PERFORMING ORGANIZATION REPORT NUMBER

10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S)

12. DISTRIBUTION/AVAILABILITY STATEMENT

Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT

see report 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF:

17. LIMITATION OF ABSTRACT

a. REPORT

b. ABSTRACT

c. THIS PAGE

unclassified

unclassified

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17

Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

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3

Linear fit to load cell cdata for unfilled rubber sample, small weight

10

3.5

3

Data 2.5 Square Window FFT

Force (pounds)

2

2

1.5

10

Aprx

1

10

1 Data 0.5

0 0

Aprx 0

0.5

1

1.5

2 2.5 Time (seconds)

3

3.5

4

10

0

5

10

15 Frequency (hz)

20

25

30

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‚„ƒ:…i†h‡rˆH‰ Šu…+‹ŒŽ!ˆ‡‘‹ ’Š‘†h‡“Ž!ˆ r AP225

AP225

300

300

data computed

data computed 250 250

200

stress

stress

200

150

150 100

100 50

50 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2

0.3

0.4

0.5

0.6 strain

0.7

0.8

0.9

1

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, gv

e

power spectrum for 3 lb tip mass

3

10

8

data computed

data computed 7

6 2

10

~

log(100|f |)

Force (pounds)

5

4

3

1

10 2

1

0

0

0

0.5

1

1.5

2 Time (sec)

2.5

3

3.5

4

10

0

5

10

15 Frequency (hz)

20

25

30

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‚„ƒ:…i†h‡rˆH‰ Šu…+‹ŒŽ!ˆ‡‘‹ ’Š‘†h‡“Ž!ˆ highly filled rubber sample

highly filled sample

30

30

25

25

20

20 Force (pounds)

Force (pounds)

computed data

15

15

10

10

5

5

0

0

0.1

0.2

0.3

0.4

0.5 Time (sec)

0.6

0.7

0.8

0.9

1

0

0

0.2

0.4

0.6

0.8 Time (sec)

1

1.2

1.4

1.6

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computed data 1

force

0

−1

−2

−3

−4

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

time

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Acceleration data and the approximated values

3

2 computed data

computed data

1

acceleration (g)

acceleration (g)

2

0 −1 −2

1

0

−1

−3 −4

0

0.01

0.02

0.03

0.04

0.05 time (sec)

0.06

0.07

0.08

0.09

−2

0.1

0

0.01

0.02

Comparison of load cell data and the model predicted values

0.05 time (sec)

0.06

0.07

0.08

0.09

0.1

15 computed data

computed data

10 load cell (lb)

10 load cell (lb)

0.04

Comparison of load cell data and the model predicted values

20

0 −10 −20 −30

0.03

5 0 −5 −10

0

0.01

0.02

0.03

0.04

0.05 time (sec)

0.06

0.07

0.08

0.09

−15

0.1

0

0.01

0.02

0.03

0.04

0.05 time (sec)

0.06

0.07

0.08

0.09

0.1

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