Transcript Maxwell Model (Exponential) R ξ The equation for this system is trivial and can be found Halliday & Resnick 6th edition4. V=ξ*e-t/ C V= Voltage (output) ξ = Battery Voltage.

Maxwell Model (Exponential)
R
ξ
The equation for this
system is trivial and can
be found Halliday &
Resnick 6th edition4.
V=ξ*e-t/
C
V= Voltage (output)
ξ = Battery Voltage (Vo)
t= time
 = RC : time constant
Maxwell model of Rubber
X error = 583248.5889
Y error = 347.4848
Predicted 1
Data 1
Load (N)
Stress Relaxation
101
100
99
98
97
96
95
94
93
0.00
20.00
40.00
60.00
Time (sec)
80.00
100.00
120.00
Ryan Palmer
Voight Model (Non Linear)
R1
Xc =
ξ
Xc
ω = 2πƒ
ƒ = 1/t
R2
Rubber
1.44E-04
-6.98E+05
60000
1.00E-04
Fo
R1
R2
C
Gelatin
1.25E-06
-3.55E+05
300000
1.00E-04
Fo
R1
R2
C
Voight Model of Rubber
X error = 1370.4587 Y error = 3.0627
Stress Relaxation
Data 1
Predicted 1
101.00
Load (N)
100.00
99.00
98.00
97.00
96.00
95.00
94.00
0.00
20.00
40.00
60.00
80.00
Time (sec)
100.00
120.00
Ryan Palmer
Kelvin Model (Non Linear)
Rubber
Xc1
ξ
R1
Vo
R1
R2
C1
C2
Xc2
Xc =
ω = 2πƒ
ƒ = 1/t
100.82
0.002393
0.0889839
7.90E+01
1.00E-04
Gelatin
Vo
R1
R2
C1
C2
1.00E-10
-4428227743.65936
4694995547.0000000
-500000
5.00E+05
Kelvin Model of Rubber
X error = 796.8549
Y error = 1.6167
Data 1
Stress Relaxation
Predicted 1
101.00
Load (N)
100.00
99.00
98.00
97.00
96.00
95.00
94.00
93.00
0.00
20.00
40.00
60.00
Time (sec)
80.00
100.00
120.00
Ryan Palmer
Maxwell Model of Gelatin
X error = 8665164.5696
Y error = 17.6484
Data A1FS
Stress Relaxation
Predicted
Load (N)
0.4
0.3
0.2
0.1
0
0
50
100
150
Time (sec)
200
250
300
Ryan Palmer
Voight Model of Gelatin
X error = 313571.7025
Y error = 0.1167
Stress Relaxation of Gelatin
Predicted A1FS
Data A1FS
4.75E-01
Load (N)
4.25E-01
3.75E-01
3.25E-01
2.75E-01
2.25E-01
1.75E-01
0
50
100
150
Time (sec)
200
250
300
Ryan Palmer
Kelvin Model of Gelatin
X error = 239135.3187
Y error = 0.1165
Data A1FS
Stress Relaxation
Predicted A1FS
0.45
Load (N)
0.4
0.35
0.3
0.25
0.2
0
50
100
150
Time (sec)
200
250
300
Ryan Palmer
Summary of Results
Type/Material
X error
Y error
Maxwell/Rubber
583248.5889
347.4848
Voight/Rubber
1370.4587
3.0627
Kelvin/Rubber
796.8549
1.6167
Maxwell/Gelatin
8665164.5696
17.6484
Voight/Gelatin
313571.7025
0.1167
Kelvin/Gelatin
239135.3187
0.1165
Ryan Palmer
Future Research

Gelatin concentrations?
 Displacement?
 Rate of displacement?
 Can Collagen, Fibrin, Thrombin and other
materials found within the skin be modeled in a
similar fashion?

I Believe that the main focus will need to turn
towards including the rate displacement, specific
displacement.
Thank you


1.
2.
3.
4.
5.
Professor Watts
Dr. Fogel
Dr. Le Blanc
Dr. Shaw
Grant Toland
References:
www.dermagraft.com
http://www.cdc.gov/diabetes/pubs/pdf/ndfs_2003.pdf
Hertzberg, Richard W. Deformation and fracture
mechanics of engineering materials. John Wiley & Sons
Inc., 1976, 1983
Halliday, Resnick, Walker. Fundamentals of Physics. 6th
edition. John Wiley & Sons Inc., 2001
http://www.brainydictionary.com/words/da/dashpot151217
.html
Gelatin

Broken down collagen (structural protein).
 Fibrous molecule that is involved in skin,
bone, and tendons (attributes to elasticity).
 Collagen cross-linking corresponds with
age, decreasing the elasticity within skin,
bones etc.
Background & Significance1

16 Million people in U.S. suffer from Diabetes ~
6% of population.
 15% of Diabetic Patients will develop a lower
extremity ulcer during their life with the disease.
 Reports indicate $6 billion annual cost for Ulcer
care and Amputations.
 82,000 non-traumatic lower-limb amputations
were performed in 2000-20012