Maxwell Model (Exponential)Maxwell Model (Exponential)
R
C
ξ
The equation for this system is trivial and can be found Halliday & Resnick 6th edition4.
V=ξ*e-t/
V= Voltage (output)ξ = Battery Voltage (Vo)t= time = RC : time constant
Maxwell model of RubberMaxwell model of RubberX error = 583248.5889 Y error = 347.4848
Stress Relaxation
93949596979899
100101
0.00 20.00 40.00 60.00 80.00 100.00 120.00Time (sec)
Load
(N)
Predicted 1Data 1
Ryan Palmer
Voight Model (Non Linear)Voight Model (Non Linear)
Xc =
ω = 2㟟 = 1/t
1.25E-06 Fo-3.55E+05 R1
300000 R21.00E-04 C
Gelatin
ξ
R1
R2Xc
Rubber1.44E-04 Fo
-6.98E+05 R1
60000 R2
1.00E-04 C
Voight Model of RubberVoight Model of RubberX error = 1370.4587 Y error = 3.0627
Stress Relaxation
94.00
95.00
96.00
97.00
98.00
99.00
100.00
101.00
0.00 20.00 40.00 60.00 80.00 100.00 120.00
Time (sec)
Load
(N)
Data 1
Predicted 1
Ryan Palmer
Kelvin Model (Non Linear)Kelvin Model (Non Linear)
ξ
Xc1 Xc2R1
Vo 1.00E-10R1 -4428227743.65936R2 4694995547.0000000C1 -500000C2 5.00E+05
Gelatin
Rubber
Xc =
ω = 2㟟 = 1/t
Vo 100.82R1 0.002393R2 0.0889839C1 7.90E+01C2 1.00E-04
Kelvin Model of RubberKelvin Model of RubberX error = 796.8549 Y error = 1.6167
Stress Relaxation
93.00
94.00
95.00
96.00
97.00
98.00
99.00
100.00
101.00
0.00 20.00 40.00 60.00 80.00 100.00 120.00Time (sec)
Load
(N)
Data 1
Predicted 1
Ryan Palmer
Maxwell Model of GelatinMaxwell Model of GelatinX error = 8665164.5696 Y error = 17.6484
Stress Relaxation
0
0.1
0.2
0.3
0.4
0 50 100 150 200 250 300Time (sec)
Lo
ad (
N)
Data A1FS
Predicted
Ryan Palmer
Voight Model of GelatinVoight Model of GelatinX error = 313571.7025 Y error = 0.1167
Stress Relaxation of Gelatin
1.75E-01
2.25E-01
2.75E-01
3.25E-01
3.75E-01
4.25E-01
4.75E-01
0 50 100 150 200 250 300
Time (sec)
Lo
ad
(N
)
Predicted A1FS
Data A1FS
Ryan Palmer
Kelvin Model of GelatinKelvin Model of GelatinX error = 239135.3187 Y error = 0.1165
Stress Relaxation
0.2
0.25
0.3
0.35
0.4
0.45
0 50 100 150 200 250 300
Time (sec)
Lo
ad (
N)
Data A1FS
Predicted A1FS
Ryan Palmer
Summary of ResultsSummary 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 0.1165Ryan Palmer
Future ResearchFuture 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 youThank you Dr. Fogel Dr. Shaw
References:1. www.dermagraft.com 2. http://www.cdc.gov/diabetes/pubs/pdf/ndfs_2003.pdf 3. Hertzberg, Richard W. Deformation and fracture
mechanics of engineering materials. John Wiley & Sons Inc., 1976, 1983
4. Halliday, Resnick, Walker. Fundamentals of Physics. 6th edition. John Wiley & Sons Inc., 2001
5. http://www.brainydictionary.com/words/da/dashpot151217.html
Professor WattsDr. Le Blanc
Grant Toland
GelatinGelatin
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 & SignificanceBackground & Significance11
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