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