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Mathematical Modeling: Stress Relaxation of Viscoelastic Materials. Ryan Palmer Faculty Advisor: Dr. Michael Shaw. The Main Objective. Understand the viscoelastic material properties of skin Apply knowledge towards healing chronic wounds. Pictures provided by Dr. Garner (USC). - PowerPoint PPT Presentation
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Mathematical Modeling:Mathematical Modeling:Stress Relaxation of Stress Relaxation of
Viscoelastic MaterialsViscoelastic Materials
Ryan Palmer
Faculty Advisor: Dr. Michael Shaw
The Main ObjectiveThe Main Objective Understand the viscoelastic material properties of
skin Apply knowledge towards healing chronic wounds
Pictures provided by Dr. Garner (USC)
ViscoelasticityViscoelasticity
Viscous: Fluid-like motion with high resistance to flowExample: Glass
Elastic: Spring-like motionExample: Rubber band
Gelatin Specimen Preparation at Gelatin Specimen Preparation at CLUCLU
R. Palmer, G. Toland
Experimental variables:– u*– du/dt– gelatin concentration Pictures and graphs provided by
Dr. Shaw (CLU)
Force-displacement-time Force-displacement-time schematic of experimentschematic of experiment
Force, F
Time, t(sec)
Displacement, u(mm)
t=0
t=180
u*=2.0 mmt=60
1. Apply controlled displacement until reach peak displacement, u*; monitor load
2. Hold peak displacement u*; monitor load relaxation
Force, F
Indentation displacement,
u
Indenter diameter = 12 mmGel diameter = 23 mmGel thickness ~ 4 mmPictures and graphs provided by Dr. Shaw (CLU)
Stress Relaxation
0
20
40
60
80
100
120
0 50 100 150
Time (sec)
Lo
ad (
N)
Ryan Palmer
Loading of specimensLoading of specimens
Stress Relaxation
93.7594.75
95.7596.7597.75
98.7599.75
100.75
55 75 95 115 135 155 175
Time (sec)
Lo
ad (
N)
Ryan Palmer
Stress-relaxation CurveStress-relaxation CurveStress Relaxation
0
20
40
60
80
100
120
0 50 100 150
Time (sec)
Lo
ad
(N
)
Viscoelastic modelsViscoelastic models
Viscoelastic materials have been modeled by a mixture of Maxwell, Voight and Kelvin models3.
These models consist of spring and dashpot setups.
Dashpot: A pneumatic or hydraulic cushion for a falling weight, to prevent shock5.
Maxwell ModelMaxwell Model
Maxwell Model:
Consists of a spring and dashpot in
series.
Voight ModelVoight Model
Voight Model:
Consists of a spring and dashpot in
parallel.
Kelvin ModelKelvin Model
Kelvin Model-
Consists of a spring in parallel with a Voight model.
Viscoelasticity and RC Viscoelasticity and RC CircuitsCircuits
Dashpot Resistor
Spring Capacitor
RC circuits are often used to simplify viscoelastic systems.Which help attain an equation to model its properties.
Stress Relaxation
94.00
95.00
96.00
97.00
98.00
99.00
100.00
101.00
60 80 100 120 140 160 180
Time (sec)
Lo
ad
(N
)
Data
Predicted
Ryan Palmer
Stress-relaxation CurveStress-relaxation CurveStress Relaxation
0
20
40
60
80
100
120
0 50 100 150
Time (sec)
Lo
ad
(N
)
Stress Relaxation
98.00
98.20
98.40
98.60
98.80
99.00
60 65 70 75 80
Time (sec)
Lo
ad (
N)
Data
Predicted
Ryan Palmer
Stress-relaxation CurveStress-relaxation CurveStress Relaxation
94.00
95.00
96.00
97.00
98.00
99.00
100.00
101.00
60 80 100 120 140 160 180
Time (sec)
Lo
ad
(N
)
Data
Predicted
Y error = Σ (Ypred. – Ydata)2
X error = Σ (Xpred. – Xdata)2
X error
Y error