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Mathematical Modeling: Stress Relaxation of Viscoelastic Materials

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).

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Mathematical Modeling: Stress Relaxation of Viscoelastic Materials

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  1. Mathematical Modeling:Stress Relaxation of Viscoelastic Materials Ryan Palmer Faculty Advisor: Dr. Michael Shaw

  2. The Main Objective • Understand the viscoelastic material properties of skin • Apply knowledge towards healing chronic wounds Pictures provided by Dr. Garner (USC)

  3. Viscous: Fluid-like motion with high resistance to flow Example: Glass Elastic: Spring-like motion Example: Rubber band Viscoelasticity

  4. Gelatin Specimen Preparation at CLU R. Palmer, G. Toland • Experimental variables: • u* • du/dt • gelatin concentration Pictures and graphs provided by Dr. Shaw (CLU)

  5. Force-displacement-time schematic of experiment Force, F Indentation displacement, u Force, F 1. Apply controlled displacement until reach peak displacement, u*; monitor load t=0 t=60 u*=2.0 mm Time, t (sec) Displacement, u (mm) 2. Hold peak displacement u*; monitor load relaxation t=180 Indenter diameter = 12 mm Gel diameter = 23 mm Gel thickness ~ 4 mm Pictures and graphs provided by Dr. Shaw (CLU)

  6. Ryan Palmer Loading of specimens

  7. Ryan Palmer Stress-relaxation Curve

  8. Viscoelastic 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.

  9. Maxwell Model Maxwell Model: Consists of a spring and dashpot in series.

  10. Voight Model Voight Model: Consists of a spring and dashpot in parallel.

  11. Kelvin Model Kelvin Model- Consists of a spring in parallel with a Voight model.

  12. Viscoelasticity and RC Circuits Dashpot Resistor Capacitor Spring RC circuits are often used to simplify viscoelastic systems. Which help attain an equation to model its properties.

  13. Ryan Palmer Stress-relaxation Curve

  14. Ryan Palmer Stress-relaxation Curve Y error = Σ (Ypred. – Ydata)2 X error = Σ (Xpred. – Xdata)2 X error Y error

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