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Linear Viscoelasticity

Linear Viscoelasticity. Elastic Response. Viscous Response. Maxwell Model. Creep. Stress Relaxation due to Maxwell. Voigt Model. Creep due to Voigt. Relaxation. Combination of Maxwell and Voigt. Burgers Model. Generalized Models. Continues Distribution: Maxwell.

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Linear Viscoelasticity

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  1. Linear Viscoelasticity

  2. Elastic Response

  3. Viscous Response

  4. Maxwell Model

  5. Creep

  6. Stress Relaxation due to Maxwell

  7. Voigt Model

  8. Creep due to Voigt Relaxation

  9. Combination of Maxwell and Voigt

  10. Burgers Model

  11. Generalized Models

  12. Continues Distribution: Maxwell

  13. Continues Distribution: Voigt

  14. Superposition Principle

  15. Dynamic Response Output: Input: Viscoelastic body For a dashpot: Stress: Moduli:

  16. Complex Representation:

  17. Time Scales

  18. TTT (if it would be right….) It is because

  19. Master curve for Polymers

  20. Composition of Relaxations: phase shift

  21. Comparison of E(T) and E(t)

  22. General Constitutive Law We can re-write this in the form: than we generalize the Elastic law: If we define and, for example: It might be shown that

  23. Laplace Transform

  24. Properties of Laplace Transform

  25. Linear Viscoelasticity (no time, so far)

  26. Laplace… Laplace transform of this function leads to Similarly for m Finally:

  27. Examples of Operators Boltzmann kernel Boltzmann without singularity No infinite rate of deformation

  28. Homework • Pick a Linear viscoelastic moduli • Solve the Lame problem

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