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

26. Linear Viscoelasticity
(no time, so far)

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

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

29. Homework
Pick a Linear viscoelastic moduli
Solve the Lame problem