1. Chapter 2 Elasticity and Viscoelasticity

2. Mechanical Testing Machine

3. Elastic Behavior Stress–strain curves in an elastic regime. (a) Linear elastic curve, typical for metals, ceramics, and some polymers. (b) Nonlinear elastic curve, typical for rubber.

4. Strain Energy Density

5. Shear Stress and Shear Strain (a) Specimen subjected to shear force. (b) Strain undergone by small cube in shear region. (c) Specimen (cylinder) subjected to torsion by a torque T.

6. Poisson’s Ratio (a) Unit cube being extended in direction Ox 3. (b) Unit cube subjected to tridimensional stress; only stresses on the three exposed faces of the cube are shown. Poisson’s ratio, ν, is the negative ratio of the transverse strain and longitudinal strain.

7. Generalized Hooke's Law

8. Mohr Circle (a) Biaxial (or bidimensional) state of stress. (b) Mohr circle construction, general orientation (c) Mohr circle and construction, principal stresses and maximum shear stresses (Method I).

9. Mohr Circle

10. Pure Shear

11. Hooke’s Law for Anisotropic Materials

12. Relations among Elastic Constants for Isotropic Materials

13. Elastic Compliance and Stiffness Matrixes

14. Compliance Matrix for a Cubic System

15. Relationships Among Elastic Constants Young’s modulus Shear modulus Bulk modulus Poisson’s ratio Lame΄ constants

16. Young’s Modulus of Monocrystalline Cu

17. Young’s Modulus Monocrystalline Zirconia

18. Young’s Modulus of Monocrystalline Zirconium

19. Voigt and Reuss Averages for Polycrystals Voigt average: isostrain Reuss average: isostress

20. Effect of Porosity on Young’s Modulus Watchman and Mackenzie:

21. Effect of Microcracks on Young’s Modulus

22. Salganik model O’connell & Budiansky model

23. Young’s Modulus of Polymers

24. Young’s Modulus of Polymers as a Function of Temperature

25. Viscoelasticity n = 0: plastic n = 1: linear viscous (Newtonian) n ≠1 : nonlinear

26. Viscosity and Fluidity Viscosity Fluidity

27. Viscoelasticity

28. Tensile storage modulus Tensile loss modulus

29. Rubber Elasticity

30. Stress-Strain Behavior of Biological Materials (a) Stress–strain response of human vena cava: circles-loading; squares-unloading. (Adapted from Y. C. Fung, Biomechanics (New York: Springer, 1993),p. 366.) (b) Representation of mechanical response in terms of tangent modulus (slope of stress–strain curve) vs. stress. (Adapted from Y. C. Fung. Biomechanics, New York: Springer,1993), p. 329.)

31. Residual Stresses in Arteries

32. Cartilage

33. Mesostructure of Cartilage (a) Mesostructure of cartilage (consisting of four zones) showing differences in structure as a function of distance from surface; the bone attachment is at bottom. (From G. L. Lucas, F. W. Cooke, and E. A. Friis, A Primer on Biomechanics (New York: Springer, 1999), p. 273.) (b) Cross-section of human cartilage showing regions drawn schematically in (a). (Courtesy of K. D. Jadin and R. I. Sah.)

34. Mechanical Behavior of Superficial Zone of Cartilage Stress–strain curve for samples from the superficial zone of articular cartilage. Samples were cut parallel and perpendicular to collagen fiber orientation. (From G. E. Kempson, Mechanical Properties of Articular Cartilage. In Adult Articular Cartilage, ed. M. A. R. Freeman (London: Sir Isaac Pitman and Sons Ltd., 1973), pp. 171–228.)

35. Mechanical Testing of DNA

36. Force vs. Extension for DNA Molecule

37. Stresses in a Thin Film Effect of stresses in a thin film on bending of substrate; (a) tensile stresses in thin film; (b) compressive stresses in thin film.

38. Elastic Constant and Bonding Two atoms with an imaginary spring between them; (a) equilibrium position; (b) stretched configuration under tensile force; (c) compressed configuration under compressive force.

39. Attraction and Repulsion between Two Atoms (a) Interaction energies (attractive and repulsive terms) as a function of separation; (b) Force between two atoms as a function of separation; slope decreases as separation increases.