Deformation - A change in shape of a material or tissue under a load.

1. Deformation - A change in shape of a material or tissue under a load. • Df = |lf - li| = ∆l • where l --> length, width, etc. • li = initial length or size • lf = final length or size • UNITS: Englishmetric • ft m • in cm, mm, µm

2. Deformation - A change in shape of a material or tissue under a load. • Df = |lf - li| = ∆l • ex. I stretch a rubber band from an initial length of 2 in to a length of 6 in. What is the deformation? • Given: li = 2 in. lf = 6 in • Find: ∆l • Formula: ∆l = |lf - li| • Solution: ∆l = |6 in - 2 in| • ∆l = 4 in

3. Mechanical Strain • Strain (e): A measure of the change in shape of a tissue or material under mechanical stress. • Expressed as a fraction or % of material length or width • e = Deformation/orig. size = ∆l/li • e = |lf - li|/li

4. Mechanical Strain • Strain (e) A measure of the change in shape of a tissue or material under mechanical stress. • UNITS: Englishmetric • ft/ft, in/in m/m, cm/cm • % or strain % or strain • 10 % = 10 strain • e = |lf - li|/li • 100 = %

5. Strain • A medial collateral ligament (MCL) of the knee is 53 mm long when relaxed at full knee flexion. At full knee extension the measure length (by MRI) is 57 mm. What is the strain? • Given: li = 53 mm lf = 57 mm • Find: e • Diagram: MCL

6. Strain • A medial collateral ligament (MCL) of the knee is 53 mm long when relaxed at full knee flexion. At full knee extension the measure length (by MRI) is 57 mm. What is the strain? • Given: li = 53 mm lf = 57 mm • Formula: e = |lf - li|/li • 100 • Solution: e = |57 mm - 53 mm|/ 53 mm • 100 • e = 4 mm|/ 53 mm • 100% • e = 0.0755 mm/mm • 100% • e = 7.55 %

7. Load, Stress, Deformation, Strain andMaterial Properties • Strength – the maximal load or maximal stress that can be withstood before injury or failure • Ex. Bone become stronger in young adults than in children • The opposite of strong is weak

8. Material Properties • Elasticity - the ability of a material to return to its original shape once deformed Ex. Rubber band, healthy tendons, muscles, ligaments, bones • The opposite of elastic is Plastic • Ex. Silly putty, tupperware, many connective tissue injuries

9. Material Properties • Stiffness – The ratio of stress to strain - the resistance of a loaded material to deformation. Stiff materials do not change their shape easily when a load or stress is applied. • (ex. iron bar, glass, bone) • Pliability – materials are pliable if the are easily deformed. pliable materials bend or stretch or compress easily • (ex. rubber band, twig in Spring)

10. Material Properties • Ductility – The ability of a material to undergo large deformation or strain before failure. • (ex. rubber band, iron bar, skeletal muscle) • Brittleness – The tendency of a material to break with little deformation or strain • (ex. glass, dead tree branch, bones in elderly).

11. Stress-Strain Curve – Relates change in stress to the change in shape it produces Stress-Strain or load-deformation curves are the keys to measuring material properties of connective tissues: • They tell us about: • Strength • Stiffness • Brittleness • Energy absorbed • Where injuries occur • Severity of the injury knee prosthesis

12. Materials Testing System Stress-strain Curves Hydraulic Wedge Grips Specimen Extensometer Instron machine http://www.instron.us/wa/home/default_en.aspx

13. Stress-Strain Curve – Relates change in stress to the change in shape it produces Stress-Strain or load-deformation curves are the keys to measuring material properties of connective tissues: • Allow us to look at the effects of: • aging, injury, rehabilitation, immobilization, Exercise

14. Load-Deformation Curve QUALITY + SIZE Load (N) Deformation (mm)

15. Stress-Strain Curve QUALITY ONLY Stress (N/m2) Strain (%)

16. Stress-Strain Curve – Relates change in stress to the change in shape it produces Contains the following regions: • elastic region – The material will return to its original shape when the stress is removed • yield point – The material starts to be permanently deformed (injuries occur just before and beyond this point). Starts at the elastic limit. • plastic region – Material shape is permanently changed. Curve flattens out • failure – The material breaks completely or separates.

17. Stress-strain curves failure pt plastic region yield point stress (N/cm2) elastic limit elastic region strain (%)

18. Stress-strain curves yield pt. failure pt Slope = ∆y/∆x stress (N/cm2) ∆y ∆x Linear part of elastic region strain (%)

19. Stress-strain curves Slope = ∆y/∆x Stiffness = ∆stress/∆strain (Young’s Modulus) failure pt stress (N/cm2) ∆y ∆x Linear part of elastic region strain (%)

20. Stress-strain curves Slope = ∆y/∆x Stiffness = ∆stress/∆strain A stress (N/cm2) B strain (%)

21. Stress-Strain Curves Strength - max. load or stress failure pt stress (N/cm2) strain (%)

22. Stress-Strain Curves yield point End of elastic region failure pt stress (N/cm2) Mild injury (Ex. mild or first degree Sprain of ligament) strain (%)

23. Stress-strain curves failure pt plastic region yield point stress (N/cm2) moderate injury (ex. greenstick fracture, moderate sprain) elastic region strain (%)

24. Stress-Strain Curves yield point plastic region failure pt stress (N/cm2) elastic region Severe injury (Ex. tear or rupture of ligament or tendon) strain (%)

25. Stress-strain curves failure pt plastic region yield point stress (N/cm2) strain (%) Ductile - max strain to failure

26. Stress-strain curves Which one is more ductile? More brittle? A stress (N/cm2) B strain (%)

27. Energy Absorption Area under curve = toughness yield point C B Stress D Failure Point ENERGY A D’ Strain

28. Stress-strain curvesEnergy absorption (area under curve) failure pt plastic region yield point stress (N/cm2) strain (%) resilience

29. Stress-strain curvesEnergy absorption failure pt plastic region yield point A stress (N/cm2) B strain (%)

30. Terms Related to Stress and Strain • Elastic – A material that bounces back into ints original shape quickly. • Viscous – A thick material which flows slowly. • Viscoelastic – A material which exhibits viscous and elastic qualities • Ex. Skeletal muscle is elastic when stretched fast, and viscous when stretched slowly Viscoelastic materials undergo “hysteresis.” This means they lose a lot of energy when a load is lifted.

31. Cyclic Loading and Unloading of a Muscle As the ligament unloads it loses energy due to hysteresis. The shaded area between the curves shows the energy lost. LOAD loading unloading DEFORMATION

32. Load and Injury • The body is designed to adapt to certain levels of mechanical stress. • This adaptation is necessary for normal development of strength and structural integrity. • A certain amount of loading beyond that which is usually encountered allows individuals to improve such qualities as strength and endurance.

33. Terms Related to Stress and Strain • Creep – The increase in strain over time with a constant loading. This principle is applied when using a series of casts to reshape limbs (clubfoot) or the spinal column (treatment of scoliosis). • Relaxation – A decrease in stress which occurs in a material when a constant deformation is present.

34. Terms Related to Stress and Strain • Resilient – An object which has a tendency to rebound from a surface or another object or to return to its original shape quickly when stress is suddenly applied and then removed without damage. A tennis ball or golf ball would be resilient. Lead would be a non-resilient material. • Damped – A material or object which returns to its original shape slowly when stress is removed. The opposite of resilient.