1. Elasticity and Deformation
Physics 1
Nicole P. Laville

2. Elasticity, Stress and Strain
Elasticity is a characteristic of all solid materials describing their behaviour under mechanical loading
It characterized by the degree of deformation caused by the force
Deformation : The change of shape of an object subjected to stress
Plastic Deformation: Object permanently changes shape
Elastic Deformation: Object changes shape and returns to its original dimensions

3. Elasticity, Stress and Strain
The elasticity of a substance can be characterized by two physical parameters:
Stress: External force applied per unit area
Strain: A Quantitative measure of the extent of deformation of an object produced as a result of the applied stress. It is a ratio of the change in dimension to the original dimension. For longitudinal/tensile strain:
Stress=Force/Area
σ= 𝐹 𝐴

4. Moduli of Elasticity
The possible kinds of elastic deformation include :
Stretch and Compression- Young’s Modulus

5. Moduli of Elasticity Shear Deformation
A shearing stress alters only the shape of the body, leaving the volume unchanged. For example, consider equal and opposite shearing forces F acting on the cube below:

6. Moduli of Elasticity
Volume Deformation

7. Stress- Strain Curve Fracture Stress Bone 200 MPa (Aluminium 90 MPa)
Collagen 100 MPa (wood 100MPa)
Arterial Wall 2 Mpa

8. Material Properties of Bone
Compact bone consists of living cells embedded in a solid framework made up of collagen and bone salt ( a mixture of calcium, phosphorus oxygen and hydrogen)
Hydroxypatite is the main material for bone structures and has great compressive strength
Collagen adds tensile strength
Collagen fibres are Anisotropic

9. Biomechanical Characteristics of Bone - Bone Tissue
Inorganic Components
(e.g., calcium and phosphate)
Organic Components
(e.g. collagen)
65-70%
(dry wt)
25-30%
(dry wt)
H2O
(25-30%)
ductile
one of the body’s hardest structures
brittle
viscoelastic

10. Mechanical Loading of Bone

11. Compressive Loading Vertebral fractures Cervical fractures
spine loaded through head
e.g., football, diving, gymnastics
once “spearing” was outlawed
in football the number of cervical
injuries declined dramatically
lumbar fractures
weight lifters, linemen, or gymnasts
spine is loaded in hyperlordotic
(aka swayback) position

12. tension can stimulate tissue growth
Tensile Loading
Main source of tensile load is muscle
tension can stimulate tissue growth
fracture due to tensile loading is usually an avulsion
other injuries include sprains, strains, inflammation, bony deposits
when the tibial tuberosity experiences excessive loads from quadriceps
muscle group develop condition known as Osgood-Schlatter’s disease

13. Shear Forces
Created by the application of compressive, tensile or a combination of these loads

14. Bending Forces
Usually a 3- or 4-point
force application

15. Torsional Forces Caused by a twisting force
produces shear, tensile, and
compressive loads
tensile and compressive loads are
at an angle
often see a spiral fracture develop
from this load

16. Relative Strength of Bone

17. Anisotropic response behavior of bone is dependent
on direction of applied load
Bone is strongest along
long axis - Why?

18. Elasticity of Ligaments, Tendons
Tendons and ligaments are much less extensible than muscle and do not have the ability to contract.
Made primarily of collagen fibres (with some elastin fibres) they will return to their normal lengths when unloaded.
However, there is an elastic limit after which the tendon or ligament
will not return to resting length (region of plasticity - 2nd degree strain). This will
take time for the body to repair.
If the ligament completely fails (3rd degree strain) this can only be restored by
surgery.

20. (elastin and microfibrils)
Collagen Fibres
 Deformation Range
small 6 - 8%
 Strength
50% of that of cortical bone tested in tension
Collagen Fibres
Stress
Strain (percent)
Elastic Fibres
(elastin and microfibrils)
Stress
Strain (percent)
Elastin Fibres
 Deformation Range
 large >100%
(150% Fawcett 1986)
 Strength
 weak 4

21. Loaded Ligament
Unloaded Ligament

22. loading of a knee ligament.
Loaded Ligament
loading of a knee ligament.
Repetitive stress causes failure at lower load than that required to cause failure in a single application. As a ligament undergoes cyclic loading it relaxation behaviour results in continuously decreasing stress (protecting ligament from fatigue failure)……..

23. Self Studying Resilience of Tendons Elasticity of Lungs
Elastic property of Blood Vessels