Deformation of a solid
When a force acts on a body it can change its shape - the amount of deformation will depend on a number of things:
(a) the size of the specimen
(b) the size of the force
(c) the material of which the specimen is made
Now there are many important cases where the deformation is important such as bridge design, buildings, flying buttresses in a cathedral, a belly flop on water and the use of oil in the hydraulics of a car brakes, even the tension in your belt to hold up your skirt or trousers!
Many materials behave as you would expect - they stretch steadily as the force on them increases but some behave oddly - the silly putty - a small force - it creeps, a larger force and it bounces and a very large force and it shatters. How elastic do your socks and tights have to be and what about your skin itself! Rubber is elastic at room temperature but if it is cooled to the temperature of liquid nitrogen it shatters when hit with a hammer.
Basic examples and uses of elasticity
Rubber bands, Clothes, Balls, Aircraft wings flexing, Bridges, Skin, Steel girders, Bats such as cricket, Glass, Lift cables, Bouncy castle, Trainers, Fishing line.
Stress and strain
Every stress produces a strain!
Stress
Every elastic stress produces an elastic strain. A stress is a measure of the cause of the deformation produced by a force:
Stress = Force per unit area units are Nm -2 or Pa .
Breaking stress
The maximum stress that a material can stand before it breaks is called the breaking stress. There are two types of breaking stress
(a) compressive breaking stress - the maximum squashing stress before fracture
(b) tensile breaking stress - the maximum stretching stress before fracture
Some examples of both of these are given in the following table
Material Compressive breaking stress/ MPa
552
Tensile breaking stress/MPa
400 - 800 Steel
Rubber
Granite 145
2.1
4.8
Concrete
Oak
21
59
Porcelain 552
Bone (compact) 170
Nylon
Glass
Carbon fibre
Cast iron
2.1
117
55
120
70
3.5 - 150
1000
30 - 140
1

Strain
Strain is a measure of the deformation produced by the stress.
Strain has no units as it is simply a ratio of two similar quantities
Linear stress and strain
When the stress is along the length of the specimen there are two ways in which it can be applied to give a strain.
(a) compressive stress
(b) tensile stress
These two numbers are not necessarily the same for a given material.
The height of a granite column
The compressive breaking stress (F) of a material can be used to work out the maximum height of a rock column that is possible on the surface of the Earth.
Maximum pressure at the base = F =
 gh where

is the density of the rock.
Therefore for granite F = 145x10 6 and

= 2500 kgm -3 so h = 145x10 6 /2500x9.81 = 5900 m h
8000 m
Granite column
This is smaller than the heig ht of many mountains but in a mountain the ‘column’ of rock would be supported from the sides by the rest of the mountain.
Example problems
1. Calculate the stress due to a force of 20 N acting on a steel wire of cross sectional area 0.2x10
-6 m 2
(about 0.5 mm diameter).
Stress = 20/0.2x10
-6 = 10 8 Nm -2
2. What is the strain in a wire, initially 1 m long, that has stretched by 3 mm?
Strain = 0.003/1 = 0.003
2