Elasticity, Stress, and Strain

Elasticity is a measure of how much an object deforms (strain) when a given stress (force) is applied.

Key Points

• Elasticity is a measure of the deformation of an object when a force is applied. Objects that are very elastic like rubber have high elasticity and stretch easily.

• Stress is force over area.

• Strain is change in length over original length.

Terms

• A transformation; change of shape.

Figures

1. Tension/Compression

Tension: The rod is stretched a length ΔL when a force is applied parallel to its length. (b) Compression: The same rod is compressed by forces with the same magnitude in the opposite direction. For very small deformations and uniform materials, ΔL is approximately the same for the same magnitude of tension or compression. For larger deformations, the cross-sectional area changes as the rod is compressed or stretched.

We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. If a bulldozer pushes a car into a wall, the car will not move once it hits the wall, but it will noticeably change shape. A change in shape due to the application of a force is a deformation. Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed. First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations. Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke’s law is obeyed. In equation form, Hooke’s law is given by $F = k \Delta L$, where $\Delta L$ is the change in length.

Elasticity is a measure of how difficult it is to stretch an object. In other words it is a measure of how small $k$ is. Very elastic materials like rubber have small $k$ and thus will stretch a lot with only a small force.

Stress is a measure of the force put on the object over the area.

Strain is the change in length divided by the original length of the object.

Experiments have shown that the change in length (ΔL) depends on only a few variables. As already noted, ΔL is proportional to the force F and depends on the substance from which the object is made. Additionally, the change in length is proportional to the original length L0 and inversely proportional to the cross-sectional area of the wire or rod. For example, a long guitar string will stretch more than a short one, and a thick string will stretch less than a thin one (Figure 1).

Key Term Glossary

application
the act of putting something into operation
Appears in these related concepts:
deformation
A transformation; change of shape.
Appears in these related concepts:
elastic
Capable of stretching; particularly, capable of stretching so as to return to an original shape or size when force is released.
Appears in these related concepts:
elasticity
The property by virtue of which a material deformed under the load can regain its original dimensions when unloaded
Appears in these related concepts:
equation
An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
Appears in these related concepts:
force
A physical quantity that denotes ability to push, pull, twist or accelerate a body which is measured in a unit dimensioned in mass × distance/time² (ML/T²): SI: newton (N); CGS: dyne (dyn)
Appears in these related concepts:
Force
A force is any influence that causes an object to undergo a certain change, either concerning its movement, direction or geometrical construction.
Appears in these related concepts:
friction
A force that resists the relative motion or tendency to such motion of two bodies in contact.
Appears in these related concepts:
Law
A concise description, usually in the form of a mathematical equation, used to describe a pattern in nature
Appears in these related concepts:
motion
A change of position with respect to time.
Appears in these related concepts:
strain
The amount by which a material deforms under stress or force, given as a ratio of the deformation to the initial dimension of the material and typically symbolized by ε is termed the engineering strain. The true strain is defined as the natural logarithm of the ratio of the final dimension to the initial dimension.
Appears in these related concepts:
stress
The internal distribution of force per unit area (pressure) within a body reacting to applied forces which causes strain or deformation and is typically symbolized by σ.