Modulus of elasticity () and the modulus of rigidity () are related by the following equation:

Here, represents a number called **Poisson’s ratio** given to the particular material. When the material is being stretched in one direction, it gets shortened in a perpendicular direction. In the direction that the material becomes elongated, the **axial strain (****) **is defined as the fractional increase in the length. In the direction that the material shortens, the **transverse strain (****)** gives the fractional *reduction* in length. The diagram below illustrates these changes in shape:

*Defining Poisson’s ratio*

In this diagram, the axial strain is:

The transverse strain is:

Note that since the object *shortens* in the direction perpendicular to the force, . Poisson’s ratio () is defined as:

The minus sign has been introduced to ensure that takes a positive value.

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