# 12.3 Stress, strain, and elastic modulus

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By the end of this section, you will be able to:
• Explain the concepts of stress and strain in describing elastic deformations of materials
• Describe the types of elastic deformation of objects and materials

A model of a rigid body is an idealized example of an object that does not deform under the actions of external forces. It is very useful when analyzing mechanical systems—and many physical objects are indeed rigid to a great extent. The extent to which an object can be perceived as rigid depends on the physical properties of the material from which it is made. For example, a ping-pong ball made of plastic is brittle, and a tennis ball made of rubber is elastic when acted upon by squashing forces. However, under other circumstances, both a ping-pong ball and a tennis ball may bounce well as rigid bodies. Similarly, someone who designs prosthetic limbs may be able to approximate the mechanics of human limbs by modeling them as rigid bodies; however, the actual combination of bones and tissues is an elastic medium.

For the remainder of this chapter, we move from consideration of forces that affect the motion of an object to those that affect an object’s shape. A change in shape due to the application of a force is known as a deformation . Even very small forces are known to cause some deformation. Deformation is experienced by objects or physical media under the action of external forces—for example, this may be squashing, squeezing, ripping, twisting, shearing, or pulling the objects apart. In the language of physics, two terms describe the forces on objects undergoing deformation: stress and strain .

Stress is a quantity that describes the magnitude of forces that cause deformation. Stress is generally defined as force per unit area . When forces pull on an object and cause its elongation, like the stretching of an elastic band, we call such stress a tensile stress    . When forces cause a compression of an object, we call it a compressive stress    . When an object is being squeezed from all sides, like a submarine in the depths of an ocean, we call this kind of stress a bulk stress    (or volume stress ). In other situations, the acting forces may be neither tensile nor compressive, and still produce a noticeable deformation. For example, suppose you hold a book tightly between the palms of your hands, then with one hand you press-and-pull on the front cover away from you, while with the other hand you press-and-pull on the back cover toward you. In such a case, when deforming forces act tangentially to the object’s surface, we call them ‘shear’ forces and the stress they cause is called shear stress    .

The SI unit of stress is the pascal (Pa). When one newton of force presses on a unit surface area of one meter squared, the resulting stress is one pascal:

$\text{one pascal}=1.0\phantom{\rule{0.2em}{0ex}}\text{Pa}=\frac{1.0\phantom{\rule{0.2em}{0ex}}\text{N}}{1.0\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}}.$

In the British system of units, the unit of stress is ‘psi,’ which stands for ‘pound per square inch’ $\left({\text{lb/in}}^{2}\right).$ Another unit that is often used for bulk stress is the atm (atmosphere). Conversion factors are

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