Stress Tensor — Lesson 3

We have been introduced to stress, now let's build upon this knowledge and learn more about its characteristics.

Let's start with a simple example: tensioning a sailing yacht. When the rope is being pulled it's in a state of tension.


Now, let's look at another system: your index finger. Press it against an object and focus on how the finger joint feels. Now lift it, hold one end of it with your other hand and gently pull it, once again focusing on how the finger joint feels. Even though the joint senses the same load (if the same force is applied) in both cases, it feels different. This is because in the former case the finger joint is in a state of compression, and in the latter, it is in a state of tension.


Now, get down on the floor and do a few pushups — mind your form! While you're at it, focus on how your chest muscles react to this physical activity. You'll notice that the muscles are in a slightly more complicated state of deformation compared to just tension and compression.


From these examples, it's obvious that when stress is developed in a body it may be distributed in different directions depending on the type of load and the nature of the body. This is why we represent stress in the form of a tensor. In this lesson, we'll learn how stress is represented in tensorial form and how to interpret each term of the tensor.


Alternate video link.


Here are the accompanying handout slides for this lesson.