MSE203 Mechanical Behaviour: Continuum Mechanics
In second year, I teach a 10-lecture course on stress tensors in the spring term. Here we learn how to deal with stress states in materials. So we define stress tensors and examine how to rotate them, both using tensor rotations and Mohr’s circle. We look at how to analyse stresses in simple bodies like shafts and pressure vessels. Then we look at strain, elasticity and how to measure strains by diffraction. We can then look at anisotropic elasticity, particularly in crystalline materials. We finish up by studying yielding and yield criteria.
As with MSE104, the course is taught by Peer Instruction, supported by notes and videos on YouTube.
The notes are here, which are also accompanied by examples here. In the tutorials, we will go through some of these examples (Tutorial 1: Q5,6,8,9 and Tutorial 2: Q20, 23,24,25); the others are discussed in the videos. Solutions are provided with the examples (but don’t look until you’ve tried them :-).
If you like lectures, then they are online on YouTube. The video numbering corresponds to the ‘lecture’ classes in which we will discuss that material. As with MSE104, there is no intention to re-lecture the material in class: instead students should review the material before class in their own time, ready to discuss and explore it in the class session.
After the end of the lectures, there is a short 1-hr test to prepare students for the exam in June.
Lecture 7. 7a: Anisotropic Elasticity
Lecture 8. 8a: Strain Measurement
Lecture 9. 9a: Yield Surfaces and Criteria
Dieter (Ch2) is really great for this course, and is probably the core reference. But, the main drawback of Dieter is that he soft-pedals the tensor mathematics.
To go further, particularly for anisotropic elasticity, the Nye’s book is the core reference. But, its quite dense and written in the style of the time.
If you are struggling to conceive of what a tensor is as a mathematical object, then I quite like this video.