Linear algebra is significant to many aspects of mechanics. For some years I have been using the book by Shilov. But this book may or may not be a good one to recommend to a student, depending on his or her prior experience. On StackExchange Mathematics, there are several excellent threads discussing textbooks of linear algebra. A particular recommendation was made for
It might be fun for us to work together to collect phenomena of large elastic deformation. These phenomena will enliven teaching and motivate research. As inspiration, here are two albums of fluid motion
Caltech has made the Feynman Lectures on Physics, Vol I, freely accessible online. The quality of the HTML file is exceptionally high. Take a look at the preface to learn how this electronic version was produced.
A single strand of polymer is a chain of a large number of monomers. The monomers are joined by covalent bonds, and two bonded monomers may rotate relative to each other. At a finite temperature, the polymer rapidly changes from one configuration to another. When the two ends of the polymer are pulled by a force, the distance between the two ends changes. The polymer is known as an entropic spring.
These notes may serve as a reminder of tensor algebra. The notes supplement the course on advanced elasticity. Several books are listed at the end of the notes.
Update on 17 April. I am now breaking up the notes on tensors, cleaning them up, and posting them as sections on linear algebra.
In the notes on the general theory of finite deformation, we have left the free energy function unspecified. The notes here describe free energy function commonly used to describe the elasticity of rubber-like materials. These notes are part of a course on advanced elasticity
These notes are part of a course on advanced elasticity. The notes recall several phenomena where both elasticity and surface energy are significant, including
The notes also contain a formulation of combined surface energy and elasticity of finite deformation.
