Content: The modelling and simulation of fluids and solids with significant coupling and thermal effects is an important area of study in applied mathematics and engineering. Necessary for such studies is a fundamental understanding of the basic principles of continuum mechanics and thermodynamics. This course focuses on the foundational theory behind these models, and closely follow the text "A First Course in Continuum Mechanics'' by Gonzalez and Stuart. Throughout, our focus is on building general theoretical understanding over solving particular cases of the equations. An indicative module outline is as follows: we begin by discussing tensors algebra and their calculus. We then use these tools to build equations which govern both fluids and solids, we will proceed to derive some commonly used models governing isothermal fluids and solids.

Aims: To provide understanding of the theoretical foundation of PDE models of solids and fluids.

Objectives: By the end of the module the student should be able to:

• Manipulate and perform calculations with tensors.
• Explain the concepts of stress and strain.
• State physical balance laws in integral form and derive their local versions as PDEs.
• Use their understanding to interpret the results of theoretical calculations.

Book(s):

Oscar Gonzalez, Andrew Stuart, A First Course in Continuum Mechanics, Cambridge University Press, 2008.