Mathematics

Continuum Mechanics (L6)

Module code: G1158
Level 6
15 credits in spring semester
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

You will be introduced to the mathematical theory of continuum mechanics where, in contrast to classical mechanics, materials are modelled as a continuum of particles, rather than point masses.

You will learn the fundamental modelling assumptions in continuum mechanics and understand how to derive mathematical models – in the form of partial differential equations – describing the motion of continuum media. As an application, a selection of standard models will be studied, leading to the famous Euler and Navier-Stokes equations for fluids, and the theory of elastic solids.

Continuum mechanics is an extremely powerful theory and underpins the modelling of all physical phenomena that occur at length-scales much larger than interatomic distances and much smaller than astronomical distances. Indeed, to name a few examples, models for materials, building structures, earthquakes, tsunamis, weather fronts, and even supernovae – the explosion of massive stars – all use continuum mechanics, allowing us to build resistant structures, forecast weather or predict climate change among others.

Module learning outcomes

• Understand systematically the algebra and calculus of tensors, and perform algebraic and differential calculations involving tensors..
• Understand systematically fundamental concepts in continuum mechanics including kinematics, the relation between the Eulerian and Lagrangian specifications, and the description of forces.
• Use the laws of conservation of mass and the balance of linear and angular momenta to derive the equations governing continuum mechanics in the Eulerian and Lagrangian descriptions, and understand the modelling of internal constraints and frame indifference.
• Apply the skills developed to derive standard models for simple fluids and elastic solids, and construct explicit solutions.