Mathematics

Continuum Mechanics

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

Topics include: 

  • kinematics (Eulerian and Lagrangian descriptions, velocity, acceleration, rate of change of physical quantities, material derivatives, streamlines)
  • deformation (stress and strain tensors, Hooke's law, equilibrium equations)
  • conservation laws for mass, momentum and energy
  • phase/group velocities of travelling wave solutions
  • models of fluid and solid mechanics.

Module learning outcomes

  • An understanding of the basic concepts in mechanics including kinematics, forces and conservation of mass and momentum including Newton's laws and Cauchy's principle.
  • Eulerian vs Lagrangian coordinates and an understanding of how to derive deterministic differential equations from integral balance and conservation laws.
  • Ability to compute surface forces using the Cauchy stress tensor as well as body forces, mass and momentum in a portion of material.
  • Ability to solve one-dimensional transport and wave initial value problems as well as some simple three-dimensional fluid boundary value problems.