## MAS310 Continuum Mechanics

Semester 1, 2019/20 | 10 Credits | ||||

Lecturer: | Prof Michael Ruderman | uses MOLE | Reading List | ||

Aims | Outcomes | Assessment |

Continuum mechanics is concerned with the mechanical behaviour of solids and fluids which change their shape when forces are applied. For example, rubber extends when pulled but behaves elastically returning to its original shape when the forces are removed. Water starts to move when the external pressure is applied. This module aims to introduce the basic kinematic and mechanical ideas needed to model deformable materials and fluids mathematically. They are needed to develop theories which describe elastic solids and fluids like water. In this course, a theory for solids which behave elastically under small deformations is developed. This theory is also used in seismology to discuss wave propagation in the Earth. An introduction in theory of ideal and viscous, incompressible and compressible fluids is given. The theory is used to solve simple problems. In particular, the propagation of sound waves in the air is studied.

**Prerequisites:** MAS280 (Mechanics and Fluids)

No other modules have this module as a prerequisite.

## Outline syllabus

- Mathematical preliminaries: Scalar and vector fields. Tensors in Euclidean space. Transformation of Cartesian coordinates. Transformation of Cartesian components of vectors and tensors. Differentiation of vectors and tensors in Cartesian and curvilinear coordinates.
- Kinematics of continuum: Lagrangian and Eulerian description of continuum motion. Velocity and acceleration. Strain tensor. Rate of strain tensor. Mass conservation equation.
- Dynamics of continuum: Stress tensor and its main properties. Momentum equation. Boundary conditions at rigid and free surfaces.
- Simple models of continuum mechanics: Ideal incompressible fluid. Classical elasticity. Viscous incompressible fluid. Ideal compressible fluid, sound waves.

## Aims

- To introduce the basic kinematic and mechanical ideas needed to model deformable solids and fluids.
- To introduce and illustrate the theory of classical elasticity with simple example of exact solutions and applications to seismology.
- To introduce the theory of ideal and viscous, incompressible and compressible fluids, and apply it to solve simple problems.

## Learning outcomes

By the end of the unit students will be able to demonstrate: 1.a knowledge of the basic kinematic and mechanical ideas needed to model deformable solids and fluids; 2. a knowledge of the theory of classical elasticity with simple example of exact solutations and applications to seismology; 3. a knowledge of the theory of ideal and viscous, incompressible and compressible fluids, and apply it to solve simple problems.20 lectures, no tutorials

## Assessment

One formal 2 hour written examination. Format: 4 questions from 5.

## Reading list

Type | Author(s) | Title | Library | Blackwells | Amazon |
---|---|---|---|---|---|

B |
Atkin and Fox | An Introduction to the Theory of Elasticity | 531.38 (A) | Blackwells | Amazon |

B |
Hunter | Mechanics of Continuous Media | 531.01 (H) | Blackwells | Amazon |

B |
Spencer | Continuum Mechanics | 531.01 (S) | Blackwells | Amazon |

B |
Thompson | An Introduction to Astrophysical Fluid Dynamics | 523.01 (T) | Blackwells | Amazon |

(

**A**= essential,

**B**= recommended,

**C**= background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.