## MAS310 Continuum Mechanics

 Semester 1, 2017/18 10 Credits Lecturer: Prof Michael Ruderman uses MOLE Timetable 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

20 lectures, no tutorials

## Assessment

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

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.

## Timetable

 Mon 10:00 - 10:50 lecture Diamond Building LT8 Thu 14:00 - 14:50 lecture Hicks Lecture Theatre E