MAGIC025: Continuum Mechanics

Course details

A specialist MAGIC course

Semester

Autumn 2007
Monday, October 8th to Friday, December 14th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
0

Timetable

Mondays
12:05 - 12:55
Wednesdays
10:05 - 10:55

Announcements

This course has now started.

Description

This is offered as a core course for Applied. The objective is to derive in a rational way the governing equations for both solids and fluids and to solve a few illustrative problems. It is intended that, by the end of the course, students will have the knowledge necessary for the in-depth study of various phenomena in linear elasticity, nonlinear elasticity, rheology, and fluid mechanics.

Recommended books:
  • P. Chadwick, Continuum Mechanics, Dover (1999).
  • S.C. Hunter, Mechanics of Continuous Media, Ellis Horwood (1976).
  • I-S, Liu, Continuum Mechanics, Springer (2002).
  • C. Truesdell, The Elements of Continuum Mechanics, Springer (reprinted 1985).
  • P.G. Drazin and N. Riley, The Navier-Stokes equations: a classification of flows and exact solutions, Cambridge University Press (2006).

Prerequisites

No prerequisites information is available yet.

Syllabus

  • Vector and tensor theory: Vector and tensor algebra, tensor product, eigenvalues and eigenvectors, symmetric, skew-symmetric and orthogonal tensors, polar decompositions, integral theorems.
  • Kinematics: The notion of a continuum, configurations and motions, referential and spatial descriptions, deformation and velocity gradients, stretch and rotation, stretching and spin, circulation and vorticity.
  • Balance laws, field equations and jump conditions: Mass, momentum, force and torque, theory of stress, equations of motion, energy, jump conditions.
  • Constitutive equations: Basic constitutive statement, examples of constitutive equations, observer transformations, reduced constitutive equations, material symmetry, internal constraints, incompressible Newtonian viscous fluids, isotropic elastic materials, viscoelastic materials, rheological models such as Reiner-Rivlin fluid and Bingham fluid.
  • Advanced formulations: Elementary continuum thermodynamics, variational formulations, conjugate measures of stress and strain, Hamiltonian formulations.
  • Illustrative problems.
  • Linear Elasticity: a cylinder deformed by its own weight, surface wave propagation
  • Nonlinear Elasticity: inflation of spherical and cylindrical shells
  • Fluid Mechanics: a selection of steady flows bounded by plane boundaries.

Lecturer

  • YF

    Professor Yibin Fu

    University
    Keele University

Bibliography

No bibliography has been specified for this course.

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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