MMath&Phys Mathematics and Physics

Year of entry: 2024

Course unit details:Continuum Mechanics

Unit code MATH45062 15 Level 4 Semester 2 Department of Mathematics No

Pre/co-requisites

Unit title Unit code Requirement type Description
Viscous Fluid Flow MATH35001 Pre-Requisite Recommended
Elasticity MATH35021 Pre-Requisite Recommended
Partial Differential Equations and Vector Calculus A MATH20401 Pre-Requisite Compulsory
Partial Differential Equations and Vector Calculus B MATH20411 Pre-Requisite Compulsory

Syllabus

• Introduction [4]: Vectors, tensors, co- and contra-variant transformation laws, invariance concepts, metric tensor, tensor calculus, divergence theorem.
• Kinematics [4]: Deformation maps, Lagrangean and Eulerian viewpoints, displacement, velocity and acceleration, material derivative, strain measures, strain invariants, deformation rates, Reynolds transport theorem.
• Forces, momentum & stress [3]: The continuum hypothesis, linear and angular momenta, stress tensors, equations of equilibrium.
• Conservation and Balance Laws & Thermodynamics [3]: Conservation of mass and energy, balance of linear and angular momenta, work conjugacy, temperature and heat, first and second laws of thermodynamics, Clausius--Duhem inequality.
• Constitutive Modelling [3]: Introduction to constitutive relationships, axiom of objectivity, objective deformation rates, constitutive modelling for an ideal gas.
• Elasticity [5]: Constitutive modelling for thermoelastic materials, Hyperelastic materials, strain energy function, homogeneous, isotropic materials, incompressibility constraints, example analytic solutions, boundary conditions, linear thermoelasticity and reduction to Navier--Lame equations.
• Fluid Mechanics [5]: Constitutive modelling for fluids, isotropic fluids, Newtonian and Reiner--Rivlin fluids, example analytic solutions, boundary conditions, reduction to Navier--Stokes equations.

Assessment methods

Method Weight
Other 20%
Written exam 80%
• Coursework - 20%: two assignments, each worth 10%; each should take aprox 7 hours.
• End of semester examination: weighting 80%

Feedback methods

• Spencer, A.J.M, Continuum Mechanics, Dover
• Gonzalez, O. and Stuart, A.M., A first course in continuum mechanics, CUP
• Irgens, F., Continuum Mechanics, Springer

Study hours

Scheduled activity hours
Lectures 12
Tutorials 12
Independent study hours
Independent study 126

Teaching staff

Staff member Role
John Gray Unit coordinator

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

·         You will normally have approximately 75-120 minutes of video content. Normally you would spend approximately 2.5-4 hrs per week studying this content independently

·         You will normally have exercise or problem sheets, on which you might spend approximately 2-2.5hrs per week

·         There may be other tasks assigned to you on Blackboard, for example short quizzes, short-answer formative exercises or directed reading

·         In some weeks you may be preparing coursework or revising for mid-semester tests

Together with the timetabled classes, you should be spending approximately 9 hours per week on this course unit.

The remaining independent study time comprises revision for and taking the end-of-semester assessment.

The above times are indicative only and may vary depending on the week and the course unit. More information can be found on the course unit’s Blackboard page.