# MMath&Phys Mathematics and Physics / Course details

Year of entry: 2022

## 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 : Vectors, tensors, co- and contra-variant transformation laws, invariance concepts, metric tensor, tensor calculus, divergence theorem.
• Kinematics : Deformation maps, Lagrangean and Eulerian viewpoints, displacement, velocity and acceleration, material derivative, strain measures, strain invariants, deformation rates, Reynolds transport theorem.
• Forces, momentum & stress : The continuum hypothesis, linear and angular momenta, stress tensors, equations of equilibrium.
• Conservation and Balance Laws & Thermodynamics : 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 : Introduction to constitutive relationships, axiom of objectivity, objective deformation rates, constitutive modelling for an ideal gas.
• Elasticity : 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 : 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.