MA40049: Elasticity
[Page last updated: 05 August 2021]
Academic Year:  2021/2 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
 Semester 2

Assessment Summary:  EX 100% 
Assessment Detail:  
Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

Requisites: 
Before taking this module you must take MA30253

Description:  Aims: To provide a unified introduction to the mathematical modelling of elastic materials.
Learning Outcomes: Students should be able to derive the governing equations of the theory of elasticity from basic principles and be able to solve simple problems.
Skills: Problem Solving T/F A
Written and Spoken Communication F (solutions to exercise sheets, problem classes)
Content: Revision: Kinematics of deformation, balance laws, Cauchy stress tensor, boundary conditions.
Analysis of strain: Polar decomposition theorem, stretch tensors, principal stretches, left and right CauchyGreen tensors, principal invariants, homogeneous deformations.
Nonlinear Elasticity: Response functions for the Cauchy and 1st PiolaKirchhoff stress tensors. Frameindifference, material symmetries, Isotropy.
Hyperelastic materials, the stored energy function, equilibrium equations and simple solutions. Examples of nonuniqueness of equilibrium solutions.
Linear Elasticity: Derivation of field equations of linear elasticity from the nonlinear theory. Linear elasticity tensor and its symmetries. Lame moduli;
Young's modulus, Poisson's ratio. Strain energy function for linear elasticity; uniqueness of equilibrium solutions. Simple problems of elastostatics: including expansion of a spherical shell, extension of a cylinder.
Further topics may be chosen from the following:
Variational approaches, symmetries and conservation laws. Constitutive assumptions and inequalities. Applications to modelling phase transitions, composite materials. Incompressible hyperelastic materials.
Linear Elastodynamics: Basic equations and general solutions; plane waves in unbounded media, simple reflection problems; surface waves.

Programme availability: 
MA40049 is Compulsory on the following programmes:
Department of Physics
 USXXAFM01 : MSci(Hons) Mathematics and Physics (Year 4)
 USXXAAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
 USXXAKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)
MA40049 is Optional on the following programmes:
Department of Mathematical Sciences
 RSMAAFM16 : Integrated PhD Statistical Applied Mathematics
 TSMAAFM17 : MRes Statistical Applied Mathematics
 TSMAAFM19 : MSc Mathematics with Data Science for Industry
 TSMAAWM19 : MSc Mathematics with Data Science for Industry
 TSMAAFM16 : MSc Statistical Applied Mathematics
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 3)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
 USMAAFB13 : BSc(Hons) Mathematics (Year 3)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
 USMAAFB05 : BSc(Hons) Statistics (Year 3)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
 USMAAFM14 : MMath(Hons) Mathematics (Year 3)
 USMAAFM14 : MMath(Hons) Mathematics (Year 4)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
Department of Physics
 USXXAFB03 : BSc(Hons) Mathematics and Physics (Year 3)
 USXXAAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
 USXXAKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)

Notes:  This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22.
 Programmes and units are subject to change in accordance with normal University procedures.
 Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any prerequisite rules.
 Find out more about these and other important University terms and conditions here.
