MA40049: Elasticity
Academic Year:  2020/1 
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:  EX 100% 
Supplementary Assessment: 

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: NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2020 
MA40049 is Compulsory on the following programmes:Department of Physics
MA40049 is Optional on the following programmes:Department of Mathematical Sciences

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