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 Academic Year: | 2017/8 |
| 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: |
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| Assessment Summary: | EX 100% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| Requisites: | Before taking this module you must take MA30253 OR take MA40065 |
| 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 Cauchy-Green tensors, principal invariants, homogeneous deformations. Nonlinear Elasticity: Response functions for the Cauchy and 1st Piola-Kirchhoff stress tensors. Frame-indifference, material symmetries, Isotropy. Hyperelastic materials, the stored energy function, equilibrium equations and simple solutions. Examples of non-uniqueness 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
MA40049 is Optional on the following programmes:Department of Mathematical Sciences
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