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Study

Advanced Mechanics

Module code: 6CCYB050

Credits: 15

Module convenor: Dr Jack Lee

Aims

This course will introduce students to linear elasticity mechanics, theory and methods for problem solving and simulation. It will emphasize topics including: kinematics, stress and strain, linear elasticity, viscoelasticity, and biomaterials.

Learning Outcomes

On completion of the course, the students will be able:

-           To demonstrate an understanding of the fundamental concepts underpinning continuum mechanics and the principles of conservation laws

-           To demonstrate a broad understanding of the major topics in solid mechanics, and the key assumptions underlying various frameworks

-           To demonstrate a systematic understanding of the theory of linear elasticity / viscoelasticity and to apply it in practical problem solving

-           To achieve a basic understanding of common biological constitutive behaviours, and to possess the necessary knowledge to understand more complex materials responses

  

The syllabus of the module includes lectures and tutorials on:

  • Concepts in continuum mechanics: Classical analysis vs continuum approach, conservation principles, elasticity, plasticity, viscoelasticity, thermoelasticity, linear vs nonlinear elasticity
  • Traction and Stress: Traction, separation of tangential & normal components, stress tensor, dyadic representation of stress, tetrahedron lemma, special cases (plane, linear, pure shear, hydrostatic stress), physiological ranges of stress
  • Deformation and Strain: Strain tensor and its physical interpretation, volume and shape changes, principal strains, compatibility, nonlinear strain-displacement relations
  • Constitutive Behaviour: Uniaxial behaviour, generalised Hooke’s law, isotropy, transverse isotropy, anisotropy, viscoelastic material, Young’s modulus, Poisson’s ratio, Lame constants, shear modulus, bulk modulus, common physical range of parameters
  • Equilibrium: Principle of linear momentum, system of equations for solution, displacement and force formulations
  • Classical Problems: Extension, bending and torsion examples 
  • 2D elasticity: plane stress / plane strain reductions, cylindrical coordinates, axisymmetry, thin-walled cylinder, Laplace’s law, thick-walled cylinder 
  • Computational linear elasticity: Practical session on using finite element software, geometry construction, meshing, boundary conditions, material parameters, problem solving, interpreting numerical outcome 
  • Viscoelasticity: Rate-dependence of material response, hysteresis, stress relaxation, creep, linear viscoelastic constitutive laws: Maxwell, Kelvin-voigt, standard linear viscoelastic model, solution technique using Laplace transform 
  • Biomaterials and Finite Elasticity: Eulerian vs Lagrangian frames, Infinitesimal vs finite strains, constitutive nonlinearity, fibres, cardiac/vascular constitutive relations
 

Summative Assessment

Details of the module's summative assessment/s

TypeWeighting

Examination (January) (2 hours)

70%

Coursework

30%

Formative Assessment

Unmarked exercises some of which will be in the form of KEATS quizzes. 

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