Show/hide main menu


Advanced Mechanics

Module code: 6CCYB050

Credits: 15

Module convenor: Dr Jack Lee


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


Examination (January) (2 hours)




Formative Assessment

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

Sitemap Site help Terms and conditions  Privacy policy  Accessibility  Modern slavery statement  Contact us

© 2021 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454