Week 1: Introduction and mathematical foundations (Module 1): Cartesian tensors, indicial notation, summation rule, Kronecker delta.
Week 2: Mathematical foundations: permutation symbol, epsilon-delta identity, vector and tensor products.
Week 3: Mathematical foundations: matrices and determinants, tensor transformations, isotropy and invariance.
Week 4: Mathematical foundations: principal values and directions, tensor calculus, integral theorems.
Week 5: Stress principles (Module 2): body and surface forces, definition of the Cauchy stress tensor, equilibrium equations.
Week 6: Stress principles: stress transformation laws, principal stresses and directions, Stress maxima and minima, Mohr’s circle, plane stress, spherical and deviatoric stress components.
Week 7: Kinematics (Module 3): configurations, deformation and motion, material and spatial coordinates, Lagrangian and Eulerian descriptions, material derivative.
Week 8: Kinematics: deformation gradient tensor, Lagrangian and Eulerian finite strain tensors, infinitesimal deformation theory and the infinitesimal strain tensor, normal and shear strain tensors, dilatation, and plane strain.
Week 9: Kinematics: differential displacement vector, infinitesimal rotation tensor, velocity gradient tensor, rate of deformation tensor, vorticity tensor, material derivatives of elements.
Week 10: Conservation laws (Module 4): (Reynolds) transport theorem, equation of the conservation of mass in Eulerian and Lagrangian forms, linear momentum principle, Piola-Kirchoff stress tensors, angular momentum principle.
Week 11: Constitutive modelling (Module 5): introduction and closure problem, 4th-order constitutive tensor, linear isotropic and anisotropic models for solids and fluids; non-linear constitutive models including hyperelasticity, plasticity, non-Newtonian fluid behaviour and viscoplasticity; time-dependent models such as viscoelasticity, creep, stress relaxation, thixotropy and rheopexy.
Week 12: Application of continuum mechanics: derivation of Navier-Stokes equation for linear and non-linear fluids; special cases; modelling and solving specific fluid dynamics problems using continuum mechanics principles.
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