Course map

Syllabus

Read sequentially or jump to a chapter. Each page is layered: a BEng-friendly narrative, then optional MEng derivations, then PhD-level depth.

Module 01

Prerequisites

Tensor algebra & analysis recap and a refresher on linear elasticity — the small-strain world we will leave behind.

  1. 00a

    Vector & Tensor Algebra & Analysis Recap

    Vectors and tensors in an orthonormal basis, Einstein summation, Kronecker δ and permutation symbol, 2nd / 3rd / 4th order tensors, eigenvalues, Cayley–Hamilton, invariants.

    BEngMEngPhD
    55 min
  2. 00b

    Linear Elasticity Recap

    Small-strain assumption, Cauchy stress and infinitesimal strain, elastic moduli, isotropic compressible and incompressible material laws.

    BEngMEngPhD
    35 min
Module 02

Foundations

Tissues as continua, motivation, and the language of finite deformation.

  1. 01

    Why Soft Tissues Need Their Own Mechanics

    Why classical linear elasticity fails for skin, artery, tendon, heart, lung and brain — and what we need instead.

    BEngMEngPhD
    20 min
  2. 02

    Continuum Kinematics for Large Deformation

    Deformation gradient, polar decomposition, strain measures — the toolkit for everything that follows.

    BEngMEngPhD
    45 min
  3. 03

    Stress in Finite Deformation

    Cauchy, first and second Piola–Kirchhoff stress. Push-forward, pull-back, and which one to use when.

    BEngMEngPhD
    35 min
Module 03

Constitutive Modelling

Strain-energy functions for incompressible, anisotropic, fibre-reinforced tissues.

  1. 04

    Hyperelasticity & Isotropic Models

    Strain-energy functions Ψ(C): isotropic baselines (Neo-Hookean, Mooney–Rivlin, Ogden) and a preview of the two anisotropic families — invariant-based (structural) and Fung-type exponential — that Chapter 05 develops in full.

    BEngMEngPhD
    50 min
  2. 05

    Fibre-Reinforced Anisotropy (HGO, Holzapfel–Ogden, Guccione)

    Transversely isotropic and orthotropic models for arteries and myocardium: Holzapfel–Gasser–Ogden, Holzapfel–Ogden, and the Fung-type Guccione law. Fibre, sheet and sheet-normal families, structural invariants I₄, I₆, I₈.

    MEngPhD
    55 min
  3. 06

    Viscoelasticity & Time-Dependent Response

    Fung QLV for vessels and lung parenchyma, relaxation, hysteresis, preconditioning, and breathing-rate dependence.

    MEngPhD
    45 min
Module 04

Advanced Topics

Damage, growth, mixture theory and experimental identification.

  1. 07

    Damage, Mullins Effect & Failure

    Softening on reloading, continuum damage formulations and failure criteria.

    PhD
    40 min
  2. 08

    Growth & Remodelling

    Multiplicative decomposition F = Fe·Fg and constrained mixture theory.

    PhD
    50 min
  3. 09

    Experiments & Parameter Identification

    Uniaxial, biaxial, inflation tests; inverse problems and identifiability.

    MEngPhD
    40 min
Module 05

References

Books and papers the course material draws on.

  1. 10

    References

    Primary textbooks and papers cited across the chapters and lesson videos.

    BEngMEngPhD
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