Undergraduate Teaching 2023-24

Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2023-24

Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2023-24

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Module Leader

Dr G McShane


Prof GN Wells and Dr GJ McShane

Timing and Structure

Lent term. 16 lectures (including examples classes). Assessment: 100% exam


3C7 assumed; 3D7 useful


The aims of the course are to:

  • develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
  • understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.


As specific objectives, by the end of the course students should be able to:

  • show a working knowledge of tensor notation
  • define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
  • use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
  • solve linear viscoelastic problems for arbitrary loading time-histories
  • understand numerical solution methods for nonlinear continuum mechanics problems.


This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.


Preliminaries (2L, Dr GJ McShane)

  • Introduction to indicial notation.
  • Vectors, tensors and their manipulation.

Linearised Continuum Mechanics (6L, Dr GJ McShane)

  • Kinematics: infinitesimal strains, compatibility.
  • Conservation laws; stress and equilibrium.
  • Linear elasticity: method of stationary potential energy.
  • Linear viscoelasticity: constitutive equations;  solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.

Nonlinear Continuum Mechanics (8L, Prof GN Wells)

  • Nonlinear kinematics.
  • Strain rates and stress measures.
  • Nonlinear elasticity:  stationary potential energy and hyper-elasticity.
  • Numerical solution methods.

Examples papers

  • Papers 1-2 - Preliminaries and linearised continuum mechanics.
  • Papers 3-4 - Nonlinear continuum mechanics


Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.


This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.


Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.


Apply appropriate quantitative science and engineering tools to the analysis of problems.


Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.


Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.


Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.


Ability to use fundamental knowledge to investigate new and emerging technologies.


Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.


Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.


Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).


A comprehensive understanding of the scientific principles of own specialisation and related disciplines.


A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 30/05/2023 15:28