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Unit information: Non-Linear Behaviour of Materials in 2015/16

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Unit name Non-Linear Behaviour of Materials
Unit code MENGM5022
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Professor. Pavier
Open unit status Not open

MENG11100, MENG21100 or equivalent



School/department Department of Mechanical Engineering
Faculty Faculty of Engineering


The unit provides fundamental aspects of the mechanical behaviour of engineering materials, illustrated by realistic engineering calculations. You will learn how to make predictions of material responses using simple elastic, plastic and creep models. You will be given an introduction to general three-dimensional non-linear analysis of solids using tensors. You will learn how complex material behaviour is simulated by numerical methods, in particular by finite elements. The course uses as a foundation the principles and fundamentals established in the first two years of Properties of Materials and Mechanics of Materials.


  • introduce examples of non-linear behaviour of materials,
  • to provide a rigorous framework within which students may solve problems in non-linear stress analysis,
  • to develop the theory of engineering plasticity,
  • to introduce numerical methods for prediction of non-linear material response.

Intended learning outcomes

On completion of the course the student should be able to:

  • make quantitative predictions of non-linear material behaviour, including plasticity and creep.
  • perform transformations on stress and strain tensors.
  • implement complex material behaviour models within finite element framework.

Teaching details

Students receive two one-hour lectures per week for 10 weeks. Notes will be handed out as appropriate and note taking will also be required. The notes may be used in the exam. Example questions will be given out; some examples will be solved during the lectures and the lecturer will state times and dates following the lecture course, when he will be available to discuss any further problems.

Self-assessment questions are given to the students by the course organiser and are used to guide the student through the course. The students are expected to consolidate and enhance the lecture material by private study. The whiteboard, digital and overhead projectors are used for the lecture work.

The teaching will be supplemented by 4 hours of computer labs where the students will have the opportunity to apply some of the course material in practice.

There will be a single piece of coursework, in which the students will have to demonstrate knowledge of the course fundamentals and their practical application.

Assessment Details

2-hour examination in May/June (3 questions out of 4)

Reading and References

  • Love, A. E. H. (1927) A Treatise on the Mathematical Theory of Elasticity, 4 edn, Cambridge University Press
  • L.D. Landau and E.M. Lifschitz (1986) Theory of elasticity, 3rd English ed. Oxford : Pergamon Press, 187 p.
  • Bonet, J. and R. D. Wood (2008) Nonlinear Continuum Mechanics for Finite Element Analysis, 2 edn, Cambridge University Press
  • Hill, R. (1998) The mathematical theory of plasticity, Oxford: Clarendon Press
  • Ted Belytschko, Wing Kam Liu, Brian Moran (2000) Nonlinear finite elements for continua and structures Chichester : John Wiley, 650 p.
  • Fionn Dunne and Nik Petrinic (2005) Introduction to computational plasticity, Oxford : Oxford University Press, 241 p.