Mechanics of Materials - 2019 entry

In this module you will learn about i) the theory of elasticity and specifically application of it using a tensor approach to tackle more advanced problems, ii) experimental stress analysis techniques to measure strains and stress in components, and iii) about failure and fracture of solids, and the methods engineers use to predict these.

An example could be a component with manufacturing defects which give rise to unexpected stress concentrations. This module will give you the knowledge and skills to calculate what these stresses are, measure them in a real component, and to re-design the component to avoid such issues. This will help prepare you for similar complex problems in professional practice, often involving measurement of stress on real components and computational modelling.

Firstly it extends students’ knowledge of elasticity towards more advanced aspects, and takes a tensorial approach as is often required in solid mechanics. The theory of elasticity and its use in tensorial form, underlies many aspects of modern engineering practice, for instance in the simulation of static and dynamic responses of components and structures in Finite Element Analysis. Professional standards of practice almost always require use of elasticity to predict the behaviour of safety critical components. This part provides a solid basis for further study of Solid Mechanics, Computational Engineering and Materials.

The module then moves on to introduce and develop experimental stress analysis techniques. It starts with a review of the physics behind a range of modern techniques, identifying how these make them suitable or unsuitable for different applications. It goes on to apply some techniques, e.g. foil resistance strain gauges, to the classic problem of a flat plate with a circular hole in a laboratory session.

In the third section it extends knowledge form earlier modules failure and fracture behaviour of materials, and particularly on analytical techniques to predict such problems. This includes laboratory demonstrations of failure/fracture and use of Finite element methods to simulate such responses.
 

This module develops understanding of the theory of elasticity, experimental methods for measurement of stress and strain, analysis of such data, and the consequences of exceeding the limits of elasticity, i.e. yield and fracture, across three equal length sections.

The intention of the first section is to extend knowledge of and skills with theory of elasticity and its application to solve more complex problems.

The aim of the second section is to give students the skills to select appropriate methods for experimental measurement of stress, and to correctly interpret resulting data.

The aim of the third section is to extend knowledge and skills of failure and fracture, including how to predict these responses and thus design safe structures.
 
 

This is a constituent module of one or more degree programmes which are accredited by a professional engineering institution under licence from the Engineering Council. The learning outcomes for this module have been mapped to the output standards required for an accredited programme, as listed in the current version of the Engineering Council’s ‘Accreditation of Higher Education Programmes’ document (AHEP-V3).

This module contributes to learning outcomes: SM1p, SM1m, SM1fl, SM2p, SM2m, EA1p, EA1m, EA2p, EA2m, EA3p, EA3m, EA1fl, EA6m, EA3fl, EP3p, EP3m, D3p, D3m, D1fl, D2fl, EP3p, EP3m, EP8p, EP8m, EP9m, EP2fl, EP3fl, G1p, G1m, G1fl
 

A full list of the referenced outcomes is provided online: http://intranet.exeter.ac.uk/emps/subjects/engineering/accreditation/

The AHEP document can be viewed in full on the Engineering Council’s website, at http://www.engc.org.uk/

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge: SM1p, SM1m, SM1fl, SM2p, SM2m, EA1p, EA1m, EA2p, EA2m, EA3p, EA3m, EA1fl, EP3p, EP3m, EP8p, EP8m

1 understand the physical concepts of stress and strain in tensorial form, demonstrate familiarity with the stress and strain patterns for certain canonical stress problems, derive principle stresses and strains for 2D and 3D elasticity problems;
2 comprehend and apply the mathematical techniques, (eg. Stress Functions) used to derive analytical solutions for these cases;
3 show familiarity with the range of experimental stress analysis techniques, their fundamental principles, application and limitations, select techniques appropriately, critically evaluate experimental data in the light of theoretical analysis and apply this to component design;
4 appreciate the fundamentals theories underpinning yield and fracture mechanics, and apply them to more complex problems including via numerical simulation.

Discipline Specific Skills and Knowledge: EA3p, EA3m, EA1fl, EP8p, EP8m, D3p, D3m, D1fl, D2fl
5 apply mathematical theory to experimental data and critically evaluate both this data and theoretical limitations;
6 display enhanced skills in determining appropriate theoretical and experimental techniques for problems;
7 demonstrate improved ability to use computational methods to model engineering problems.
 

Personal and Key Transferable/ Employment Skills and  Knowledge:

8 write clear accounts (of laboratory experiments and demonstrations);

9 reveal a high level of proficiency in analysing information;

10 exemplify excellent organisational and time management skills, and the ability to learn independently, through planning your own work;
11 prove strong communication skills, through presenting your work orally and in writing.

Section 1. Theory of Elasticity

mathematical concepts of stress and strain; stress vector/tensor; Hooke's Law; 2nd rank tensors: representation, mathematical theory, notations; plane stress and plane strain; 2D Cartesian problems; force balance equations for stress, boundary conditions, compatibility; airy stress function and some simple solutions; 2D problems in polar co-ordinates; solution via analytical and numerical techniques; evaluation of strain from stress solution; plane strain, governing equations in 2D, including body forces;

Section 2. Experimental Stress Analysis
strain measurement basics;
physical methods and limitations, including electrical resistance strain gauges: underlying physics, their application, data acquisition and analysis methods; semi-conductor and fibre optic strain gauges, principles of operation, applications and limitations; optical methods including Moire interferometry and digital image correlation yield and strength failure criteria; 

Section 3. Failure and Fracture
ductile and brittle materials, including Mohr-Coulomb, Tresca, von Mises; plasticity; non hardening multi-axial plasticity; stress concentration factors; linear elastic fracture mechanics.
 

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 50% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

ELE – http://vle.exeter.ac.uk

Reading list for this module: