School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2021/22 Last Updated: 23 September 2021

MAT-40012 - Continuum Mechanics

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Level 6 Partial differential Equations MAT-30003

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Although every type of solid material or fluid has a discrete structure at a small enough lengthscale, many of them can be idealized as a continuum if the phenomena that we are trying to explain have a large enough lengthscale. Simple experiments show that when water is set in motion the shear stress is linearly proportional to the velocity gradient, and when a steel bar is stretched the internal stress is linearly proportional to length extension. Such simple observations and related engineering applications led to the development of Linear Elasticity and Newtonian Fluid Mechanics in the first half of the 20th century. However, with the emergence of rubber material and increased use of liquids other than water in the second half of the 20th century, it was soon recognized that existing linear theories were inadequate, and rather than treating the newly emerging, highly nonlinear materials separately in an ad hoc manner, a unified treatment of continua based on a common set of basic principles would be far superior. This gave rise to the establishment of the new discipline of Continuum Mechanics.

Continuum Mechanics is nowadays finding applications wherever soft materials are involved. It is being continuously extended to include more and more non-classical materials such as bio-materials (e.g. bones and arteries), and electroelastic/magnetoelastic materials (e.g. dielectric elastomers used in actuators and transducers). As a result, Continuum Mechanics underpins a variety of engineering and bio-medical applications.

This module develops the following Keele Graduate Attributes:

1. an open and questioning approach to ideas, demonstrating curiosity and independence of thought;

2. an appreciation of the development and value of Mathematics and the links between different areas of the subject;

4. the ability creatively to solve problems using a range of different approaches and techniques, and to determine which techniques are appropriate for the problem at hand;

6. the ability to communicate clearly and effectively in written and verbal forms.

Continuum Mechanics is nowadays finding applications wherever soft materials are involved. It is being continuously extended to include more and more non-classical materials such as bio-materials (e.g. bones and arteries), and electroelastic/magnetoelastic materials (e.g. dielectric elastomers used in actuators and transducers). As a result, Continuum Mechanics underpins a variety of engineering and bio-medical applications.

This module develops the following Keele Graduate Attributes:

1. an open and questioning approach to ideas, demonstrating curiosity and independence of thought;

2. an appreciation of the development and value of Mathematics and the links between different areas of the subject;

4. the ability creatively to solve problems using a range of different approaches and techniques, and to determine which techniques are appropriate for the problem at hand;

6. the ability to communicate clearly and effectively in written and verbal forms.

The aims of the module are to introduce the basic principles governing the motion/deformation of all types of continuum,

derive the governing equations for elastic solids and Newtonian fluids, and illustrate the theories by solving some simple

boundary value problems involving fluids or solids.

derive the governing equations for elastic solids and Newtonian fluids, and illustrate the theories by solving some simple

boundary value problems involving fluids or solids.

describe how the performance of different devices and structures in present-day engineering is underpinned by continuum mechanics: 1

state the basic principles governing the motion/deformation of all types of continua: 1

use the basic principles of continuum mechanics to derive the governing equations for non-linear elastic solids and Newtonian fluids: 1

solve boundary value problems: 1

demonstrate, by solving problems, an ability to algebraically manipulate vectors and tensors: 1

state the basic principles governing the motion/deformation of all types of continua: 1

use the basic principles of continuum mechanics to derive the governing equations for non-linear elastic solids and Newtonian fluids: 1

solve boundary value problems: 1

demonstrate, by solving problems, an ability to algebraically manipulate vectors and tensors: 1

48 hours classes.

149 hours private study.

3 hours exam

149 hours private study.

3 hours exam

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Closed-book exam

A closed-book examination combining seen and unseen material.