| CODE | GSC3105 | ||||||||
| TITLE | Continuum Mechanics for Geoscientists | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Geosciences | ||||||||
| DESCRIPTION | The study-unit provides a comprehend introduction to continuum mechanics. It will start with an overview of vector algebra before introducing the notion of tensors. Various properties of tensors will be discussed including the indicial notation and tensor calculus. This will provide the bases for discussing the kinematics of a continuum followed by the description of the state of stress and the basic principles of continuum physics. Then the elastic behavior of solids will be presented followed by practical applications in geoscience. Study-unit Aims: Continuum mechanics provides a description of the mechanical behaviour of materials modelled as if they are composed of a continuum system rather than made of discrete particles. It a general framework that encompasses both solid and fluid mechanics. The study-unit aims at providing the basic mathematical tools underlying the theory. Starting off from the basic definition of tensors, it provides the detail of their mathematical treatment before proceeding to derive the equations of motion of continuous media. Beyond this point, the focus will be on the application of the theory to solid mechanics, starting with a description of the constituent equations. The notions learned will then be applied to waves propagating in solid media, which are important in seismology. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: - explain the importance of continuum mechanics; - identify a tensor and specify its properties; - work out problems involving vector and tensor algebra; - distinguish between the material and spatial description of a particle; - define the material derivative; - explain the physical meaning of the components of the infinitesimal strain tensor; - define the principal strains, the stress vector and the stress tensor; - state the equations of motion for any continuum in motion; - identify boundary conditions; - state the equations for stress power, rate of heat flow into an element by conduction and the energy equation; - state the definitions of Young's modulus, Poisson's ratio, shear modulus, and bulk modulus; - state the Navier equations of motion for elastic medium; - distinguish between S and P waves. 2. Skills By the end of the study-unit the student will be able to: - use the material derivative to find the velocity and acceleration of a particle; - use the kinematic equations for rigid body motion to solve problems; - determine the strain tensor from the displacement field; - determine the principal strains of a given strain tensor; - calculate the dilatation, change in area and change in volume induced on a body; - determine the stress vector and stress tensor; - determine the principal stress of and the maximum shear induced by a given stress tensor; - use the equations of motion for any continuum in motion and boundary conditions to solve problems; - use the equations for stress power, rate of heat flow into an element by conduction and the energy equation to solve problems; - use Young's modulus, Poisson's ratio, shear modulus and bulk modulus to solve problems; - use the Navier equations of motion for elastic medium to solve problems; - apply the concepts of continuum mechanics to problems in geosciences. Main Text/s and any supplementary readings: Main Textbooks: - WM Lai, D Rubin and E Krempl, Introduction to Continuum Mechanics, Fourth Edition, Butterworth-Heinemann, Oxford, UK 2010. - T Lay and T Wallace, Modern Global Seismology, First Edition, Academic Press, London, UK, 1995. Supplementary Reading: - K Aki and PG Richards, Quantitative Seismology Second Edition, University Science Books, California, USA, 2009. - WI Newman, Continuum Mechanics in the Earth Sciences, Cambridge University Pressi, UK, 2012. |
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| ADDITIONAL NOTES | An A-Level knowledge of Mathematics in particular differentiation, partial differentiation, matrices, vector algebra, integration and solution of different equations. Follow from Study-Unit: PHY3225 |
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| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2025/6. It may be subject to change in subsequent years. |
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