This course introduces concepts and methods of continuum mechanics, as used to describe some of the physical properties of rock and other earth materials. The aim is to provide a clear picture of some of the basic concepts applicable to all continua, a thorough introduction to certain types (notably elastic solids), and an overview of other areas, to the level that the student will know where to find out more. Because of time limits, methods for the solutions of specific problems will be discussed only briefly. The course is intended for first-year graduate students with a good undergraduate background in math and physics.
4 units, 3 lecture hours/week
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Vectors and (Cartesian) tensors, including calculus. |
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Deformation: infinitesimal strain in 2-D and 3-D, elementary finite strain. |
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Stress tensor and conservation equations |
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Constitutive equations: elasticity |
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Elastic waves in an unbounded medium |
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2-d elasticity problems, elastic dislocations |
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Viscoelasticity; attenuation in nearly-elastic materials; |
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Thermodynamics of continua. |
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Failure and friction in rock. |
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Porous media: fluid flow and poroelasticity |
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Finite strain, and the effect of large hydrostatic pressures. |
Except for the material on vectors and tensors, the main source will be the fairly detailed class notes The mathematical material will come from Malvern, Introduction to the Mechanics of a Continuous Medium, which is to some extent the model for the course notes. This is in print, unfortunately only as a shoddy and expensive paperback. A good supplement to the notes is Continuum Mechanics by George Mase, in the Schaum’s Outline Series.