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http://hdl.handle.net/10012/7099
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| Title: | The two-space homogenization method |
| Authors: | Murley, Jonathan |
| Keywords: | homogenization
poroelasticity
partial differential equations |
| Approved Date: | 4-Oct-2012 |
| Date Submitted: | 2012 |
| Abstract: | In this thesis, we consider the two-space homogenization method, which produces macroscopic expressions out of descriptions of the behaviour of the microstructure. Specifically, we focus on its application to poroelastic media. After describing the method, we provide examples to demonstrate that the resultant expressions are equivalent to an explicit derivation, which might not always be possible, and to outline the method for proving that the expressions converge to their macroscopic equivalents. Upon providing the basis for this method, we follow Burridge and Keller’s work for using this to prove the existence of Biot’s consolidation equations for poroelastic media and to provide expressions for the derivation of the parameters of these equations from the microstructure [5]. We then discuss the benefits and challenges that arise from this formulation of Biot’s consolidation equations. |
| Program: | Applied Mathematics |
| Department: | Applied Mathematics |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/7099 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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