Predicting the effective elastic properties of a composite material based on the elastic properties of the constituent materials is extremely difficult, even when the microstructure is known. However, there are cases where certain properties in constituents always carry over to a composite, regardless of the microstructure of the composite. We call such instances exact relations. The general theory of exact relations allows us to find all of these instances in a wide variety of contexts including elasticity, conductivity, and piezoelectricity. We combine this theory with ideas from representation theory to find all exact relations for fiber-reinforced polycrystalline composites. We further extend these ideas to the concept of links. When two composites have the same microstructure but different constituent materials, their effective tensors may be related. We use the theory of exact relations to find such relations, which we call links. In this work we describe a special set of links between elasticity tensors of fiber-reinforced polycrystalline composites. These links allow us to generalize certain results from specific examples to generate new information about this widely-used class of composites. In particular, we apply the link to obtain information about composites made from two transversely isotropic materials and polycrystals made from one orthotropic material. / Mathematics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/1413 |
| Date | January 2012 |
| Creators | Hegg, Meredith Michelle |
| Contributors | Grabovsky, Yury, Berhanu, Shiferaw, Seibold, Benjamin, Moskow, Shari |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 98 pages |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/1395, Theses and Dissertations |
Page generated in 0.0019 seconds