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    Exact Relations and Links for Fiber-Reinforced Elastic Composites

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    Genre
    Thesis/Dissertation
    Date
    2012
    Author
    Hegg, Meredith Michelle
    Advisor
    Grabovsky, Yury
    Committee member
    Berhanu, Shiferaw
    Seibold, Benjamin
    Moskow, Shari
    Department
    Mathematics
    Subject
    Materials Science
    Applied Mathematics
    Mathematics
    Composite Materials
    Exact Relations
    Fiber-reinforced Composite
    Linear Elasticity
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/1413
    
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    DOI
    http://dx.doi.org/10.34944/dspace/1395
    Abstract
    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.
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