Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Conservation laws and canonical forms in the Stroh formalism of anisotropic elasticity


Author: Gary A. Hatfield
Journal: Quart. Appl. Math. 54 (1996), 739-758
MSC: Primary 73C02; Secondary 35Q72, 73B40
DOI: https://doi.org/10.1090/qam/1417237
MathSciNet review: MR1417237
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Abstract: We find and classify all first-order conservation laws in the Stroh formalism. All possible non-semisimple degeneracies are considered. The laws are found to depend on three arbitrary analytic functions. In some instances, there is an ``extra'' law which is quadratic in $ \nabla u$. Separable and inseparable canonical forms for the stored energy function are given for each type of degeneracy and they are used to compute the conservation laws. The existence of a real Stroh eigenvector is found to be a necessary and sufficient condition for separability. The laws themselves are stated in terms of the Stroh eigenvectors.


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DOI: https://doi.org/10.1090/qam/1417237
Article copyright: © Copyright 1996 American Mathematical Society


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