On the independence of strain invariants of two preferred direction nonlinear elasticity
Author
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Shariff, M. H. B. M.
Author
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Bustamante Plaza, Roger
Admission date
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2015-12-29T20:23:12Z
Available date
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2015-12-29T20:23:12Z
Publication date
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2015
Cita de ítem
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International Journal of Engineering Science 97 (2015) 18–25
en_US
Identifier
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DOI: 10.1016/j.ijengsci.2015.08.002
Identifier
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https://repositorio.uchile.cl/handle/2250/136051
General note
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Artículo de publicación ISI
en_US
Abstract
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It is often assumed in the literature that the nine classical strain invariants, which are used to characterize the strain energy of a compressible anisotropic elastic solid with two preferred non-orthogonal directions are independent. In this paper, it is shown that only six of the classical strain invariants are independent, and syzygies exist between the classical invariants. Alternatively, using principal axis techniques, it is simply proven that, only six of the classical strain invariants are independent and syzygies exist between the principal axis strain invariants. Consequently, all other sets of strain invariants, proposed in the literature, which are uniquely related to the set of principal axis strain invariants, have only six independent invariants. Due to syzygies, it is shown that the number of ground state constants required to fully describe the quadratic linear strain energy function of two-fibre solids is fourteen, not thirteen, as assumed in the literature.