Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Generalisation of Hooke's law for finite strain to include the elastic range of strain-hardening materials


Author: E. W. Billington
Journal: Quart. Appl. Math. 62 (2004), 781-795
MSC: Primary 74B20; Secondary 74A20, 74C15
DOI: https://doi.org/10.1090/qam/2104274
MathSciNet review: MR2104274
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Abstract: The representation theorem for isotropic tensor-valued functions of symmetric second-order tensors is considered in the context of two parameters based on the Lode and Fromm parameters. A geometrical representation is established using the concept of a characteristic representation intensity function. It is shown that this geometrical representation identifies the only admissible form of the representation intensity function to be piecewise linear and continuous. This conclusion imposes a restriction on how the representation theorem can be used to formulate constitutive equations. The representation theorem is used to formulate a generalisation of Hooke's law for finite strain that is applicable to the initial elastic range of strain-hardening materials, including the elastic conditions at initial yield.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/qam/2104274
Article copyright: © Copyright 2004 American Mathematical Society


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