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Mathematics > Analysis of PDEs

arXiv:1812.03053 (math)
[Submitted on 7 Dec 2018]

Title:Do we need Truesdell's empirical inequalities? On the coaxiality of stress and stretch

Authors:Christian Thiel, Jendrik Voss, Robert J. Martin, Patrizio Neff
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Abstract:Truesdell's empirical inequalities are considered essential in various fields of nonlinear elasticity. However, they are often used merely as a sufficient criterion for semi-invertibility of the isotropic stress strain-relation, even though weaker and much less restricting constitutive requirements like the strict Baker-Ericksen inequalities are available for this purpose. We elaborate the relations between such constitutive conditions, including a weakened version of the empirical inequalities, and their connection to bi-coaxiality and related matrix properties. In particular, we discuss a number of issues arising from the seemingly ubiquitous use of the phrase "$X,Y$ have the same eigenvectors" when referring to commuting symmetric tensors $X,Y$.
Subjects: Analysis of PDEs (math.AP)
MSC classes: 74B20, 74A20, 74A10
Cite as: arXiv:1812.03053 [math.AP]
  (or arXiv:1812.03053v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1812.03053
Related DOI: https://doi.org/10.1016/j.ijnonlinmec.2019.02.004

Submission history

From: Jendrik Voss [view email]
[v1] Fri, 7 Dec 2018 14:56:29 UTC (41 KB)
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