2001
DOI: 10.1098/rspa.2001.0818
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Constitutive inequalities for an isotropic elastic strain-energy function based on Hencky's logarithmic strain tensor

Abstract: In general, h and τ do not constitute a pair of conjugate variables in the sense of Hill's workconjugacy notion (see Ogden (1984) for detail). For the particular case of isotropy, however, it may be shown (Bruhns et al. 2000) that h and τ are a conjugate pair. Thus, the Hencky strain-energy function (1.4) is indeed a potential function, and equation (1.5) below exactly defines a hyperelastic relation.

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Cited by 87 publications
(87 citation statements)
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“…• with the axes 16 ; but it is easy to prove that the tangential load, T r, is maximum for the planes of no distortion. These are also the planes of maximum tangential strain 17 .…”
Section: B Notationmentioning
confidence: 99%
See 1 more Smart Citation
“…• with the axes 16 ; but it is easy to prove that the tangential load, T r, is maximum for the planes of no distortion. These are also the planes of maximum tangential strain 17 .…”
Section: B Notationmentioning
confidence: 99%
“…This condition is often restated as the convexity of the mapping log U → W (log U) for U ∈ PSym(3). This inequality is independent of the rank-one convexity of the energy: for example, while it is easy to see that the quadratic Hencky strain energy fulfils Hill's inequality, it is not rank-one convex [16,54]. …”
mentioning
confidence: 99%
“…Written with relative indexes this is the transformation rule (50). The extensivity relation is absolute and therefore Galilean invariant, because it is the absolute timelike part of an four-vector equation:…”
Section: 3mentioning
confidence: 99%
“…One can define infinite number of deformation measures that are objective in the sense of Noll, and even more that are not. It is remarkable that the space-time requirements distinguish a single concept of deformation [46,47,48], which turned out to be advantageous from other points of view, too [49,50,51,52,53]. (3) Flow-frames.…”
Section: Introductionmentioning
confidence: 99%
“…[55,76]). We assume that material stability is not an issue in the elastic-only regime (this issue is discussed in reference [23]). …”
Section: Continuum Model 1: J2-plasticitymentioning
confidence: 99%