On the relationship between the logarithmic strain rate and the stretching tensor

Gurtin, Morton E.; Spear, Kathleen

doi:10.1016/0020-7683(83)90054-9

Cited by 90 publications

(34 citation statements)

References 2 publications

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“…As Jonas et al have pointed out in their paper, 4) it is true that the axes of the Hencky strain and its increment do not coincide during simple shear deformation. It is also true that, in papers published in the 1980s, 10,11) we find the consensus on the inapplicability of the Hencky strain to cases where the principal strain axes rotate during deformation. However, understanding on the Hencky strain has changed in the mid1990s.…”

Section: Rotation Of the Principal Axes Of Strainmentioning

confidence: 99%

Appropriateness of the Hencky Equivalent Strain as the Quantity to Represent the Degree of Severe Plastic Deformation

Onaka

2012

Mater. Trans.

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The Hencky strain is a logarithmic strain extended to a three-dimensional analysis. Although Onaka has shown that the Hencky equivalent strain is an appropriate measure of large simple-shear deformation (2010), Jonas et al. (2011) have recently presented a paper claiming that the application of the Hencky strain to large simple-shear deformation is in error. In the present paper, it is shown that the claim of Jonas et al. is contrary to recent accepted knowledge on the Hencky strain.

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Section: Rotation Of the Principal Axes Of Strainmentioning

confidence: 99%

Appropriateness of the Hencky Equivalent Strain as the Quantity to Represent the Degree of Severe Plastic Deformation

Onaka

2012

Mater. Trans.

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“…(68) is relation (2.13) with Eqs. (2.11) and (2.15) in Bruhns and Lehmann [4], which says that the Jaumann rate of h should exactly give D in some cases; see also: Gurtin and Spear [19] and Hoger [30]. The main idea in finding Eq.…”

Section: The Logarithmic Rate and Related Propertiesmentioning

confidence: 99%

“…Nevertheless, this measure was considered as "essentially intractable" and of "particular usefulness" (refer e.g. to Fitzgerald [13] and Gurtin and Spear [19] and the references therein). Knowing the today's computational possibilities, however, we should overcome this position and use Hencky strains in descriptions of finite deformations.…”

Section: The Step Toward Finite Deformationsmentioning

confidence: 99%

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The Prandtl‐Reuss equations revisited

Bruhns

2013

Z Angew Math Mech

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At the beginning of the last century two different types of constitutive relations to describe the complex behavior of elastoplastic material were presented. These were the deformation theory originally developed by Hencky and the Prandtl-Reuss theory. Whereas the former provides a direct solid-like relation of stress as function of strain, the latter has been based on an additive composition of elastic and plastic parts of the increments of strains. These in turn were taken as a solid-and fluid-like combination of the de Saint-Venant/Lévy theory with an incremental form of Hookes law.Even nowadays this Prandtl-Reuss theory is still accepted within the restriction of small elastic deformations, i.e. it is generally stated in most textbooks on plasticity that this theory due to a number of defects can not be applied to large deformations. In the present article it is shown that this restrictive statement may be no longer true. Introducing a specific objective time derivative it could be shown that these defects disappear.

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“…In Section 6 we apply the general results of the preceding sections to the logarithmic strain tensors. We give a rigorous proof of an approximate formula for (In U)' due to Hill [4], and we obtain an improved version of an approximate formula for (ln V)° due to Gurtin and Spear [2].…”

Section: F(v) By F(v)= F(v)° + Wf(v) -F(v)wmentioning

confidence: 99%

Time Rates of Generalized Strain Tensors. Part 2. Approximate Basis-Free Formulas

Scheidler¹

1991

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On the relationship between the logarithmic strain rate and the stretching tensor

Cited by 90 publications

References 2 publications

Appropriateness of the Hencky Equivalent Strain as the Quantity to Represent the Degree of Severe Plastic Deformation

Appropriateness of the Hencky Equivalent Strain as the Quantity to Represent the Degree of Severe Plastic Deformation

The Prandtl‐Reuss equations revisited

Time Rates of Generalized Strain Tensors. Part 2. Approximate Basis-Free Formulas

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