Logarithmic strain, logarithmic spin and logarithmic rate

Xiao, Heng; Bruhns, Otto T.; Meyers, A.

doi:10.1007/bf01213020

Cited by 297 publications

(210 citation statements)

References 24 publications

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“…In a response to this paper, Onaka has shown 14) that the Hencky strain is an appropriate measure of strain for large deformations including large simple-shear deformation. That is to say, the problems of the Hencky formulation pointed out by Jonas et al 4) and Shrivastava et al 8) on the strain increments have been already solved with the help of the D-frame 12) or the log-spin 13) concept. As shown in recent papers in the field of applied mechanics, for example in Ref.…”

Section: Rotation Of the Principal Axes Of Strainmentioning

confidence: 99%

“…However, understanding on the Hencky strain has changed in the mid1990s. 12,13) In a recent paper, Shrivastava et al 8) have also pointed out this limited applicability of the Hencky formulation. In a response to this paper, Onaka has shown 14) that the Hencky strain is an appropriate measure of strain for large deformations including large simple-shear deformation.…”

Section: Rotation Of the Principal Axes Of Strainmentioning

confidence: 99%

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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%

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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“…Only the logarithmic rate of the Hencky strain can be identified with D. Any other strain measure and any other objective rate are excluded [23].…”

Section: Summarisationmentioning

confidence: 99%

View on a Traditional Elastoplasticity Model<SUP>1</SUP>

Meyers¹

2013

Proceedings of the Indian National Science Academy

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In recent years large deformation plasticity based on the additive decomposition of the stretching has become less popular. Constitutive relations of elastoplasticity have come up that are complicated in nature and mostly formulated in Lagrangean frame. Here i t i s sh o wn t h at t rad i t i o n al E u l eri an el ast o p l ast i ci t y may b e a seri o u s al t ern at i ve. It s st ru ct u re i s si mp l e an d t h e fo rmu l at i o n i s st rai gh t fo rward .

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“…= ( )( )( ) (19) in which is the rotation of the Eulerian axis of the plastic stretch tensor and is the symmetric left plastic stretch tensor satisfying:…”

Section: -Proposed Constitutive Model Of Elastoplasticitymentioning

confidence: 99%

“…Sources of such issues have been associated with hypoelastic model non-integrability as a Cauchy and Green elastic material (see for example references [11,15,16]). To resolve such issues, following the work of Lehmann et al [17], Reinhardt and Dubey [18], and Xiao et al [19], a new objective rate of stress, called the D or logarithmic rate, was introduced. Furthermore, Bruhns et al [10] investigated the integrability conditions of the classical hypoelastic model and showed that the grade zero hypoelastic model is unconditionally integrable as a Cauchy and Green elastic material when the logarithmic (D) rate is used in the model.…”

Section: -Introductionmentioning

confidence: 99%