Eulerian strain-rate as a rate of logarithmic strain

Reinhardt, Wolf; Dubey, R. N.

doi:10.1016/0093-6413(95)00008-9

Cited by 47 publications

(17 citation statements)

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“…was proved by Lehmann et al [20], see also Reference [21]. Here, h • log is the logarithmic corotational rate of the spatial logarithmic strain.…”

Section: Twirl Tensor Of the Eulerian Triad Ementioning

confidence: 82%

“…Lehmann et al [20] proved that the objective logarithmic rate of the spatial logarithmic strain is equivalent to the deformation rate. This equivalence was also certiÿed by Reinhardt and Dubey [21]. Systematic and integrated studies on objective corotational rates of objective spatial order-two tensors were performed by Xiao et al [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Numerical study of consistency of rate constitutive equations with elasticity at finite deformation

Lin

2002

Numerical Meth Engineering

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SUMMARYThe present work is concerned with the numerical study of the elasticity consistency of the spatial rate equations using the conventional Oldroyd, Truesdell, Cotter-Rivlin, Jaumann and Green-Naghdi rates and the three novel co-rotational E -and L -based, logarithmic rates, and of the rotated material rate equation describing the relationship between the material time derivatives of the rotated Kirchho stress and material logarithmic strain. To this end, three integration procedures for updating stress are presented. The stress responses of several typical deformation processes are simulated. According to the numerical results we know that among the spatial rate equations only the logarithmic rate equation is consistent with elasticity under constant material parameters. Integrating the other spatial rate equations will provide path-dependent stress response. These numerical conclusions support the arguments in H. Xiao et al. (Acta Mechanica 1999; 138:31-50). The reasons leading to elasticity inconsistency of spatial rate equations are analysed. If the material parameters are assumed to be strain-dependent, the logarithmic rate equation loses also its elasticity-consistent property. The numerical results prove also that the spatial logarithmic and rotated material rate equations are equivalent to each other.

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“…was proved by Lehmann et al [20], see also Reference [21]. Here, h • log is the logarithmic corotational rate of the spatial logarithmic strain.…”

Section: Twirl Tensor Of the Eulerian Triad Ementioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Numerical study of consistency of rate constitutive equations with elasticity at finite deformation

Lin

2002

Numerical Meth Engineering

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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%

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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“…Later, Eq. (71) was also rediscovered by Reinhardt and Dubey [74,75]. This relationship was derived in the general sense of studying Eq.…”

Section: The Logarithmic Rate and Related Propertiesmentioning

confidence: 99%

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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Eulerian strain-rate as a rate of logarithmic strain

Cited by 47 publications

References 1 publication

Numerical study of consistency of rate constitutive equations with elasticity at finite deformation

Numerical study of consistency of rate constitutive equations with elasticity at finite deformation

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

The Prandtl‐Reuss equations revisited

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