A critical review of the state of finite plasticity

Naghdi, P. M.

doi:10.1007/bf00959986

Cited by 237 publications

(38 citation statements)

References 149 publications

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“…This C e can be used to characterize the free energy w, i.e. w wC e Y T [18]. It is to be noted that an equivalent tensor to C e was introduced by Green and Naghdi [25], denoted by R T P C e R p in their notation.…”

Section: Deformation Measuresmentioning

confidence: 99%

“…for elastic response, unloading and neutral loading, H is given by the ®rst two terms on the right-hand side (RHS) of (26) which represent the thermoelastic fourth-order stiffness tensor. Also, since H T H CY C p is linearly dependent on C [18]. Note that for hyperelasticity, where the stress is derived from the free energy, H is directly linked to w which needs to be de®ned.…”

Section: The Tangent Matrixmentioning

confidence: 99%

“…The speci®c assumptions given in [e.g. 10,18] are repeated here using the notation given in [19] for the¯ow rule and the mechanical isotropic hardening rate…”

Section: The Tangent Matrixmentioning

confidence: 99%

“…The quantity R, which designates mechanical isotropic hardening, requires an evolution equation for R, while / is the yield function such that / 0 describes the elasticity limit. The loading conditions in strain-space formulation are given by [17,18] /`0 elastic state 0 and / /`0 unloading from elastic-plastic state 0 and / / 0 neutral loading 0 and / / b 0 loading…”

Section: The Tangent Matrixmentioning

confidence: 99%

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Objective localization criterion and behavior for finite deformation plasticity - a Lagrangian formulation

Khen¹,

Désoyer

Dragon

1998

Archive of Applied Mechanics (Ingenieur Archiv)

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In this paper, the condition for strain localization bifurcation is studied using Lagrangian description. The localization criterion with respect to the reference con®guration is obtained by relating the rate of the second Piola-Kirchoff stress to the rate of Cauchy-Green deformation tensor. When transferred to the present con®guration, it is equivalent to the one which is obtained when Truesdell rate of Cauchy stress is used in the rate problem. An example for the localization response for a set of triaxial extensions is presented using a speci®c ®nite-deformation thermo-elastic-plastic model.When a small-deformation based localization criterion is used, i.e. when some terms in the localization criterion are neglected, the localization response, at some loading paths, becomes signi®cantly different from that obtained in the presence of these terms. It is therefore concluded that ®nite deformation tools should be employed when localization analysis is performed even when the small deformation hypothesis is otherwise considered as valid.

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Section: Deformation Measuresmentioning

confidence: 99%

Section: The Tangent Matrixmentioning

confidence: 99%

“…The speci®c assumptions given in [e.g. 10,18] are repeated here using the notation given in [19] for the¯ow rule and the mechanical isotropic hardening rate…”

Section: The Tangent Matrixmentioning

confidence: 99%

Section: The Tangent Matrixmentioning

confidence: 99%

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Objective localization criterion and behavior for finite deformation plasticity - a Lagrangian formulation

Khen¹,

Désoyer

Dragon

1998

Archive of Applied Mechanics (Ingenieur Archiv)

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“…There have been areas of disagreement between various ®nite-strain elastoplasticity theories, and a number of fundamental issues between them have been discussed and debated extensively in literature, as shown in a comprehensive and informative review by Naghdi [6]. In particular, the shear oscillation phenomena disclosed in [22,23], [24], [25], promoted reexamination of some basic aspects in ®nite elastoplasticity modeling, such as the de®nition of appropriate objective stress rates, decompositions of the total deformation and the total deformation rate into elastic and plastic parts, etc.…”

Section: Introductionmentioning

confidence: 99%

Large-strain response of isotropic-hardening elastoplasticity with logarithmic rate: Swift effect in torsion

Bruhns¹,

Xiao²,

Meyers³

2001

Archive of Applied Mechanics (Ingenieur Archiv)

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Recently, a new Eulerian rate-type isotropic-hardening elastoplasticity model has been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among all isotropic hardening elastoplastic models with all possible objective corotational stress rates and other known objective stress rates by virtue of the self-consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The simple shear response of this model has been studied and shown to be reasonable for both the shear and normal stress components. The objective of this work is to further study the large deformation response of this model, in particular, the secondorder effects, including the well-known Swift effect, in torsion of thin-walled cylindrical tubes with free ends. An analytical perturbation solution is derived, and numerical results are presented by means of the Runge±Kutta method. It is shown that the prediction of this model for the shear stress is in good accord with experimental data, but the predicted axial length change is negligibly small and much less than experimental data. This suggests that the strain-induced anisotropy may be the main cause of the Swift effect.

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References

2020

Elastoplastic Modeling

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A critical review of the state of finite plasticity

Cited by 237 publications

References 149 publications

Objective localization criterion and behavior for finite deformation plasticity - a Lagrangian formulation

Objective localization criterion and behavior for finite deformation plasticity - a Lagrangian formulation

Large-strain response of isotropic-hardening elastoplasticity with logarithmic rate: Swift effect in torsion

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