Hardening rules for finite deformation micropolar plasticity: Restrictions imposed by the second law of thermodynamics and the postulate of Il'iushin

Grammenoudis, P.; Tsakmakis, Ch.

doi:10.1007/s001610100055

Cited by 35 publications

(44 citation statements)

References 28 publications

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“…It is important to notice thatK p in Grammenoudis and Tsakmakis [22] is related to some gradient terms relative to the reference configuration and hence should satisfy some kind of compatibility conditions, but such compatibility conditions are not considered in [22]. Therefore, strictly speaking, that constitutive theory is wrong.…”

Section: The Micropolar Plasticity Modelmentioning

confidence: 95%

“…Therefore, strictly speaking, that constitutive theory is wrong. However, one can defineK p to be only a linear map, which otherwise fulfills the same transformations conditions asK p in [22]. Then, the constitutive theory developed in Grammenoudis and Tsakmakis [22] will be correct, and this version is adopted here.…”

Section: The Micropolar Plasticity Modelmentioning

confidence: 97%

“…(1), a thermodynamically consistent micropolar plasticity theory has been proposed by Grammenoudis and Tsakmakis [22]. Focusing attention on isotropic hardening only, and using the notation introduced in [22], the most relevant constitutive relations of that theory, relative to the plastic intermediate configuration, are given as follows.…”

Section: The Micropolar Plasticity Modelmentioning

confidence: 99%

“…Focusing attention on isotropic hardening only, and using the notation introduced in [22], the most relevant constitutive relations of that theory, relative to the plastic intermediate configuration, are given as follows.…”

Section: The Micropolar Plasticity Modelmentioning

confidence: 99%

“…A constitutive model for finite-deformation micropolar plasticity exhibiting kinematic and isotropic hardening in a thermodynamically consistent way has been proposed by Grammenoudis and Tsakmakis [22][23][24]. While kinematic hardening separately addresses effects due to strain and rotation gradients, isotropic hardening in these papers was formulated in a unified manner, i.e., the influence of strain and rotation gradient terms on isotropic hardening is not accounted for separately.…”

Section: Introductionmentioning

confidence: 98%

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Isotropic hardening in micropolar plasticity

Grammenoudis

Tsakmakis

2008

Arch Appl Mech

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Experimental evidence for length scale effects in plasticity has been provided, e.g., by Fleck et al. (Acta Metall. Mater. 42:475-487, 1994). Results from torsional loadings on copper wires, when appropriately displayed, indicated that, for the same shear at the outer radius, the normalized torque increased with decreasing specimen radius. Modeling of the constitutive behavior in the framework of micropolar plasticity is a possibility to account for length scale effects. The present paper is concerned with this possibility and deals with the theory developed by Grammenoudis and Tsakmakis (Contin. ). Both isotropic and kinematic hardening are present in that theory, with isotropic hardening being captured in a unified manner. Here, we discuss isotropic hardening composed of two parts, responsible for strain and gradient effects, respectively.

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Section: The Micropolar Plasticity Modelmentioning

confidence: 95%

Section: The Micropolar Plasticity Modelmentioning

confidence: 97%

Section: The Micropolar Plasticity Modelmentioning

confidence: 99%

Section: The Micropolar Plasticity Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 3 more Smart Citations

Isotropic hardening in micropolar plasticity

Grammenoudis

Tsakmakis

2008

Arch Appl Mech

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Finite element implementation of large deformation micropolar plasticity exhibiting isotropic and kinematic hardening effects

Grammenoudis

Tsakmakis

2005

Int. J. Numer. Meth. Engng

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SUMMARYMicropolar theories offer a possibility to model size effects in the constitutive behaviour of materials. Typical feature of such models is that they deal with a microrotation, which is supposed to represent an independent state variable, and its space gradient. As a consequence, the stress tensor is no longer symmetric and couple stresses enter the theory. Accordingly, a micropolar plasticity law exhibiting kinematic hardening effects should account for both, a back-stress tensor and a back-couple stress tensor. This has been considered in the micropolar plasticity model developed by Grammenoudis and Tsakmakis. The purpose of the current paper is to specify some constitutive functions in this model, to elucidate the finite element implementation as well as to demonstrate its capabilities in describing size effects.

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Micropolar hyper‐elastoplasticity: constitutive model, consistent linearization, and simulation of 3D scale effects

Bauer

Dettmer

Perić

et al. 2012

Numerical Meth Engineering

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SUMMARY A computational model for micropolar hyperelastic‐based finite elastoplasticity that incorporates isotropic hardening is developed. The basic concepts of the non‐linear micropolar kinematic framework are reviewed, and a thermodynamically consistent constitutive model that features Neo‐Hooke‐type elasticity and generalized von Mises plasticity is described. The integration of the constitutive initial value problem is carried out by means of an elastic‐predictor/plastic‐corrector algorithm, which retains plastic incompressibility. The solution procedure is developed carefully and described in detail. The consistent material tangent is derived. The micropolar constitutive model is implemented in an implicit finite element framework. The numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented. The results of the finite element simulations demonstrate (i) that the methodology is capable of capturing the size effect in three‐dimensional elastoplastic solids in the finite strain regime, (ii) that the formulation possesses a regularizing effect in the presence of strain localization, and (iii) that asymptotically quadratic convergence rates of the Newton–Raphson procedure are achieved. Throughout this paper, effort is made to present the developments as a direct extension of standard finite deformation computational plasticity. Copyright © 2012 John Wiley & Sons, Ltd.

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Hardening rules for finite deformation micropolar plasticity: Restrictions imposed by the second law of thermodynamics and the postulate of Il'iushin

Cited by 35 publications

References 28 publications

Isotropic hardening in micropolar plasticity

Isotropic hardening in micropolar plasticity

Finite element implementation of large deformation micropolar plasticity exhibiting isotropic and kinematic hardening effects

Micropolar hyper‐elastoplasticity: constitutive model, consistent linearization, and simulation of 3D scale effects

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