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#### Elastic-plastic modeling of kinematic hardening materials based on F = FeFp decomposition and the logarithmic strain tensor

, Article Proceedings of the 7th Biennial Conference on Engineering Systems Design and Analysis - 2004, Manchester, 19 July 2004 through 22 July 2004 ; Volume 1 , 2004 , Pages 337-342 ; 0791841731 (ISBN); 9780791841730 (ISBN) ; Naghdabadi, R ; Sharif University of Technology
American Society of Mechanical Engineers
2004

Abstract

In this paper, based on the multiplicative decomposition of the deformation gradient tensor an elastic-plastic modeling of kinematic hardening materials is introduced. In this model, the elastic constitutive equation as well as the flow rule and hardening equation are expressed in terms of the corotational rate of the elastic and plastic logarithmic strains. As an application, the simple shear problem is solved and the stress components are plotted versus shear displacement for a kinematic hardening material

####
Determination of Primary Function and Associated Spin Tensor For Linear Rate Type Isotropic Tensor Functions

,
M.Sc. Thesis
Sharif University of Technology
;
Sohrabpour, Saeed
(Supervisor)
;
Asghari, Mohsen
(Supervisor)
Abstract

In modelling of large deformations in deformable solids, rate type constitutive equations are of great importance. In order to fulfill the material objectivity conditions it is necessary to choose an objective rate of stress tensor. On the other hand, using corotational rates, because of their special properties (which are resulted of the fact that varaition of parameters are computed from an observer connected to a rotated triad), in rate type non-linear elastic constitutive equations (called hypo-elastic equations) are notable. In this thesis, the necessary conditions for a linear rate type isotropic tensor-valued function of a tensor argument and its rate to be integrable are driven. In...

#### On the objective corotational rates of eulerian strain measures

, Article Journal of Elasticity ; Volume 90, Issue 2 , 2008 , Pages 175-207 ; 03743535 (ISSN) ; Naghdabadi, R ; Sharif University of Technology
2008

Abstract

In the present paper, some new basis-free expressions for an arbitrary objective corotational rate of the general Eulerian strain measures are provided which are in compact form. Moreover, a complete discussion on the requirements for the continuity of the objective corotational rates are presented. © 2008 Springer Science+Business Media B.V

#### Spin tensors associated with corotational rates and corotational integrals in continua

, Article International Journal of Solids and Structures ; Volume 44, Issue 16 , 2007 , Pages 5222-5235 ; 00207683 (ISSN) ; Naghdabadi, R ; Sharif University of Technology
2007

Abstract

In many cases of constitutive modeling of continua undergoing large deformations, use of corotational rates and integrals is inevitable to avoid the effects of rigid body rotations. Making corotational rates associated with specific spin tensors is a matter of interest, which can help for a better physical interpretation of the deformation. In this paper, for a given kinematic tensor function, say G, a tensor valued function F as well as a spin tensor Ω0 is obtained in such a way that the corotational rate of F associated with the spin tensor Ω0, becomes equal to G. In other words, F is the corotational integral of G associated with the spin tensor Ω0. Here, G is decomposed additively into...

#### An eulerian multiplicative constitutive model of finite elastoplasticity

, Article European Journal of Mechanics, A/Solids ; Volume 28, Issue 6 , 2009 , Pages 1088-1097 ; 09977538 (ISSN) ; Vafai, A ; Desai, C ; Sharif University of Technology
2009

Abstract

An Eulerian rate-independent constitutive model for isotropic materials undergoing finite elastoplastic deformation is formulated. Entirely fulfilling the multiplicative decomposition of the deformation gradient, a constitutive equation and the coupled elastoplastic spin of the objective corotational rate therein are explicitly derived. For the purely elastic deformation, the model degenerates into a hypoelastic-type equation with the Green-Naghdi rate. For the small elastic- and rigid-plastic deformations, the model converges to the widely-used additive model where the Jaumann rate is used. Finally, as an illustration, using a combined exponential isotropic-nonlinear kinematic hardening...

#### Corotational analysis of elastic-plastic hardening materials based on different kinematic decompositions

, Article ASME PVP2006/ICPVT-11 Conference, Vancouver, BC, 23 July 2006 through 27 July 2006 ; Volume 2006 , 2006 ; 0277027X (ISSN) ; 0791837823 (ISBN); 9780791837825 (ISBN) ; Naghdabadi, R ; Sharif University of Technology
2006

Abstract

In this paper, two corotational modeling for elastic-plastic, mixed hardening materials at finite deformations are introduced. In these models, the additive decomposition of the strain rate tensor as well as the multiplicative decomposition of the deformation gradient tensor is used. For this purpose, corotational constitutive equations are derived for elastic-plastic hardening materials with the non-linear Armstrong-Frederick kinematic hardening and isotropic hardening models. As an application of the proposed constitutive modeling, the governing equations are solved numerically for the simple shear problem with different corotational rates and the stress components are plotted versus the...

#### Elastic-plastic modeling of the hardening materials based on an Eulerian strain tensor and a proper corotational rate

, Article 2005 ASME Pressure Vessels and Piping Conference, PVP2005, Denver, CO, 17 July 2005 through 21 July 2005 ; Volume 2 , 2005 , Pages 201-206 ; 0277027X (ISSN) ; Ghavam, K ; Sharif University of Technology
2005

Abstract

In this paper a model for analyzing elastic-plastic kinematic hardening materials is introduced, based on the additive decomposition of the corotational rate of an Eulerian strain tensor In this model, the elastic constitutive equation as well as the flow rule and the hardening equation is expressed in terms of the elastic and plastic parts of the corotational rate of the mentioned Eulerian strain tensor and its conjugate stress tensor. In the flow rule, the plastic part of the corotational rate of the Eulerian strain tensor is related to the difference of the deviatoric part of the conjugate stress and the back stress tensors. A proportionality factor is used in this flow rule which must be...

#### A study on a grade-one type of hypo-elastic models

, Article ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis, ESDA 2014 ; Vol. 1 , 2014 ; Asghari, M ; Sharif University of Technology
Abstract

In Hypo-elastic constitutive models an objective rate of the Cauchy stress tensor is expressed in terms of the current state of the stress and the deformation rate tensor D in a way that the dependency on the latter is a homogeneously linear one. In this work, a type of grade-one hypo-elastic models (i.e. models with linear dependency of the hypo-elasticity tensor on the stress) is considered for isotropic materials based on the objective corotational rates of stress. A positive real parameter denoted by n is involved in the considered type. Different values can be selected for this parameter, each selection leads to a specific model within the class of grade-one hypo-elasticity. The spin of...

#### Elastic-plastic modeling of hardening materials using a corotational rate based on the plastic spin tensor

, Article 2007 ASME Pressure Vessels and Piping Conference, PVP 2007, San Antonio, TX, 22 July 2007 through 26 July 2007 ; Volume 3 , 2008 , Pages 439-446 ; 0277027X (ISSN); 0791842819 (ISBN); 9780791842812 (ISBN) ; Naghdabadi, R ; Sharif University of Technology
2008

Abstract

In this paper based on the multiplicative decomposition of the deformation gradient, the plastic spin tensor and the plastic spin corotational rate are introduced. Using this rate (and also lograte), an elastic-plastic constitutive model for hardening materials are proposed. In this model, the Armstrong-Frederick kinematic hardening and the isotropic hardening equations are used. The proposed model is solved for the simple shear problem with the material properties of the stainless steel SUS 304. The results are compared with those obtained experimentally by Ishikawa [1]. This comparison shows a good agreement between the results of proposed theoretical model and the experimental data. As...

#### Hardening materials modeling in finite elastic-plastic deformations based on the stretch tensor decomposition

, Article Materials and Design ; Volume 29, Issue 1 , 2008 , Pages 161-172 ; 02613069 (ISSN) ; Naghdabadi, R ; Sharif University of Technology
Elsevier Ltd
2008

Abstract

In this paper, finite elastic-plastic deformations of hardening materials are analyzed based on the modified multiplicative decomposition of the left stretch tensor. This decomposition is the modified form of the Metzger and Dubey's decomposition used in the frame work of the principal axes of the left stretch tensor. For this purpose, basis-free corotational constitutive equations are derived for elastic-plastic hardening materials with the Armstrong-Frederick kinematic hardening and isotropic hardening models. The proposed governing equations are solved with different corotational rates for the simple shear problem with the material properties of the stainless steel SUS 304. The results...

#### Axial effects investigation in fixed-end circular bars under torsion with a finite deformation model based on logarithmic strain

, Article International Journal of Mechanical Sciences ; Volume 48, Issue 1 , 2006 , Pages 75-84 ; 00207403 (ISSN) ; Naghdabadi, R ; Sharif University of Technology
2006

Abstract

In this paper the torsion problem of a circular bar with fixed ends is solved using a finite deformation constitutive model based on the corotational rates of the logarithmic strain. The logarithmic, Green-Naghdi and Eulerian corotational rates of the logarithmic strain are used in the model. The solution is based on a von Mises type yield function that incorporates isotropic and kinematic hardenings. For the kinematic hardening, a modified Armstrong-Fredrick hardening model with the corotational rate of the logarithmic strain is used. Assuming incompressible behavior, the fixed-end torsion problem is simplified to the simple shear problem. Solving the problem, the stress components are...

#### Application of corotational rates of the logarithmic strain in constitutive modeling of hardening materials at finite deformations

, Article International Journal of Plasticity ; Volume 21, Issue 8 , 2005 , Pages 1546-1567 ; 07496419 (ISSN) ; Yeganeh, M ; Saidi, A. R ; Sharif University of Technology
2005

Abstract

In this paper a finite deformation constitutive model for rigid plastic hardening materials based on the logarithmic strain tensor is introduced. The flow rule of this constitutive model relates the corotational rate of the logarithmic strain tensor to the difference of the deviatoric Cauchy stress and the back stress tensors. The evolution equation for the kinematic hardening of this model relates the corotational rate of the back stress tensor to the corotational rate of the logarithmic strain tensor. Using Jaumann, Green-Naghdi, Eulerian and logarithmic corotational rates in the proposed constitutive model, stress-strain responses and subsequent yield surfaces are determined for rigid...

#### Expressions for Objective Co-Rotational Rates of Eulerian Stress Tensors

, M.Sc. Thesis Sharif University of Technology ; Asghari, Mohsen (Supervisor)
Abstract

Stress tensors and their rates are fundamental quantities in modeling the behavior of materials in the field of nonlinear continuum mechanics. One of the most remarkable applications of stress rates is their presence in the rate type constitutive equations of materials.

Co-rotational rates are corresponding to the rates which are measured by an observer who is in a reference rotating coordinate system. In general, under some specific conditions for the spin of a co-rotational rate, the rate of an Eulerian tensor would be objective. In this thesis, the objective co-rotational rates of Eulerian stress tensors for isotropic elastic materials under large deformations are obtained for the...

Co-rotational rates are corresponding to the rates which are measured by an observer who is in a reference rotating coordinate system. In general, under some specific conditions for the spin of a co-rotational rate, the rate of an Eulerian tensor would be objective. In this thesis, the objective co-rotational rates of Eulerian stress tensors for isotropic elastic materials under large deformations are obtained for the...

#### Nonlinear plastic modeling of materials based on the generalized strain rate tensor

, Article ASME 2008 Pressure Vessels and Piping Conference, PVP2008, Chicago, IL, 27 July 2008 through 31 July 2008 ; Volume 3 , July , 2008 , Pages 499-505 ; 0277027X (ISSN); 9780791848265 (ISBN) ; Naghdabadi, R ; Pressure Vessels and Piping ; Sharif University of Technology
2008

Abstract

In this paper, a method for modeling of elastic-plastic hardening materials under large deformations is proposed. In this model the generalized strain rate tensor is used. Such a tensor is obtained on the basis of the method which was introduced by the authors. Based on the generalized strain rate tensor, a flow rule, a Prager-type kinematic hardening equation and a kinematic decomposition is proposed and the governing equations for such materials are obtained. As an application, the governing equations for the simple shear problem are solved and some results are compared with those in the literature. Copyright © 2008 by ASME

#### Constitutive modeling of temperature and strain rate dependent elastoplastic hardening materials using a corotational rate associated with the plastic deformation

, Article International Journal of Plasticity ; Volume 27, Issue 9 , 2011 , Pages 1445-1455 ; 07496419 (ISSN) ; Naghdabadi, R ; Sharif University of Technology
Abstract

In this paper, a constitutive model with a temperature and strain rate dependent flow stress (Bergstrom hardening rule) and modified Armstrong-Frederick kinematic evolution equation for elastoplastic hardening materials is introduced. Based on the multiplicative decomposition of the deformation gradient,new kinematic relations for the elastic and plastic left stretch tensors as well as the plastic deformation-dependent spin tensor are proposed. Also, a closed-form solution has been obtained for the elastic and plastic left stretch tensors for the simple shear problem.To evaluate model validity, results are compared with known experimental data for SUS 304 stainless steel, which shows a good...