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Article
Publication date: 1 January 2009

X.Q. Zhang

widely‐used hypoelastic model for four well‐known objective stress rates under a four‐phase stress cycle associated with axial tension and/or torsion of thin‐walled…

Abstract

widely‐used hypoelastic model for four well‐known objective stress rates under a four‐phase stress cycle associated with axial tension and/or torsion of thin‐walled cylindrical tubes. Here, two kinds of models based upon the Cauchy stress and the Kirchhoff stress will be treated. The reduced systems of differential equations of these rate constitutive equations are derived and studied for Jaumann, Green‐ Naghdi, logarithmic and Truesdell stress rates, separately. Analytical solutions in some cases and numerical solutions in all cases are obtained using these reduced systems. Comparisons between the residual deformations are made for different cases. It may be seen that only the logarithmic stress rate results in no residual deformation. In particular, results indicate that Green‐Naghdi rate would generate unexpected residual deformation effect that is essentially different from that resulting from Jaumann rate. On the other hand, it is realized that this study accomplishes an alternative, direct proof for the nonintegrability problem of Truesdell’s hypoelastic rate equation with classical stress rates. This problem has been first treated successfully by Simo and Pister in 1984 using Bernstein’s integrability conditions. However, such treatment needs to cope with a coupled system of nonlinear partial differential equations in Cauchy stress. Here, a different idea is used. It is noted that every integrable hypoelastic equation is just an equivalent rate form of an elastic equation and hence should produce no residual deformations under every possible stress cycle. Accordingly, a hypoelastic model with a stress rate has to be non‐integrable, whenever a stress cycle can be found under which this model generates residual deformation. According to this idea of reductio ad absurdum, a well‐designed stress cycle is introduced and the corresponding residual deformations are calculated. Unlike the treatment of Bernstein’s integrability conditions, it may be a simple and straightforward matter to calculate the final deformations for a given stress cycle. This has been done in this study for several well‐known stress rates.

Details

Multidiscipline Modeling in Materials and Structures, vol. 5 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 3 August 2015

Mark Messner, Armand Beaudoin and Robert Dodds

The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element…

Abstract

Purpose

The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element framework.

Design/methodology/approach

Starting from the key kinematic assumptions of CP, the presentation develops the necessary CP correction terms to several common objective stress rates and the consistent linearization of the stress update algorithm. Connections to models for slip system hardening are isolated from these processes.

Findings

A kinematically consistent implementation is found to require a correction to the stress update to include plastic vorticity developed by slip deformation in polycrystals. A simpler, more direct form for the algorithmic tangent is described. Several numerical examples demonstrate the capabilities and computational efficiency of the formulation.

Research limitations/implications

The implementation assumes isotropic slip system hardening. With simple modifications, the described approach extends readily to anisotropic coupled or uncoupled hardening functions.

Practical implications

The modular formulation and implementation support streamlined development of new models for slip system hardening without modifications of the stress update and algorithmic tangent computations. This implementation is available in the open-source code WARP3D.

Originality/value

In the process of developing the CP formulation, this work realized the need for corrections to the Green-Naghdi and Jaumann objective stress rates to account properly for non-zero plastic vorticity. The paper describes fully the consistent linearization of the stress update algorithm and details a new scheme to implement the model with improved efficiency.

Details

Engineering Computations, vol. 32 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1999

A.F. Marcon, E. Bittencourt and G.J. Creus

Discusses an alternative formulation for the incremental determination of stresses in strain measures that can be used to replace the stress rates currently employed. The…

Abstract

Discusses an alternative formulation for the incremental determination of stresses in strain measures that can be used to replace the stress rates currently employed. The formulation is based on Doyle‐Hill generalized definition of strain, the corresponding conjugate stresses and an isotropic hyperelastic constitutive equation. When used to analyze the simple shear deformation, the proposed formulation avoids the pathologies usually observed (oscillations, pressure build up, path dependence). The origin and importance of these pathologies is then discussed in relation to different materials behavior. It is shown that the incremental procedure used together with the logarithmic definition of strain is the most convenient, but that other approximations may be used in well defined particular situations. The numerical algorithms proposed are detailed in an Appendix.

Details

Engineering Computations, vol. 16 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 9 August 2011

Praveen Ailawalia, Shilpy Budhiraja and Baljeet Singh

The purpose of this paper is to study the deformation of Green‐Naghdi (type III) thermoelastic solid half‐space under hydrostatic initial stress and rotation.

Abstract

Purpose

The purpose of this paper is to study the deformation of Green‐Naghdi (type III) thermoelastic solid half‐space under hydrostatic initial stress and rotation.

Design/methodology/approach

The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress and temperature distribution.

Findings

The numerical results are given and presented graphically when mechanical/thermal source is applied.

Originality/value

Comparisons are made in the presence and absence of hydrostatic initial stress and rotation and their effect is shown graphically.

Details

Multidiscipline Modeling in Materials and Structures, vol. 7 no. 2
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 15 August 2019

Mohamed I.A. Othman, Samia Said and Marin Marin

In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III…

Abstract

Purpose

In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III) are used to study the influence of the gravity field on a two-temperature fiber-reinforced thermoelastic medium.

Design/methodology/approach

The analytical expressions for the displacement components, the force stresses, the thermodynamic temperature and the conductive temperature are obtained in the physical domain by using normal mode analysis.

Findings

The variations of the considered variables with the horizontal distance are illustrated graphically. Some comparisons of the thermo-physical quantities are shown in the figures to study the effect of the gravity, the two-temperature parameter and the reinforcement. Also, the effect of time on the physical fields is observed.

Originality/value

To the best of the author’s knowledge, this model is a novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium, and gravity plays an important role in the wave propagation of the field quantities. It explains that there are significant differences in the field quantities under the G-N II theory, the G-N III theory and the 3PHL model because of the phase-lag of temperature gradient and the phase-lag of heat flux.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 12
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 22 February 2021

Devender Sheoran, Rajesh Kumar, Seema Thakran and Kapil Kumar Kalkal

The purpose of this paper is to study two-dimensional deformations in a nonlocal, homogeneous, isotropic, rotating thermoelastic medium with temperature-dependent…

Abstract

Purpose

The purpose of this paper is to study two-dimensional deformations in a nonlocal, homogeneous, isotropic, rotating thermoelastic medium with temperature-dependent properties under the purview of the Green-Naghdi model II of generalized thermoelasticity. The formulation is subjected to a mechanical load.

Design/methodology/approach

The normal mode analysis technique is adopted to procure the exact solution of the problem.

Findings

For isothermal and insulated boundaries, discussions have been made to highlight the influences of rotational speed, nonlocality, temperature-dependent properties and time on the physical quantities.

Originality/value

The exact expressions for the displacement components, stresses and temperature field are obtained in the physical domain. These are also calculated numerically for a magnesium crystal-like material and depicted through graphs to observe the variations of the considered physical quantities. The present study is useful and valuable for the analysis of problems involving mechanical shock, rotational speed, nonlocal parameter, temperature-dependent properties and elastic deformation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 23 April 2020

Ashraf M. Zenkour

The thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized…

Abstract

Purpose

The thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized thermoelasticity theory have been proposed.

Design/methodology/approach

Some models with and without energy dissipation have been presented as well as the simple forms of Green–Naghdi (G–N) theories. These novel multi- and single-/dual-phase-lag models are presented to investigate the thermo-diffusion of the solid cylinder. The closed-form solution of thermo-diffusion governing equations of solid cylinder has been obtained to deduce all field variables.

Findings

A comparison study between the simple G–N II and III models and their improved models has been presented. The validations of outcomes are acceptable and so benchmarks are reported to help other investigators in their future comparisons.

Originality/value

The modified Green and Naghdi theories of types II and III are presented to get novel and accurate models of single- and dual-phase-lag of multiterms. The heat of mass diffusion equation as well as the constitutive equations for the stresses and chemical potential of a solid cylinder is added to the present formulation. The system of three differential coupled equations is solved, and all field variables are obtained for the thermal diffusion of the solid cylinder. Some validation examples and applications are presented to compare the simple and modified Green and Naghdi theories of types II and III. Sample plots are illustrated along the radial direction of the solid cylinder. Some results are tabulated to serve as benchmark results for future comparisons with other investigators. The reported and illustrated results show that the simple G–N II and III models yield the largest values of all field quantities. The single-phase-lag models give the smallest values. However, the dual-phase-lag model yields results that are intermediate between those of the simple and single-phase-lag G–N models.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 6
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 May 2003

A.R. Khoei, A. Bakhshiani and M. Mofid

In this paper, a new rate type endochronic constitutive model is introduced to describe deformations in the finite strain range. A new material dependent objective rate of…

Abstract

In this paper, a new rate type endochronic constitutive model is introduced to describe deformations in the finite strain range. A new material dependent objective rate of Cauchy stress is suggested based on the general form of spin tensors, defining objective stress rates. The endochronic constitutive equations are extended using the concept of corotational stress rates and additive decomposition of deformation rate. The constitutive relations are specialized for thin‐walled tubes under torsion and a procedure for solving the ordinary differential equations for cases of simple and pure torsion is developed. The axial effects for various materials, subjected to simple and pure torsion, are simulated and compared with experimental data. The results clearly indicate that the new combined rate endochronic model can be effectively used to describe the behavior of material in the finite strain range.

Details

Engineering Computations, vol. 20 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 January 2009

Mohamed Othman and Ya Qin Song

The theory of generalized thermoelasticity, based on the Lord‐Shulman theory (LS) with one relaxation time and the Green‐Naghdi theory (GN) (of type II) without energy…

Abstract

The theory of generalized thermoelasticity, based on the Lord‐Shulman theory (LS) with one relaxation time and the Green‐Naghdi theory (GN) (of type II) without energy dissipation, as well as the classical dynamical coupled theory (CD), is used to study the electromagneto‐thermoelastic interactions in a semi‐infinite perfectly conducting solid subjected to a thermal shock on its surface. The entire elastic medium is rotating with a uniform angular velocity. There acts an initial magnetic field parallel to the plane boundary of the half‐space. The medium deformed because of thermal shock, the rotation and due to the application of the magnetic field. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the variables considered are represented graphically for two different cases. From the distributions, the wave type heat propagation in the medium can be found. This indicates that the generalized heat conduction mechanism is completely different in essence from the classic Fourier’s law. Comparisons are made with the results predicted by the three theories in the presence and absence of rotation and a magnetic field.

Details

Multidiscipline Modeling in Materials and Structures, vol. 5 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 March 2009

Mohamed I.A. Othman and Kh. Lotfy

under the effect of temperature dependent properties is established. The modulus of elasticity is taken as a linear function on reference temperature. The formulation is…

Abstract

under the effect of temperature dependent properties is established. The modulus of elasticity is taken as a linear function on reference temperature. The formulation is applied under three theories of the generalized thermoelasticity: Lord‐Shulman and Green‐Naghdi (of type II) without energy dissipation, as well as the coupled theory. The normal mode analysis is used to obtain the expressions for the temperature, displacement components and the thermal stresses distributions. Numerical results are illustrated graphically for each problem considered. A Comparison is made with the results predicted by the three theories in the presence and absence of magnetic field and with the case where the modulus of elasticity is independent of temperature.

Details

Multidiscipline Modeling in Materials and Structures, vol. 5 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

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