Search results

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.

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.

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.

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.

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

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.

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.

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.

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.

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

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

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

In this work, the thermoelastic response in a micro-stretch thermoelastic half-space submerged in an unlimited non-viscous fluid under gravity, the medium is studied using the three-phase-lag model (3PHL) and Green-Naghdi theory (G-N III).

The normal mode analysis was the analytic technique used to obtain the exact formula of the physical quantities.

The magnesium crystal element is used as an application to compare the predictions induced by gravity on microstretch thermoelastic immersed in an infinite fluid of the three-phase-lag model with those for Green–Naghdi. Gravity has been noticed to have a major effect on all physical quantities. Comparisons were also made for three values of wave number and three values of the real part frequency.

This work is concerned with the thermoelastic micro-stretch solid immersed in an infinite and inviscid fluid and subjected to a gravitational field. The governing equations are formulated in the context of the 3PHL model and G-N theory. An analytical solution to the problem is obtained by employing normal mode analysis. Comparisons of the physical quantities are shown in figures to study the effects of gravity, wave number and the real part of the frequency.

In the present article, the three-phase-lag (3PHL) model and the Green-Naghdi theory of types II, III with memory-dependent derivative is used to study the effect of rotation on a nonlocal porous thermoelastic medium.

In this study normal mode analysis is used to obtain analytical expressions of the physical quantities. The numerical results are given and presented graphically when mechanical force is applied.

The model is illustrated in the context of the Green-Naghdi theory of types II, III and the three-phase lags model. Expressions for the physical quantities are solved by using the normal mode analysis and represented graphically.

Comparisons are made with the results predicted in the absence and presence of the rotation as well as a nonlocal parameter. Also, the comparisons are made with the results of the 3PHL model for different values of time delay.

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.

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.

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.

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.

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.

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.

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.