• Structural Engineering and Mechanics
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• v.30 no.6
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• pp.665-678
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• 2008

The beams components subjected to the loading such as axial, bending and cyclic thermal loads were studied in this research. The used constitutive equations are those of elasto-plasticity coupled to ductile and/or creep damage. The nonlinear kinematic hardening behavior was considered in elastoplasticity modeling. The unified damage law proposed for ductile failure and fatigue by the author of Sermage et al. (2000) and Kachanov's creep damage model applied to cyclic creep and low cycle fatigue of beams. Based on the results of the analysis, the shakedown limit loads were determined through the calculation of the residual strains developed in the beam analysis. The iterative technique determines the shakedown limit load in an iterative manner by performing a series of full coupled elastic-plastic and continuum damage cyclic loading modeling. The maximum load carrying capacity of the beam can withstand, were determined and imposed on the Bree's interaction diagram. Comparison between the shakedown diagrams generated by or without creep and/or ductile damage for the loading patterns was presented.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1075-1083
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• 2000

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method. The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.11
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• pp.3516-3524
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• 1996

Service conditions for structures at elevated temperatures in nuclear power plant involve transient thermal and mechanical load levels that are severe enough to caeuse inelastic deformations due to creep and plasticity. Therefore, a systematic mehtod of inelastic analysis is needed for the design of structural components in nuclear poser plants subjected to such loading conditions. In the present investigation, the Chabodhe model, one of the unified viscoplastic constitutive equations, was selected for systematic inelastic analysis. The material response was integrated based on GMR ( generallized mid-point rule) time integral scheme and provided to ABAQUS as a material subroutine, UMAT program. By comparing results obtaned from uniaxial analysis using the developed UMAT program with those from Runge-Kutta solutions and experimentaiton, the validity of the adopted Chaboche model and the numerical stability and accuracy of the developed UMAT program were verified. In addition, the developed material subroutine was applied for uniaxial creep and tension analyses for the plate with a hole in the center. The application further demonstrates usefulness of the developed program.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.3
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• pp.816-824
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• 1996

The densification behaviors of copper powder under high temperature processing were investigated. Experimental data were obtained for copper powder under hot isostatic pressing, hot pressing and uniaxial compression. Finite element calculations from the constitutive models by McMeeking and co-workers were compared with the experimental data, The agreements between experimental data and theoretical calculations are reasonably good when hydrostatic stress is dominant, but not as good then deviatoric stress increases.

• Steel and Composite Structures
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• v.30 no.6
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• pp.567-576
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• 2019

Time-dependent creep analysis of a rotating functionally graded cantilever beam with trapezoidal longitudinal cross section subjected to thermal and inertia loading is investigated using first-order shear deformation theory (FSDT). The model described in this paper is a simple simulation of a turbine blade working under creep condition. The material is a metal based composite reinforced by a ceramic where the creep properties of which has been described by the Sherby's constitutive model. All mechanical and thermal properties except Poisson's ratio are assumed to be variable longitudinally based on the volume fraction of constituent. The principle of virtual work as well as first order shear deformation theory is used to derive governing equations. Longitudinal distribution of displacements and stresses are investigated for various volume fractions of reinforcement. Method of successive elastic solution is employed to obtain history of stresses and creep deformations. It is found that stresses and displacements approach their steady state values after 40000 hours. The results presented in this paper can be used for selection of appropriate longitudinal distribution of reinforcement to achieve the desired stresses and displacements.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3061-3071
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• 2000

Densification behavior of titanium alloy powder was investigated under hot pressing at various pressures and temperatures. Experimental date were obtained for densification of titanium alloy powder under an instantaneous loading and subsequent creep deformation during hot pressing. The constitutive models of Fleck et al. and the modified Gurson were employed for thermo-phastic deformation under the instantaneous loading and that f Abouaf and co-workers for creep deformation of titanium alloy powder during hot pressing. By implementing these constitutive equations into a finite element program(ABAQUS), finite element results were compared with experimental data during hot pressing. To investigate the effect of friction between the power and die wall, density distributions of power compacts were measured and compared with finite element calculations. Finite element results from the models of Fleck et al. and the modified Gurson agreed reasonably good with experimental data for densification and density distribution of titanium alloy powder under the instantaneous loading during hot pressing. Finite element results from the model of Abouaf and co-workers, however, somewhat overestimate experimental data for creep deformation of power compacts during hot pressing.

• Macromolecular Research
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• v.9 no.3
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• pp.164-170
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• 2001

Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the pom-pom equations have been derived by McLeish and Larson on the basis of the reptation dynamics with simplified branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for the simplified differential version of these constitutive equations. It is proved that they are globally Hadamard stable except for the case of maximum constant backbone stretch (λ = q) with arm withdrawal s$\_$c/ neglected, as long as the orientation tensor remains positive definite or the smooth strain history in the now is previously given. However this model is dissipative unstable, since the steady shear How curves exhibit non-monotonic dependence on shear rate. This type of instability corresponds to the nonlinear instability in simple shear flow under finite amplitude disturbances. Additionally in the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady now curves, the constitutive equations will possibly violate the positive definiteness of the orientation tensor and thus become Hadamard unstable.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.1
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• pp.43-48
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• 2010

The heat sink system for a main board in a network server computer is built on printed circuit board by an anchor structure, mounted by eutectic SnPb solder. The solder creeping is caused by a constant high temperature condition in the computer and it eventually makes fatal failures. The FE model is used to calculate the stress and predict the life of soldered anchor in the computer. In the model, Anand constitutive equation is employed to simulate creep characteristics of solder. The creep test is conducted to verify and calibrate the solder model. A special jig is designed to mitigate the flexure of printed circuit board and to get the creep deformation of solder only in the test. Test results are compared with analysis and calibration is conducted on Anand model's constants. Precise life prediction of soldered anchor in creep condition can be performed by this model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.253-261
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• 2005

In decades, a substantial body of work on a unified viscoplastic model which considers the mechanism of plastic deformation and creep deformation has developed. The systematic scheme for numerical analysis of unified model is necessary because the dominant failure mechanism is the defect growth and coalescence in materials. In the present study, the unified viscoplastic model for materials with defects suggested by Suquet and Michel was employed for numerical analysis. The constitutive equations are integrated based on the generalized mid-point rule and implemented into a finite element program (ABAQUS) by means of user-defined subroutine (UMAT). To evaluate the validity of the developed UMAT code and the assessment of the adopted viscoplastic model, the results obtained from the UMAT code was compared with the numerical reference solution and experimental data. The unit cell analysis also has been investigated to study the effect of strain rate, temperature, stress triaxiality and initial defect volume fraction on the growth and coalescence of the defect.

• Geomechanics and Engineering
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• v.8 no.5
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• pp.707-726
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• 2015

This paper investigates the time dependent behaviour of Haarajoki test embankment on soft structured clay deposit. Half of the embankment is constructed on an area improved with prefabricated vertical drains, while the other half is constructed on the natural deposit without any ground improvement. To analyse the PVD-improved subsoil, axisymmetric vertical drains were converted into equivalent plane strain conditions using three different approaches. The construction and consolidation of the embankment are analysed with the finite element method using a recently developed anisotropic model for time-dependent behaviour of soft clays. The constitutive model, namely ACM-S accounts for combined effects of plastic anisotropy, interparticle bonding and degradation of bonds and creep. For comparison, the problem is also analysed with isotropic Soft Soil Creep and Modified Cam Clay models. The results of the numerical analyses are compared with the field measurements. The results show that neglecting effects of anisotropy, destructuration and creep may lead to inaccurate predictions of soft clay response. Additionally, the numerical results show that the matching methods accurately predict the consolidation behaviour of the embankment on PVD improved soft clays and provide a useful tool for engineering practice.