• Transactions of Materials Processing
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• v.9 no.1
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• pp.59-65
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• 2000

Most studies of failure analysis in ductile metals have been based on the classical plasticity theory using the local constitutive relations. These frequently yields a physically unrealistic solution, in which a numerical prediction of the onset of a deformation localization shows an inherent mesh-size sensitivity. A one way to remedy the spurious mesh sensitivity resulted in the unreasonable results is to incorporate the non-local plasticity into the simulation model, which introduce an internal (material) length-scale parameter into the classical constitutive relations. In this paper, a non-local version of the modified Gurson constitutive relation has been introduced into the finite element formulation of the simulation for plane strain compression of the visco elastic-plastic void material. By introducing the non-local constitutive relations we could successfully removed the inherent mesh-size sensitivity for the prediction of the deformation localization. The effects of non-local constitutive relation are discussed in terms of the load-stroke curve and the strain distributions accross the shear band.

• International Journal of Precision Engineering and Manufacturing
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• v.6 no.4
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• pp.55-59
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• 2005

This paper presents a feasibility study whether Shida's constitutive equation being widely used for plain carbon steel in steel manufacturing industry can be extended to alloy steels with a due carbon equivalent model. T,he constitutive relation of the alloy steels (SAE9254, AISI52100 and AISI4140) is measured using hot deformation simulator (GLEEBLE 3500C) at high temperatures ($800^{\circ}C{\~}1000^{\circ}C$) within strain rates of $0.05{\~}40\;s^{-1}$. It has been found the predicted flow stress behavior (constitutive relation) of AISI52100 steel is in agreement with the measured one. On the other hand, the measured flow stress behavior of SAE9254 and AISI4140 steel partly concords with the predicted one when material experiences relatively high strain rate ($10{\~}40\;s^{-1}$) deformation at low temperature ($800^{\circ}C$). It can be deduced that, for AISI52100 steel, Shida's equation with the carbon equivalent model can be applicable directly to the roughing and intermediate finishing stand in hot rolling process for calculating the roll force and torque.

• Structural Engineering and Mechanics
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• v.39 no.2
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• pp.169-186
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• 2011

This paper is devoted to the development of the equations which describe the elastic response of a curved laminate subjected to in-plane loads and bending moments. Similar to the classic $6{\times}6$ ABD matrix constitutive relation of a flat laminate, a new $6{\times}6$ matrix constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures for a curved laminate is formulated. This curved lamination theory will provide the fundamental basis for the analyses of curved laminated structures. The stress predictions by the present curved lamination theory are compared to those by the curved laminate analysis that neglected the nonlinear terms in the derivation of the constitutive relation. The results show that the curved laminate analysis that neglected the nonlinear terms cannot reflect the effect of curvature and can no longer predict the stresses accurately as the curvature becomes noticeable. In this paper, a curved lamination theory that retains the nonlinear terms and, therefore, accounts for the effect of the non-flat geometry of the structure will be developed.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.84-88
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• 1997

The Jonhnson-Cook constitutive relation has been used in dynamic plasticities. The constants of the Jonhson-Cook relation of sheet metals for an autobody is not known yet. In this paper, the material properties of SPCEN, SPCC and SPRC in the high strain rate states have been acquired. A new tension split Hopkinson bar was used in high speed tensile tests of sheet metals. The experimental results acquired from the apparatus are used to determine the constants of Johnson-Cook constitutive relation of sheet metals. This results can be used to analysis of crashworthness.

• Journal of the Korean Geotechnical Society
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• v.19 no.3
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• pp.15-22
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• 2003

The appropriate description of the stress-anisotropy and time-dependent behavior of cohesive soils is very important in representing the real soil behavior. In this study, two constitutive relations have been incorporated based on the generalized viscous theory: one is the plastic constitutive relation adopted to capture the stress-anisotropy with a few model parameters; the other is the rate-dependent constitutive relation adopted to describe the strain rate-dependent behavior, an important time-dependent behavior in cohesive soils. The incorporated and proposed constitutive model has relatively a few model parameters and their values need not to be re-evaluated at different strain rates. The proposed model has been verified and investigated with the anisotropic triaxial test results obtained by using the artificial homogeneous specimens.

• International Journal of Automotive Technology
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• v.1 no.1
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• pp.35-41
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• 2000

The crashworthiness of vehicles with finite element methods depends on the geometry modeling and the material properties. The vehicle body structures are generally composed of various members such as frames, stamped panels and deep-drawn parts from sheet metals. In order to ensure the impact characteristics of auto-body structures, the dynamic behavior of sheet metals must be examined to provide the appropriate constitutive relation. In this paper, high strain-rate tensile tests have been carried out with a tension type split Hopkinson bar apparatus specially designed for sheet metals. Experimental results from both static and dynamic tests with the tension split Hopkinson bar apparatus are interpolated to construct the Johnson-Cook and a modified Johnson-Cook equation as the constitutive relation, that should be applied to simulation of the dynamic behavior of auto-body structures. Simulation of auto-body structures has been carried out with an elasto-plastic finite element method with explicit time integration. The stress integration scheme with the plastic predictor-elastic corrector method is adopted in order to accurately keep track of the stress-strain relation for the rate-dependent model accurately. The crashworthiness of the structure with quasi-static constitutive relation is compared to the one with the rate-dependent constitutive model. Numerical simulation has been carried out for frontal frames and a hood of an automobile. Deformed shapes and the Impact energy absorption of the structure are investigated with the variation of the strain rate.

• Transactions of Materials Processing
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• v.33 no.1
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• pp.18-35
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• 2024

In the present work, the evolution rules for the internal variables including continuum damage factors are obtained using the thermodynamic framework, which are in turn facilitated to derive the elastic-plastic constitutive relation for the particulate composites. Using the Mori-Tanaka scheme, the homogenization on state and internal variables such as back-stress and damage factors is carried out to procure the rate independent plasticity relations. Moreover, the degradation of mechanical properties of constituents is depicted by the distinctive damages such that the phase and interfacial damages are treated individually accordingly, whereas the kinematic hardening is depicted by combining the Armstrong-Frederick and Phillips' back-stress evolutions. On the other hand, the present constitutive relation for each phase is expressed in terms of the respective damage-free effective quantities, then, followed by transformation into the damage affected overall nominal relations using the aforementioned homogenization concentration factors. An emphasis is placed on the qualitative analyses for strain localization by observing the perturbation growth instead of the conventional bifurcation analyses. It turns out that the proposed constitutive model offers a wide range of strain localization behavior depending on the evolution of various internal variable descriptions.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.1018-1021
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• 1988

This study is concerned with modeling an elastomer constitutive relation by utilizing the truncated Volterra series. Actual experimental data from the Instron Tester are obtained for combined input, i.e. constant strain rate followed by a constant strain input. These data are then estimated for step inputs and utilized for the truncated Volterra series models. One second order and one third order truncated Volterra series models have been employed to estimated the force-displacement relation which is one of the prominent properities to characterize the viscoelastic material. The third order Volterra series model has better results, compared with those of the second order Volterra series model.

• Structural Engineering and Mechanics
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• v.22 no.6
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• pp.741-759
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• 2006

A general theory which describes the elastic response of a curved anisotropic plate subjected to stretching and bending will be developed by considering the nonlinear effect that reflecting the non-flat geometry of the structure. By applying a newly derived $6{\times}6$ matrix constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures, the governing differential equations for a curved anisotropic plate is developed in the usual manner, namely, by consideration of the constitutive relation and equilibrium equations. Solutions are obtained for simply-supported boundary conditions and compared to corresponding solutions that neglecting the nonlinear effect in the analysis. The comparisons indicate that the nonlinear terms in the equations that caused by the curvature of the structure is crucial for the curved plate analysis. Under certain curved plate geometries the unreasonable results will be induced by neglecting the nonlinear effect in the analysis.

• Proceedings of the Korea Concrete Institute Conference
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• 2004.11a
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• pp.493-496
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• 2004

The change of creep deformation mechanism due to the persistent change of stress conditions requires the constitutive relation for the analysis of long tenn behaviors considering age dependent material properties of concrete. In the present research, the process of time dependent behaviors in structure is divided into two stages; the non-mechanical deforming level which causes creep and shrinkage deformations, and the mechanical deforming level which causes mechanical deformations by the restraints of non-mechanical deformations due to internal or external factors. The incremental constitutive relation is derived by expanding the total stress-strain relation on the present time, with respect to the reference time using the Taylor series, and the modulus of elasticity in early ages of concrete was defined thru this process.