• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.215-219
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• 2003

Buckling and post-buckling Analysis of Ludwick type and modified Ludwick type elastic materials was carried out. Because the constitutive equation, or stress-strain relationship is different from that of linear elastic one, a new governing equation was derived and solved by $4^{th}$ order Runge-Kutta method. Considered as a special case of combined loading, the buckling under both point and distributed load was selected and researched. The final solution takes distinguished behavior whether the constitutive relation is chosen to be modified or non-modified Ludwick type as well as linear or non-linear. We also derived strain energy function for non-linear elastic constitutive relationship. By doing so, we calculated the criterion function which estimates the stability of the equilibrium solutions and determines critical buckling load for non-linear cases. We applied this theory to the constitutive relationship of fabric, which also is the non-linear equation between the applied moment and curvature. This results has both technical and mathematical significance.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.565-589
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• 2004

The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.591-607
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• 2004

The substance of the use of the derived non-linear creep constitutive equations under variable stress levels (see first part of the paper, Kmet 2004) is explained and the strategy of their application is outlined using the results of one-step creep tests of the steel spiral strand rope as an example. In order to investigate the creep strain increments of cables an experimental set-up was originally designed and a series of tests were carried out. Attention is turned to the individual main steps in the production and application procedure, i.e., to the one-step creep tests, definition of loading history, determination of the kernel functions, selection and definition of constitutive equation and to the comparison of the resulting values considering the product and the additive forms of the approximation of the kernel functions. To this purpose, the parametrical study is performed and the results are presented. The constitutive equations of non-linear creep of cable under variable stress history offer a strong tool for the real simulation of stochastic variable load history and prediction of realistic time-dependent response (current deflection and stress configuration) of structures with cable elements. By means of suitable stress combination and its gradual repeating various loads and times effects can be modelled.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.557-561
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• 2008

Shape memory alloys (SMA) have interesting features which are the superelastic effect (SE), shape memory effect (SME), two-way SME (TWSME), and so on. These are utilized in actuation factor. The thermo-mechanical constitutive equations of SMA proposed by Lagoudas et al. were employed in the present study for simulating SMA truss structures. The constitutive equation includes the necessary internal variables to account for the material transformations and is utilized in the non-linear finite element procedure of three dimensional truss structures that composed SMA bar (wholly or partially). In this study, we observed which element should be actuated to get a desired shape (actuation shape) from computational analysis. To reach this goal, we apply SMA constitutive equation to non-linear finite element formulation. And then, we simulate two-way shape memory effect as well as superelastic effect of various three dimensional truss using SMA.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.181-188
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• 1994

Generally, the structural material shows rate dependent behaviors, which require to constitute different strain-stress relations according to strain rates. Conventional rate- independent constitutive equations used in general purpose finite analysis programs are inadequate for dynamic finite strain problems. In this paper, a rate dependent constitutive equation for elastic-plastic material was developed. The plastic stretch rate was modeled based on slip model with dislocation velocity and density so that there is no yielding condition, and no loading conditions. Non-linear hardening rule was also introduced for finite strain. Material constants of present constitutive equation were determined by experimental data of mild steel. The constitutive equation was applied to uniaxile tension. It was appeared that the present constitutive equation well simulates rate dependent behaviors of mild steel.

• Journal of the Society of Naval Architects of Korea
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• v.34 no.1
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• pp.77-86
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• 1997

The advanced development in many fields of engineering and science has caused much interests and demands for crashworthiness and non-linear dynamic transient analysis of structure response. Crash and impact problems have a dominant characteristic of large deformation with material plasticity for short time scales. The structural material shows strain rate-dependent behaviors in those cases. Conventional rate-independent constitutive equations used in the general purposed finite analysis programs are inadequate for dynamic finite strain problems. In this paper, a rate-dependent constitutive equation for elastic-plastic material is developed. The plastic stretch rate is modeled based on slip model with dislocation velocity and its density so that there is neither yielding condition, nor loading conditions. Non-linear hardening rule is also introduced for finite strain. Material constants of present constitutive equation are determined by experimental data of mild steel, and the constitutive equation is applied to uniaxile tension loading.

• Journal of the Society of Naval Architects of Korea
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• v.48 no.3
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• pp.200-206
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• 2011

The mechanical properties of the most widely used cryogenic materials, i.e. austenitic stainless steel (ASS), aluminum alloy and invar steel, strongly depend on temperatures and strain rates. These phenomena show very complicated non-linear behaviors and cannot be expressed by general constitutive equation. In this study, an unified constitutive equation was proposed to represent the effect of temperature and strain rate on the materials. The proposed constitutive equation has been based on Tomita/Iwamoto and Bodner/Partom model for the expression of 2nd hardening due to martensite phase transformation of ASS. To simulate ductile fracture, modified Bodner/Chan damage model was additionally applied to the model and the model validity was verified by comparison of experimental and simulation results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.289-294
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• 2001

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically. The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytic solutions of the system. The frequency-response curves show that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear phenomena.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.1
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• pp.57-64
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• 2002

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytical solutions of the system. The frequency-response curves sallow that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear Phenomena.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2001.02a
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• pp.102-103
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• 2001

In this paper we calculate the AC Loss in the superconducting slab carrying ac transport current. Magnetic diffusion equation for computation of the electric field and current distribution are based on Maxwell's equations and non-linear constitutive equation. The E-J characteristics of superconductor are applied to computation. We will present the result of the high-temperature superconductor case comparison with the slab of low temperature superconductor.