• Nuclear Engineering and Technology
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• v.28 no.2
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• pp.103-117
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• 1996

A mathematical model of vapor explosion propagation is presented. The model predict two-dimensional, transient flow fields and energies of the four fluid phases of melt drop, fragmented debris, liquid coolant and vapor coolant by solving a set of governing equations with the relevant constitutive relations. These relations include melt fragmentation, coolant-phase-change, and heat and momentum exchange models. To allow thermodynamic non-equilibrium between the coolant liquid and vapor, an equation of state for oater is uniquely formulated. A multiphase code, TRACER, has been developed based on this mathematical formulation. A set of base calculations for tin/water explosions show that the model predicts the explosion propagation speed and peak pressure in a reasonable degree although the quantitative agreement relies strongly on the parameters in the constitutive relations. A set of calculations for sensitivity studies on these parameters have identified the important initial conditions and relations. These are melt fragmentation rate, momentum exchange function, heat transfer function and coolant phase change model as well as local vapor fractions and fuel fractions.

• Journal of the Korea Concrete Institute
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• v.17 no.5 s.89
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• pp.857-868
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• 2005

This paper deals with the accumulated damage in concrete structures due to the cyclic freeze-thaw as an environmental load. The cyclic ice body nucleation and growth processes in porous systems are affected by the thermo-physical and mass transport properties, and gradients of temperature and chemical potentials. Furthermore, the diffusivity of deicing chemicals shows significantly higher value under cyclic freeze-thaw conditions. Consequently, the disintegration of concrete structures is aggravated at marine environments, higher altitudes, and northern areas. However, the properties of cyclic freeze-thaw with crack growth and diffusion of chloride ion effects are hard to be identified in tests, and there has been no analytic model for the combined degradations. The main objective is to determine the driving force and evaluate the reduced strength and stiffness by freeze-thaw. For the development of computational model of those coupled deterioration, micro-pore structure characterization, pore pressure based on the thermodynamic equilibrium, time and temperature dependent super-cooling with or without deicing salts, nonlinear-fracture constitutive relation for the evaluation of internal damage, and the effect of entrained air pores (EA) has been modeled numerically. As a result, the amount of ice volume with temperature dependent surface tensions, freezing pressure and resulting deformations, and cycle and temperature dependent pore volume has been calculated and compared with available test results. The developed computational program can be combined with DuCOM, which can calculate the early aged strength, heat of hydration, micro-pore volume, shrinkage, transportation of free water in concrete. Therefore, the developed model can be applied to evaluate those various practical degradation cases as well.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.10
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• pp.1057-1068
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• 2014

This paper proposes elastic-plastic constitutive relations for a composite material with two phases-inclusion and matrix phases-using a homogenization scheme. A thermodynamic framework is employed to develop non-local plasticity constitutive relations, which are specifically represented in terms of the second-order gradient terms of the internal state variables. A combined two back-stress evolution equation is also established and the degradation of the state and internal variables is expressed by continuum damage mechanics in terms of the damage factor. Then, deformation localization is analyzed; the analysis results show that the proposed model yields a wide range of shear band formation behaviors depending on the evolution of the specific internal state variables. The analysis results also show good agreement with the results of simplified Rice instability analyses.

• Computational Structural Engineering
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• v.9 no.1
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• pp.65-76
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• 1996

The initiation and growth of microcracks or microvoids inside concrete results in the progressive degradation of concrete. This damage processing along processing along with plastic deformation is main cause of nonlinear behavior of concrete. In this study, a continuum damage model of concrete is developed for the analysis of the nonlinear behavior of concrete due to damage and elasto-plastic deformation. Anisotropic damage tensor is used to describe the anisotropy of concrete and hypothesis of equivalent elastic energy is used to define the effective elastic tensor. The damage model including the damage evolution law and constitutive equation is derived with damage variable and damage surface which is defined by damage energy release rate by using the Helmholtz free energy and dissipation potential based on the thermodynamic principles. By adopting a typical plasticity model of concrete, plasticity of concrete is included to this model. Afinite element analysis program implemented with this model was developed and finite element analysis was performed for the analyses of concrete subjected to uniaxial and biaxial loadings. Comparison of the results of analysis with those of experiments and other models shows that the model successfully predicts the nonlinear behavior of concrete.