• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.1-16
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• 1994

A unified theory has recently been developed for reinforced concrete structures (Hsu 1993), subjected to the four basic actions - bending, axial load, shear and torsion. The theory has five components, namely, the struts-and-ties model, the equilibrium (or plasticity) truss model, the Bernoulli compatibility truss model, the Mohr compatibility truss model and the softened truss model. Because the last three models can satisfy the stress equilibrium, the strain compatibility and the constitutive laws of materials, they can predict not only the strength, but also the load-deformation history of a member. In this paper the five models are summarized to illustrate their intrinsic consistency.

• Korea-Australia Rheology Journal
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• v.18 no.1
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• pp.9-14
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• 2006

We show that some network and pom-pom constitutive models are essentially the same. Instead of the usual confrontation, we suggest that the two approaches can offer useful mutual support: vital information about network destruction rates found from detailed pom-pom calculations can be used to improve the network models, while deductions about network creation rates can pinpoint areas needing further attention in the tube modelling area. A new form of the PTT model, the PTT-X model, results in improved shear and elongational flow descriptions, plus an improved recoil behaviour. The remaining problems of strain-time separation, second normal stress difference description, and reduction of parameters are also discussed and some suggestions for progress are offered.

• Geomechanics and Engineering
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• v.24 no.2
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• pp.193-203
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• 2021

The time-history finite element analysis is usually used to evaluate the seismic response of shallow foundations. However, the literature lacks studies on the influence of the soil constitutive model complexity on the seismic response of shallow foundations. This study, thus, aims to fill this gap by investigating the seismic response of shallow foundation resting on dry silica sand using the linear elastic (LE) model, elastic-perfectly-plastic (EPP) model, and hardening soil with small strain stiffness (HS small) model. These models have been used because it is intended to compare the results of a soil constitutive model that accurately captures the seismic response of the soil-structure interaction problems (which is the HS small model) with simpler models (the LE and EPP models) that are routinely used by practitioners in geotechnical designs. The results showed that the LE model produces a very small seismic settlement value which is approximately equal to zero. The EPP model predicts a seismic settlement higher than that produced using the HS small model for earthquakes with a peak ground acceleration (PGA) lower than 0.25 g for a relative density of 45% and 0.40 g for a relative density of 70%. However, the HS small model predicts a seismic settlement higher than the EPP model beyond the aforementioned PGA values with the difference between both models increases as the PGA rises. The results also showed that the LE and EPP models predict similar trend and magnitude of the acceleration-time relationship directly below the foundation, which was different than that predicted using the HS small model. The results reported in this paper provide a useful benchmark for future numerical studies on the response of shallow foundations subjected to seismic shake.

• International Journal of Railway
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• v.3 no.4
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• pp.117-122
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• 2010

In transportation geotechnical engineering, stress-strain behavior of earth structures has been analyzed by numerical simulations with the implemented plasticity constitutive model. It is a fact that many advanced plasticity constitutive models on predicting the mechanical behavior of soils have been developed as well as experimental research works for geotechnical applications in the past decades. In this study, recently developed, a unified constitutive model for both clay and sand, which is referred to as CASM (clay and sand model), was compared with a classical constitutive model, Cam-Clay model. Moreover, integration methods of stress-strain rate equations using CASM were presented for simulation of undrained and drained triaxial compression tests. As a conclusion, it was observed that semi-implicit integration method has more improved accuracy of capturing strain rate response to applied stress than explicit integration by the multiple correction and iteration.

• Transactions of Materials Processing
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• v.31 no.4
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• pp.194-199
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• 2022

In finite element method (FEM) simulations, constitutive models are widely used and developed to represent a wide range of true stress-strain curves using a small number of modeling parameters. Nevertheless, many studies has been conducted to find a suitable constitutive model and optimal modeling parameters to represent experimentally obtained true stress-strain curves. Therefore, in this study, a new constitutive modeling approach using the combined Swift and Voce model is suggested, and confirmed through comparisons of the experimental results with the FEM simulation results.

• Structural Engineering and Mechanics
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• v.61 no.4
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• pp.463-473
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• 2017

Reinforced concrete is a complex material to be modeled in finite element domain. A proper material model is necessary to represent the nonlinear behaviour accurately. Though the nonlinear analysis of RC structures evolved long back, still an accurate and reliable model to predict the realistic behaviour of components are limited. It is observed from literature that there are three well-known models to represent the nonlinear behaviour of concrete. These models include Chu model (1985), Hsu model (1994) and Saenz model (1964).A new stress-strain model based on Weibull distribution has been proposed in the present study. The objective of the present study is to analyze a reinforced concrete beam under flexural loading by employing all the models. Nonlinear behaviour of concrete is considered in terms of stress vs. strain, damage parameter, tension stiffening behaviour etc. The ductility of the RC beams is computed by using deflection based and energy based concepts. Both deflection ductility and energy based ductility is compared and energy based concept is found to be in good correlation with the experiments conducted. The behavior of RC beam predicted using ABAQUS has been compared with the corresponding experimental observations. Comparison between numerical and experimental results confirms that these four constitutive models are reliable in predicting the behaviour of RC structures and any of the models can be employed for analysis.

• 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.

• Computers and Concrete
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• v.25 no.2
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• pp.181-192
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• 2020

Nowadays, steel fiber reinforced concretes (SFRCs) are widely used in practical applications. Significant experimental research has thus been carried out to determine the constitutive equations that represent the behavior of SFRCs under multiaxial loadings. However, numerical modelling of SFRCs via FEM has been challenging due to the complexities of the implementation of these constitutive equations. In this study, following the literature, a plasticity model is constructed for the behavior of SFRCs that involves the Willam-Warnke failure surface with the relevant evolution laws and a non-associated flow rule for determining the plastic deformations. For the precise (yet rapid) integration of the constitutive equations, an explicit substepping scheme consisting of yield intersection and drift correction algorithms is employed and thus implemented in ABAQUS via UMAT. The FEM model includes various material parameters that are determined from the experimental data. Three sets of parameters are used in the numerical simulations. While the first set is from the experiments that are conducted in this study on SFRC specimens with various contents of steel fibers, the other two sets are from the experiments reported in the literature. The response of SFRCs under multiaxial compression obtained from various numerical simulations are compared with the experimental data. The good agreement between numerical results and the experimental data indicates that not only the adopted plasticity model represents the behavior of SFRCs very well but also the implemented integration scheme can be employed in practical applications of SFRCs.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.11-27
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• 2014

In this paper, we propose closures for multi-phase flow models, which satisfy boundary conditions and conservation constraints. The models governing the evolution of the fluid mixing are derived by applying an ensemble averaging procedure to the microphysical equations characterized by distinct phases. We consider compressible multi species multi-phase flow with surface tension and transport.

• Korea-Australia Rheology Journal
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• v.12 no.1
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• pp.1-25
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• 2000

In this paper, we review recent progress in the development of constitutive models for both dilute and entangled polymeric liquids. The status of recent applications of these models for fluid dynamics predictions is then discussed, as well as possible future research directions.