• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.225-240
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• 1999

This paper presents a mechanistic approach to uniaxial viscoelastic constitutive modeling of asphalt concrete that accounts for damage evolution under cyclic loading conditions. An elasticviscoelastic correspondence principle in terms of pseudo variables is applied to separately evaluate viscoelasticity and time-dependent damage growth in asphalt concrete. The time-dependent damage growth in asphalt concrete is modeled by using a damage parameter based on a generalization of microcrack growth law. Internal state variables that describe the hysteretic behavior of asphalt concrete are determined. A constitutive equation in terms of stress and pseudo strain is first established for controlled-strain mode and then transformed to a controlled-stress constitutive equation by simply replacing physical stress and pseudo strain with pseudo stress and physical strain. Tensile uniaxial fatigue tests are performed under the controlled-strain mode to determine model parameters. The constitutive equations in terms of pseudo strain and pseudo stress satisfactorily predict the constitutive behavior of asphalt concrete all the way up to failure under controlled-strain and -stress modes, respectively.

• Steel and Composite Structures
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• v.19 no.5
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• pp.1055-1075
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• 2015

In order to investigate the accuracy and applicability of steel equivalent constitutive model, the calculated results were compared with typical tests of steel frames under static and dynamic loading patterns firstly. Secondly, four widely used models for time history analysis of steel frames were compared to discuss the applicability and efficiency of different methods, including shell element model, multi-scale model, equivalent constitutive model (ECM) and traditional beam element model (especially bilinear model). Four-story steel frame models of above-mentioned finite element methods were established. The structural deformation, failure modes and the computational efficiency of different models were compared. Finally, the equivalent constitutive model was applied in seismic incremental dynamic analysis of a ten-floor steel frame and compared with the cyclic hardening model without considering damage and degradation. Meanwhile, the effects of damage and degradation on the seismic performance of steel frame were discussed in depth. The analysis results showed that: damages would lead to larger deformations. Therefore, when the calculated results of steel structures subjected to rare earthquake without considering damage were close to the collapse limit, the actual story drift of structure might already exceed the limit, leading to a certain security risk. ECM could simulate the damage and degradation behaviors of steel structures more accurately, and improve the calculation accuracy of traditional beam element model with acceptable computational efficiency.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.6
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• pp.579-585
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• 2009

In this paper, a series of finite element analyzes were carried out to evaluate the performance of the RC beams strengthened with sprayed fiber reinforced polymer(SFRP) coating. A damage constitutive model based on the micromechanical constitutive model(Lee, 2001) in conjunction with the damage models(Lee 등, 2000) for SFRP coating was implemented into the finite element code ABAQUS. The present prediction results were compared with experimental data(Ha, 2007; Ha 등, 2009) to assess the accuracy of the damage constitutive model. It was concluded from the comparative study that the computational model developed by implementing the damage constitutive model into ABAQUS is suitable for the prediction of the performance of RC beams strengthened with SFRP coating.

• Selected Papers of The Society of Naval Architects of Korea
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• v.2 no.1
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• pp.106-128
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• 1994

An elasto-plastic-damage constitutive model for ductile materials is proposed within the framework of a thermodynamic approach of continuum damage mechanics (CDM) in which internal irreversible thermodynamic changes of micro-structure of materials such as plastic deformation and damage evolution are considered as thermodynamic state variables. The new constitutive model can predict not only the elasto-plastic behaviors but also the sequential stiffness degradation process of ductile materials more rationally.

• Journal of Ocean Engineering and Technology
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• v.14 no.2
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• pp.70-75
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• 2000

In this paper a new constitutive model for ductile materials was proposed. This model can describe the material degradation due to the evolution of isotropic damage during elasto-platic deformation. The plastic flow rule was derived under the framework of thermodynamic approach of continuum damage mechanics(CDM) in which plastic strain hardening parameters and isotropic damage were taken as thermodynamic state variables. And the process to determine material constants for constitutive model using an experimental data was presented.

• International Journal of Concrete Structures and Materials
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• v.1 no.1
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• pp.19-28
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• 2007

A dynamic constitutive damage model for reinforced concrete (RC) structures and formulations of blast loading for contact or near-contact charges are considered and adapted from literatures. The model and the formulations are applied to the input parameters needed in commercial finite element method (FEM) codes which is validated by the laboratory blast tests of RC slabs from literature. The results indicate that the dynamic constitutive damage model based on the damage mechanics and the blast loading formulations work well. The framework on the dynamic constitutive damage model and the blast loading equations can therefore be used for the simulation of failure of bridge components in engineering applications.

• Geomechanics and Engineering
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• v.21 no.4
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• pp.349-356
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• 2020

Rock brittleness, which is closely related to the failure modes, plays a significant role in the design and construction of many rock engineering applications. However, the brittle-ductile failure transition is mostly ignored by the current statistical damage constitutive model, which may misestimate the failure strength and failure behaviours of intact rock. In this study, a new statistical damage model considering rock brittleness is proposed for brittle to ductile behaviour of rocks using brittleness index (BI). Firstly, the statistical constitutive damage model is reviewed and a new statistical damage model considering failure mode transition is developed by introducing rock brittleness parameter-BI. Then the corresponding damage distribution parameters, shape parameter m and scale parameter F₀, are expressed in terms of BI. The shape parameter m has a positive relationship with BI while the scale parameter F₀ depends on both BI and ε_e. Finally, the robustness and correctness of the proposed damage model is validated using a set of experimental data with various confining pressure.

• Computers and Concrete
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• v.27 no.2
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• pp.153-162
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• 2021

This paper aims to simulate the isotropic elastic damage theory of Liu Jun (2012) using the self-programmed UMAT subroutine in the interface of ABAQUS. Liu Jun (2012)'s method based on the mechanic theory can not be used interactively with the currently commonly used finite element software ABAQUS. The advantage of this method in the paper is that it can interact with ABAQUS and provide a constitutive program framework that can be modified according to user need. The model retains the two scalar damage variables and the corresponding two energy dissipation mechanisms and damage criteria for considering the tensile and compressive asymmetry of concrete. Taking C45 concrete as an example, the relevant damage evolution parameters of its tensile and compressive constitutive model are given. The study demonstrates that the uniaxial tensile stress calculated by the subroutine is almost the same as the Chinese Concrete Design Specification (GB50010) before the peak stress, but ends soon after the peak stress. The stress-strain curve of uniaxial compression calculated by the subroutine is in good agreement with the peak stress in Chinese Concrete Design Specification (GB50010), but there is a certain deviation in the descending stage. In addition, this paper uses the newly compiled subroutine to simulate the shear bearing capacity of the shear key in a new structural system, namely the open-web sandwich slab. The results show that the damage constitutive subroutine has certain reliability.

• Geomechanics and Engineering
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• v.15 no.5
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• pp.1081-1089
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• 2018

The deformation and strength of brittle rocks are significantly influenced by the crack closure behavior. The relationship between the strength and deformation of rocks under uniaxial loading is the foundation for design and assessment of such scenarios. The concept of relative crack closure strain was proposed to describe the influence of the crack closure behavior on the deformation and strength of rocks. Considering the crack compaction effect, a new damage constitutive model was developed based on accumulated AE counts. First, a damage variable based on the accumulated AE counts was introduced, and the damage evolution equations for the four types of brittle rocks were then derived. Second, a compaction coefficient was proposed to describe the compaction degree and a correction factor was proposed to correct the error in the effective elastic modulus instead of the elastic modulus of the rock without new damage. Finally, the compaction coefficient and correction factor were used to modify the damage constitutive model obtained using the Lemaitre strain equivalence hypothesis. The fitted results of the models were then compared with the experimental data. The results showed that the uniaxial compressive strength and effective elastic modulus decrease with an increase in the relative crack closure strain. The values of the damage variables increase exponentially with strains. The modified damage constitutive equation can be used to more accurately describe the compressive deformation (particularly the compaction stage) of the four types of brittle rocks, with a coefficient of determination greater than 0.9.

• Steel and Composite Structures
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• v.1 no.3
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• pp.283-294
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• 2001

In the present work a constitutive model is developed which permits the assessment of the structural performance through a criterion based on cumulative damage. For it, a damage index is defined and is evaluated through the application of the Miner's rule in low-cycle fatigue. However, the damage index is not considered as a posteriori variable since is incorporated explicitly as an internal variable in the constitutive equations which produces a direct coupling between the damage and the structural mechanical behaviour allowing the possibility of considering as a whole different coupled phenomena. For the elaboration of this damage model, the concepts of the mechanics of continuum medium are applied on lumped dissipative models in order to obtain a coupled simplified model. As a result an elastoplastic model coupled with damage and fatigue damage is obtained.