• Structural Engineering and Mechanics
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• v.70 no.6
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• pp.781-791
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• 2019

Earthquakes most often induce damage to structures, resulting in the degradation or deterioration of integrity. In this paper, based on the experimental study on 5 RC frames with different span length and different layout of buckling-restrained braces, the seismic damage evaluation law of RC frame with buckling-restrained braces was analyzed, and then the seismic damage for different specimens was calculated using different damage models to study the damage evolution. By analyzing and comparing the observation in test and the calculated results, it could be found that, damage evolution models including Gosain model, Hwang model as well as Ou model could better simulate the development of damage during cyclic loading. Therefore, these 3 models were utilized to analyze the development of damage to better demonstrate the evolution law for structures with different layout of braces and under different axial compression ratios. The results showed that from all layouts of braces studied, the eccentrically braced frame behaved better under larger deformation with the damage growing slowly. It could be deduced that the link beam benefited the seismic performance of structure and alleviated the damage by absorbing high values of energy.

• Structural Engineering and Mechanics
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• v.10 no.2
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• pp.139-156
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• 2000

This paper concerns the development of a computational model for the damage evolution of engineering materials under dynamic loading. Two models describing the anisotropic damage evolution of a material are presented; the first is based on a power function of the effective equivalent stress and the second on the damage strain energy release rate. The methods for computing the damage accumulated in structural components and their implementation in a finite element programme are presented together with some numerical results. The dynamic response of a damaged structural component and the dynamic behaviour of a damaged material have been studied numerically. This study shows that the frequency spectrum of a damaged structure is down-shifted, while the damping ratio of damaged materials becomes higher, the amplitude of the response significantly increases and the resonance ensuing from the damage growth still occurs in a damaged structure.

• Geomechanics and Engineering
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• v.12 no.4
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• pp.627-637
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• 2017

The high positive correlation between plastic strain of loaded coal-rock and AE (acoustic emission) characteristic parameter was studied and proved through AE experiment during coal-rock uniaxial compression process. The results show that plastic strain in the whole process of uniaxial compression can be gained through the experiment. Moreover, coal-rock loaded process can be divided into four phases through analyzing the change of the plastic strain curve : pressure consolidation phase, apparent linear elastic phase, accelerated deformation phase, rupture and development phase, which corresponds to conventional elastic-plastic change law of loaded coal-rock. The theoretical curve of damage constitutive model is in high agreement with the experimental curve. So the damage evolution law of coal rock damage can be indicated by both acoustic emission and plastic strain. The results have great academic and realistic significance for further study of both AE signal characteristics during loaded coal-rock damaged process and the forecasting of coal-rock dynamic disasters.

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.279-301
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• 2008

This paper develops a 3D homogenization based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage coordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The loading/unloading criterion during cyclic loading is based on the scalar product of the strain increment and the normal to the damage surface in strain space. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensors. The HCDM model parameters are calibrated from homogenization of micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenization. Finally, the potential of HCDM model as a design tool is demonstrated through macro-micro analysis of monotonic and cyclic damage progression in composite structures.

• Computers and Concrete
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• v.23 no.5
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• pp.321-327
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• 2019

Experimental isotherm compressive tests show that concrete behaviour is dependent on temperature. The aim of such tests is to reproduce how concrete will behave under environmental changes within a moderate range of temperature. In this paper, a novel constitutive elastic damage behaviour law is proposed based on a free energy with an apparent damage depending on temperature. The proposed constitutive behaviour leads to classical theory of thermo-elasticity at small strains. Fixed elastic mechanical characteristics and fixed evolution law of damage independent of temperature and the material volume element size are considered. This approach is applied to compressive tests. The model predicts compressive strength and secant modulus of elasticity decrease as temperature increases. A power scaling law is assumed for specific entropy as function of the specimen size which leads to a volume size effect on the stress-strain compressive behaviour. The proposed model reproduces theoretical and experimental results from literature for tempertaures ranging between $20^{\circ}C$ and $70^{\circ}C$. The effect of the difference in the coefficient of thermal expansion between the mortar and coarse aggregates is also considered which gives a better agreement with FIB recommendations. It is shown that this effect is of a second order in the considered moderate range of temperature.

• Proceedings of the Korea Concrete Institute Conference
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• 1994.04a
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• pp.91-96
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• 1994

The growth and propagation of microcracks existed in concrete cause failure of concrete. This is called "damage". The concepts of two principles, equivalent strain principle and equivalent energy principle, are reviewed and compared in the case of uniaxial compressior to concrete. The damage evolution law and constitutive equation are derived by using the Helmholz free energy and the dissipation potential by means of the thermodynamic principles.rinciples.

• Geomechanics and Engineering
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• v.31 no.4
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• pp.365-373
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• 2022

In order to investigate the damage evolution law of rock specimens under cyclic loading, cyclic loading tests under constant loads with different amplitudes were carried out on limestone specimens with high strength and brittleness values using acoustic emission (AE) technology and the energy evolution and AE characteristics were evaluated. Based on dissipated energy density and AE counts, the damage variable of specimen was characterized and two damage evolution processes were analyzed and compared. The obtained results showed that the change of AE counts was closely related to radial deformation. Higher cyclic loading values result in more significant radial strain of limestone specimen and larger accumulative AE counts of cyclic loading segment, which indicated Felicity effect. Regarding dissipated energy density, the damage of limestone specimen was defined without considering the influence of radial deformation, which made the damage value of cyclic loading segment higher at lower amplitude loads. The damage of cyclic loading segment was increased with the magnitude of load. When dissipated energy density was applied to define damage, the damage value at unloading segment was smaller than that of AE counts. Under higher cyclic loading values, rocks show obvious damage during both loading and unloading processes. Therefore, during deep rock excavation, the damages caused by the deformation recovery of unloading rocks could not be ignored when considering the damage caused by abutment pressure.

• Composites Research
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• v.28 no.4
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• pp.182-190
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• 2015

The phenomenological evolution laws of damage can be defined either based on residual life or residual strength. The failure of a specimen can be defined immediately after or before fracture. The former is called in this paper by "failure defined by approach I" and the latter "failure defined by approach II." Usually at failure there is a discontinuity of loading variables and, because of this, damage at failure is discontinuous. Therefore the values of damage at failure by two different approaches are not the same. Based on this idea the sequence effects of the phenomenological evolution law of damage given by $dD/dN=g(D)f({\Phi})$ were studied. Thin-walled graphite/epoxy tubes consisting of four of $[{\pm}45]_s$ laminates were used for the experimental study of sequence effects and the effects of mean stress on fatigue life. It was found that the sequence effects in two step uniaxial fatigue for $[{\pm}45]_s$ graphite/epoxy tubular specimen showed that a high-low block loading sequence was less damaging than a low-high one.

• Computers and Concrete
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• v.1 no.3
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• pp.261-284
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• 2004

Two enhancements to a recently developed plastic-damage-contact model for concrete are presented. The model itself, which uses planes of degradation that can undergo damage and separation but that can regain contact according to a contact law, is described. The first enhancement is a new damage evolution function which provides a completely smooth transition from the undamaged to the damaged state and from pre-peak to post-peak regions. The second is an improved contact function that governs the potential degree of contact with increasing opening on a crack plane. The use of a damage evolution function with a pre-peak has implications for the consistent tangent matrix/stress recovery algorithm developed for the model implementation, and amendments to this algorithm to accommodate the new function are described. A series of unpublished experimental tests on notched specimens undertaken in Cardiff in the mid 1990s are then described. These include notched beam tests as well as prismatic and cylindrical torsion tests. The tests are then considered in three dimensional finite element analyses using the modified Craft model implemented in the finite element program LUSAS. Comparisons between experimental and numerical data show reasonable agreement except that the numerical simulations do not fully describe the latter stages of the softening responses for the torsion examples. Finally, it is concluded that the torsion tests described provide useful benchmark examples for the validation of three-dimensional numerical models for concrete.

• 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.