• Computers and Concrete
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• 제4권5호
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• pp.377-402
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• 2007

The paper presents quasi-static plane strain FE-simulations of strain localization in reinforced concrete beams without stirrups. The material was modeled with two different isotropic continuum crack models: an elasto-plastic and a damage one. In case of elasto-plasticity, linear Drucker-Prager criterion with a non-associated flow rule was defined in the compressive regime and a Rankine criterion with an associated flow rule was adopted in the tensile regime. In the case of a damage model, the degradation of the material due to micro-cracking was described with a single scalar damage parameter. To ensure the mesh-independence and to capture size effects, both criteria were enhanced in a softening regime by nonlocal terms. Thus, a characteristic length of micro-structure was included. The effect of a characteristic length, reinforcement ratio, bond-slip stiffness, fracture energy and beam size on strain localization was investigated. The numerical results with reinforced concrete beams were quantitatively compared with corresponding laboratory tests by Walraven (1978).

• Computers and Concrete
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• 제23권5호
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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.

• Earthquakes and Structures
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• 제25권2호
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• pp.125-134
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• 2023

In the present work, a new global damage index is proposed for the seismic performance and failure analysis of concrete gravity dams. Unlike the existing indices of concrete structures, this index doesn't need scaling with an ultimate or an upper value. For this purpose, the Beni-Haroun dam in north-eastern Algeria, is considered as a case study, for which an average seismic capacity curve is first evaluated by performing several incremental dynamic analyses. The seismic performance point of the dam is then determined using the N2 method, considering multiple modes and taking into account the stiffness degradation. The seismic demand is obtained from the design spectrum of the Algerian seismic regulations. A series of recorded and artificial accelerograms are used as dynamic loads to evaluate the nonlinear responses of the dam. The nonlinear behaviour of the concrete mass is modelled by using continuum damage mechanics, where material damage is represented by a scalar field damage variable. This modelling, which is suitable for cyclic loading, uses only a single damage parameter to describe the stiffness degradation of the concrete. The hydrodynamic and the sediment pressures are included in the analyses. The obtained results show that the proposed damage index faithfully describes the successive brittle failures of the dam which increase with increasing applied ground accelerations. It is found that minor damage can occur for ground accelerations less than 0.3 g, and complete failure can be caused by accelerations greater than 0.45 g.

• Computers and Concrete
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• 제3권2_3호
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• pp.103-122
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• 2006

Drying shrinkage of concrete occurs due to the loss of moisture and thus, it is controlled by moisture diffusion process. On the other hand, the shrinkage causes cracking of concrete and affects its moisture diffusion properties. Therefore, moisture diffusion and drying shrinkage are two coupled processes and their interactive effect is important for the durability of concrete structures. In this paper, the two material parameters in the moisture diffusion equation, i.e., the moisture capacity and humidity diffusivity, are modified by two different methods to include the effect of drying shrinkage on the moisture diffusion. The effect of drying shrinkage on the humidity diffusivity is introduced by the scalar damage parameter. The effect of drying shrinkage on the moisture capacity is evaluated by an analytical model based on non-equilibrium thermodynamics and minimum potential energy principle for a two-phase composite. The mechanical part of drying shrinkage is modeled as an elastoplastic damage problem. The coupled problem of moisture diffusion and drying shrinkage is solved using a finite element method. The present model can predict that the drying shrinkage accelerates the moisture diffusion in concrete, and in turn, the accelerated drying process increases the shrinkage strain. The coupling effects are demonstrated by a numerical example.

• Steel and Composite Structures
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• 제44권1호
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• pp.65-79
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• 2022

The main goal of this paper is to study the vibration of damaged core laminated annular plates with FG face sheets based on a three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. In this study the effect of microcracks on the vibrational characteristic of the sandwich plate is considered. In particular, the structures are made by an isotropic core that undergoes a progressive uniform damage, which is modeled as a decay of the mechanical properties expressed in terms of engineering constants. These defects are uniformly distributed and affect the central layer of the plates independently from the direction, this phenomenon is known as "isotropic damage" and it is fully described by a scalar parameter. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular plate is assumed to have any arbitrary boundary conditions at the circular edges including simply supported, clamped and, free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution, and boundary conditions.

• Interaction and multiscale mechanics
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• 제5권3호
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• pp.229-265
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• 2012

Hygroexpansion of wood is a known and undesired characteristic in civil engineering. When wood is exposed to changing environmental humidity, it adsorbs or desorbs moisture and warps. The resulting distortions or - at restrained conditions - cracks are a major concern in timber engineering. We herein present a multiscale model for prediction of the macroscopic hygroexpansion behavior of individual pieces of softwood from their microstructure, demonstrated for spruce. By applying poromicromechanics, we establish a link between the swelling pressure, driving the hygroexpansion of wood at the nanoscale, and the resulting macroscopic dimensional changes. The model comprises six homogenization steps, which are performed by means of continuum micromechanics, the unit cell method and laminate theory, all formulated in a poromechanical framework. Model predictions for elastic properties of wood as functions of the moisture content closely approach corresponding experimental data. As for the hygroexpansion behavior, the swelling pressure has to be back-calculated from macroscopic hygroexpansion data. The good reproduction of the anisotropy of wood hygroexpansion, based on only a single scalar calibration parameter, underlines the suitability of the model. The multiscale model constitutes a valuable tool for studying the effect of microstructural features on the macroscopic behavior and for assessing the hygroexpansion behavior at smaller length scales, which are inaccessible to experiments. The model predictions deliver input parameters for the analysis of timber at the structural scale, therewith enabling to optimize the use of timber and to prevent moisture-induced damage or failure.