• Structural Engineering and Mechanics
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• v.38 no.4
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• pp.503-516
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• 2011

Uncertainty in concrete properties, including concrete modulus of elasticity and modulus of rupture, are predicted by developing a microstructural homogenization model. The homogenization model is developed by analyzing a concrete representative volume element (RVE) using the finite element (FE) method. The concrete RVE considers concrete as a three phase composite material including: cement paste, aggregate and interfacial transition zone (ITZ). The homogenization model allows for considering two sources of variability in concrete, randomly dispersed aggregates in the concrete matrix and uncertain mechanical properties of composite phases of concrete. Using the proposed homogenization technique, the uncertainty in concrete modulus of elasticity and modulus of rupture (described by numerical cumulative probability density function) are determined. Deflection uncertainty of reinforced concrete (RC) beams, propagated from uncertainties in concrete properties, is quantified using Monte Carlo (MC) simulation. Cracked plane frame analysis is used to account for tension stiffening in concrete. Concrete homogenization enables a unique opportunity to bridge the gap between concrete materials and structural modeling, which is necessary for realistic serviceability prediction.

• Composites Research
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• v.25 no.1
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• pp.1-8
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• 2012

In order to predict the thermoelastic behavior of porous composites, poroelastic parameters are measured by using micromechanics-based finite element models. The expanding deformation caused by pore pressure, and the degradation of homogenized elastic moduli with pores are calculated for the assessment of the poroelastic parameters. Various representative volume elements considering the shape, size, and array pattern of pores are modeled and analyzed by a finite element method. The effects of porosity and material anisotropy, and the distribution of stain energy density are investigated carefully. In addition, the measured poroelastic parameters are verified by predicting the thermo-pore-elastic behavior of carbon/phenolic composites.

• Composites Research
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• v.16 no.1
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• pp.42-49
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• 2003

Brittle matrix composites often have interfacial debonding between the fiber and matrix which may lead to strength and stiffness degradation. The effect of interfacial debonding and fiber volume fraction on the mechanical properties of composite material were studied by using finite element method. Firstly, the modelling of fiber and matrix constituting the composite material was simplified under some assumptions. Traction and displacement continuity conditions were imposed along the boundary of adjacent representative volume elements. In order to obtain the effective material properties of composite material, stiffness constants were inverted. Numerical values of longitudinal moduli in case of perfect bonding were compared with theoretical values obtained by rule of mixtures and yielded consistency. Material properties of composite with large debonding an81e were found to decrease even though the fiber volume fraction increased.

• Computers and Concrete
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• v.3 no.5
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• pp.301-312
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• 2006

Experimental research revealed that the spatial dispersion of aggregate grains exerts pronounced influences on the mechanical and durability properties of concrete. Therefore, insight into this phenomenon is of paramount importance. Experimental approaches do not provide direct access to three-dimensional spacing information in concrete, however. Contrarily, simulation approaches are mostly deficient in generating packing systems of aggregate grains with sufficient density. This paper therefore employs a dynamic simulation system (with the acronym SPACE), allowing the generation of dense random packing of grains, representative for concrete aggregates. This paper studies by means of SPACE packing structures of aggregates with a Fuller type of size distribution, generally accepted as a suitable approximation for actual aggregate systems. Mean free spacing $\bar{\lambda}$, mean nearest neighbour distance (NND) between grain centres $\bar{\Delta}_3$, and the probability density function of ${\Delta}_3$ are used to characterize the spatial dispersion of aggregate grains in model concretes. Influences on these spacing parameters are studied of volume fraction and the size range of aggregate grains. The values of these descriptors are estimated by means of stereological tools, whereupon the calculation results are compared with measurements. The simulation results indicate that the size range of aggregate grains has a more pronounced influence on the spacing parameters than exerted by the volume fraction of aggregate. At relatively high volume density of aggregates, as met in the present cases, theoretical and experimental values are found quite similar. The mean free spacing is known to be independent of the actual dispersion characteristics (Underwood 1968); it is a structural parameter governed by material composition. Moreover, scatter of the mean free spacing among the serial sections of the model concrete in the simulation study is relatively small, demonstrating the sample size to be representative for composition homogeneity of aggregate grains. The distribution of ${\Delta}_3$ observed in this study is markedly skew, indicating a concentration of relatively small values of ${\Delta}_3$. The estimate of the size of the representative volume element (RVE) for configuration homogeneity based on NND exceeds by one order of magnitude the estimate for structure-insensitive properties. This is in accordance with predictions of Brown (1965) for composition and configuration homogeneity (corresponding to structure-insensitive and structure-sensitive properties) of conglomerates.

• Computers and Concrete
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• v.15 no.5
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• pp.735-758
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• 2015

This work deals with unilateral effect of quasi-brittle materials, such as concrete. For this propose, a two-dimensional meso-scale model is presented. The material is considered as a three-phase material consisting of interface zone, matrix and inclusions - each constituent modeled by an appropriate constitutive model. The Representative Volume Element (RVE) consists of inclusions idealized as circular shapes randomly placed into the specimen. The interface zone is modeled by means of cohesive contact finite elements developed here in order to capture the effects of phase debonding and interface crack closure/opening. As an initial approximation, the inclusion is modeled as linear elastic as well as the matrix. Our main goal here is to show a computational homogenization-based approach as an alternative to complex macroscopic constitutive models for the mechanical behavior of the quasi-brittle materials using a finite element procedure within a purely kinematical multi-scale framework. A set of numerical examples, involving the microcracking processes, is provided. It illustrates the performance of the proposed model. In summary, the proposed homogenization-based model is found to be a suitable tool for the identification of macroscopic mechanical behavior of quasi-brittle materials dealing with unilateral effect.

• Smart Structures and Systems
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• v.12 no.5
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• pp.579-594
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• 2013

A new enthalpy - based procedure for the homogenization of the electromechanical material parameters of composite piezoelectric modules with integrated electrodes is presented. It is based on a finite element (FE) modeling of the latter's representative volume element (RVE). In contrast to most previously published homogenization approaches that are based on averaged quantities, the presented method uses a direct evaluation of the electromechanical enthalpy. Hence, for the linear orthotropic piezoelectric composite behavior full set of elastic, piezoelectric, and dielectric material parameters, 17 load cases (LC) are used where each load case leads directly to one material parameter. This gives the possibility to elaborate a very strict and easy to program processing. In conjunction with the 17 LC, the enthalpy - based homogenization is particularly suitable for laminated composite piezoelectric modules with integrated electrodes. In this case, the electric load has to be given at the electrodes rather than at the RVE FE model boundaries. The proposed procedure is validated through its comparison to literature available results on a classical 1-3 piezoelectric micro fiber (longitudinally polarized) reinforced composite and a $d_{15}$ shear piezoelectric macro-fiber (transversely polarized) composite module.

• Geotechnical Engineering
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• v.13 no.6
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• pp.147-164
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• 1997

This study has the assumption that scale effects in rock mass properties are atrributed to the discontinuous and inhomogeneous nature of rock masses. In order to escape the general equivalent material approach applied to the concept of representative volume element, this study presents the new method considering irregular i oink geometry and arbitrary numbers of i oink and arbitrary joint orientations. Based on the theoretical approach, this theory is applied to a real engineering project. Showing the property variations with size of rock mass element, various numerical experiments about scale effect are conducted. Particularly, to prove the adequacy of the verification process in scale effect with nomerical method, and to investigate the detailed source of scale effect, 4 models with increas ins number of joints are tested. On the basis of the experimental results, the test results of scale effects in 3-D rock mass are presented. From these experiments the effects of the mechanical properties of rock joints on the scale effects in rock mass strength and elastic constants are discussed. To verify the mechanism of scale effects in jointed rock mass, two models with different j oink geometries are studied.

• Structural Engineering and Mechanics
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• v.58 no.5
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• pp.931-947
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• 2016

The effects of nanotechnology and smartness on the buckling reduction of pipes are the main contributions of present work. For this ends, the pipe is simulated with classical piezoelectric polymeric cylindrical shell reinforced by armchair double walled boron nitride nanotubes (DWBNNTs), The structure is subjected to combined electro-thermo-mechanical loads. The surrounding elastic foundation is modeled with a novel model namely as orthotropic nonhomogeneous Pasternak medium. Using representative volume element (RVE) based on micromechanical modeling, mechanical, electrical and thermal characteristics of the equivalent composite are determined. Employing nonlinear strains-displacements and stress-strain relations as well as the charge equation for coupling of electrical and mechanical fields, the governing equations are derived based on Hamilton's principal. Based on differential quadrature method (DQM), the buckling load of pipe is calculated. The influences of electrical and thermal loads, geometrical parameters of shell, elastic foundation, orientation angle and volume percent of DWBNNTs in polymer are investigated on the buckling of pipe. Results showed that the generated ${\Phi}$ improved sensor and actuator applications in several process industries, because it increases the stability of structure. Furthermore, using nanotechnology in reinforcing the pipe, the buckling load of structure increases.

• Composites Research
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• v.17 no.2
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• pp.34-39
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• 2004

In this paper, a modified and representative unit cell model was employed to study the tensile behaviour of closed-cell metallic foams with varying spatial density distribution as well as material imperfections. The density variation was assumed to follow a statistical probability distribution of the Gaussian type. A multiple cell finite element model, utilising the modified unit cell, was developed. The model exhibits deformation patterns similar to those observed in tensile testing. The nominal stress-strain curve obtained from quasistatic tensile of the foam was compared with experimental findings and was found to be in good agreement in the scheme of maximum strength only if the appropriate density distribution and volume fraction of internal imperfections are taken into account. Moreover, maximum tensile strength of the aluminium foam was found to be more sensitive to the volume fraction of imperfection than standard deviation of the density.

• Nuclear Engineering and Technology
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• v.45 no.7
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• pp.839-846
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• 2013

This paper describes a finite element model of the microstructure of dispersion type nuclear fuels, which can be used to determine the effective thermal conductivity of the fuels during irradiation. The model simulates a representative region of the fuel as a prism shaped unit cell made of brick elements. The elements within the unit cell are assigned material properties of either the fuel or the matrix depending on position, in such a way as to represent randomly distributed fuel particles with a size distribution similar to that of the as manufactured fuel. By applying an appropriate heat flux across the unit cell it is possible to determine the effective thermal conductivity of the unit cell as a function of the volume fraction of the fuel particles. The presence of a fuel/matrix interaction layer is simulated by the addition of a third set of material properties that are assigned to the finite elements that surround each fuel particle. In this way the effective thermal conductivity of the material may also be determined as a function of the volume fraction of the interaction layer. Work is on going to add fission gas bubbles in the fuel as a fourth phase to the model.