• Composites Research
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• v.33 no.2
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• pp.81-89
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• 2020

In this review paper, we introduce recent research studied effective physical properties of the reinforced composite using mean-field homogenization. We address homogenization for effective stiffness and expand it to effective thermal/electrical conductivity and dielectric constant. Multiphysics problems like piezoelectricity and thermoelectricity are considered by simplifying the constitutive equation into the linear equations like Hooke's law. We present a generalized theoretical formula for predicting effective physical properties of composite and validation by against finite element analysis.

• Computers and Concrete
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• v.2 no.6
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• pp.499-516
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• 2005

A composite model is used to represent the heterogeneity of plain concrete consisting of coarse aggregates, mortar matrix and the mortar-aggregate interface. The composite elements of plain concrete are modeled using triangular finite element units which have six interface nodes along the sides. Fracture is captured through a constitutive single branch softening-fracture law at the interface nodes, which bounds the elastic domain inside each triangular unit. The inelastic displacement at an interface node represents the crack opening or sliding displacement and is conjugate to the internodal force. The path-dependent softening behaviour is developed within a quasi-prescribed displacement control formulation. The crack profile is restricted to the interface boundaries of the defined mesh. No re-meshing is carried out. Solutions to the rate formulation are obtained using a mathematical programming procedure in the form of a linear complementary problem. An event by event solution strategy is adopted to eliminate solutions with simultaneous formation of softening zones in symmetric problems. The composite plain concrete model is compared to experimental results for the tensile crack growth in a Brazilian test and three-point bending tests on different sized specimens. The model is also used to simulate wedge-type shear-compression failure directly under the loading platen of a Brazilian test.

• Computers and Concrete
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• v.1 no.1
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• pp.47-60
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• 2004

The influence of the fracture process zone (FPZ) on the fracture properties is one of the hottest topics in the field of fracture mechanics for cementitious materials. Within the FPZ in front of a traction free crack, cohesive forces are distributed in accordance with the softening stress-separation constitutive relation of the material. Therefore, further crack propagation necessitates energy dissipation, which is the work done by the cohesive forces. In this paper $g_f$, the local fracture energy characterizing the energy consumption due to the cohesive forces, is discussed. The computational expression of $g_f$ in the FPZ can be obtained for any stage during the material fracture process regarding the variation of FPZ, whether in terms of its length or width. $G_{fa}$, the average energy consumption along the crack extension region, has also been computed and discussed in this paper. The experimental results obtained from the wedge splitting tests on specimens with different initial notch ratios are employed to investigate the property of the local fracture energy $g_f$ and the average value $G_{fa}$ over the crack extension length. These results can be used to indicate the influence of the FPZ. Additionally, changes in the length of the FPZ during the fracture process are also studied.

• Steel and Composite Structures
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• v.20 no.1
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• pp.205-225
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• 2016

In this study the finite element method is utilized to predict the deflection and vibration characteristics of rectangular plates made of saturated porous functionally graded materials (PFGM) within the framework of the third order shear deformation plate theory. Material properties of PFGM plate are supposed to vary continuously along the thickness direction according to the power-law form and the porous plate is assumed of the form where pores are saturated with fluid. Various edge conditions of the plate are analyzed. The governing equations of motion are derived through energy method, using calculus of variations while the finite element model is derived based on the constitutive equation of the porous material. According to the numerical results, it is revealed that the proposed modeling and finite element approach can provide accurate deflection and frequency results of the PFGM plates as compared to the previously published results in literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as porosity volume fraction, material distribution profile, mode number and boundary conditions on the natural frequencies and deflection of the PFGM plates in detail. It is explicitly shown that the deflection and vibration behaviour of porous FGM plates are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FGM plates with porosity phases.

• Steel and Composite Structures
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• v.28 no.1
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• pp.111-121
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• 2018

It has been argued that fracture energy of composite laminates depends on their thickness and number of layers. In this paper a modified direct energy balance approach (DEBA) has been developed to evaluate the mode-II shear fracture energy for E-glass/Epoxy laminates from finite element model at an arbitrary thickness. This approach considers friction and damage/plasticity deformations using cohesive zone modeling (CZM) and nonlinear finite element modeling. The presence of compressive stress and resulting friction was argued to be a possible cause for the thickness dependency of fracture energy. In the finite element modeling, CZM formulation has been developed with bilinear cohesive constitutive law combined with friction consideration. Also ply element have been developed with shear plastic damage model. Modified direct energy balance approach has been proposed for estimation of mode-II shear fracture energy. Experiments were performed on laminates of glass epoxy specimens for characterization of material parameters and determination of mode-II fracture energies for different thicknesses. Effect of laminate thickness on fracture energy of transverse crack tension (TCT) and end notched flexure (ENF) specimens has been numerically studied and comparison with experimental results has been made. It is shown that the developed numerical approach is capable of estimating increase in fracture energy due to size effect.

• Structural Engineering and Mechanics
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• v.55 no.5
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• pp.953-964
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• 2015

A model has been proposed that can predict the ultimate torsional strength of single-box multi-cell reinforced concrete box girder under combined loading of bending, shear and torsion. Compared with the single-cell box girder, this model takes the influence of inner webs on the distribution of shear flow into account. According to the softening truss theory and thin walled tube theory, a failure criterion is presented and a ultimate torsional strength calculating procedure is established for single-box multi-cell reinforced concrete box girder under combined actions, which considers the effect of tensile stress among the concrete cracks, Mohr stress compatibility and the softened constitutive law of concrete. In this paper the computer program is also compiled to speed up the calculation. The model has been validated by comparing the predicted and experimental members loaded under torsion combined with different ratios of bending and shear. The theoretical torsional strength was in good agreement with the experimental results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1429-1437
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• 1992

A new finite element formulation based on the relaxation type hereditary integral is presented for a time-domain analysis of isotropic, linear viscoelastic problems. The semi-discrete variational approximation and elastic-viscoelastic correspondence principle are used in the theoretical development of the proposed method. In a time-stepping procedure of final, linear algebraic system equations, only a small additional computation for past history is required since the equivalent stiffness matrix is constant. The viscoelasticity matrices are derived and the stress computation algorithm is given in matrix form. The effect of time increment and Gauss point numbers on the numerical accuracy is examined. Two dimensional numerical examples of plane strain and plane stress are solved and compared with the analytical solutions to demonstrate the versatility and accuracy of the present method.

• Journal of Welding and Joining
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• v.31 no.6
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• pp.32-36
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• 2013

The large-scale structures have the possibility that there are defects such as cracks due to stress concentration caused by geometric discontinuities in the structure. In this respect, the assessment of fatigue life and the development of structural health monitoring(SHM) are very important. Fatigue design of structure is typically accomplished either using a set of stress cycle (S-N) data obtained from fatigue tests or using the fracture mechanics approach. The stress intensity factor(SIF) is required for the estimation of fatigue crack propagation life from the linear elastic fracture mechanics (LEFM) perspective. In this study, Macro Fiber Composie(MFC) sensor for the measurement of SIF of two dimensional cracks is used. The SIF based on the piezoelectric constitutive law and fracture mechanics are calculated. The measured values of the SIF are later used for the prediction of the crack propagation life. In this study, the measured value of the SIF and the fatigue life are compared with the theoretical results.

• Advances in aircraft and spacecraft science
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• v.5 no.3
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• pp.295-318
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• 2018

This research studies thermo-elastic behavior of rotating micro discs that are employed in various micro devices such as micro gas turbines. It is assumed that material is functionally graded with a variable profile thickness, density, shear modulus and thermal expansion in terms of radius of micro disc and as a power law function. Boundary condition is considered fixed-free with uniform thermal loading and elastic field is symmetric. Using incompressible material's constitutive equation, we extract governing differential equation of four orders; to solution this equation, we utilize general differential quadrature (GDQ) method and the results are schematically pictured. The obtained result in a particular case is compared with another work and coincidence of results is shown. We will find out that surface effect tends to split micro disc's area to compressive and tensile while nonlocal parameter tries to converge different behaviors with each other; this convergence feature make FGIMs capable to resist in high temperature and so in terms of thermo-elastic behavior we can suggest, using FGIMs in micro devices such as micro turbines (under glass transition temperature).

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.457-466
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• 2019

This paper presents an efficient higher-order nonlocal beam theory for the Critical buckling, of functionally graded (FG) nanobeams with porosities that may possibly occur inside the functionally graded materials (FG) during their fabrication, the nonlocal elastic behavior is described by the differential constitutive model of Eringen. The material properties of (FG) nanobeams with porosities are assumed to vary through the thickness according to a power law. The governing equations of the functionally graded nanobeams with porosities are derived by employing Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, Illustrative examples are given also to show the effects of porosity volume fraction, and thickness to length ratios on the critical buckling of the FG beams.