The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Chun-ron Chiang - One of the best experts on this subject based on the ideXlab platform.
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Stress concentration of a crack-like spheroidal cavity lying on the prism plane of hexagonal crystals
Engineering Fracture Mechanics, 2017Co-Authors: Chun-ron ChiangAbstract:Abstract Stress concentration factors around a crack-like spheroidal cavity lying on the prism plane of hexagonal crystals are determined by the Equivalent Inclusion Method. The stress concentration factor is shown to be a product of two factors. One of the factors is purely geometric: the aspect ratio of the cavity and the other is characterized by the elastic properties of the material. The stress intensity factors of the related penny-shaped crack are deduced from the numerical results by reducing the aspect ratio of the cavity to zero. Results of several hexagonal single crystals including beryllium, graphite, magnesium, titanium and zinc are presented to show the influence of the material properties on the solution.
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Eshelby’s tensor for cubic piezoelectric crystals and its application to cavity problems
Engineering Fracture Mechanics, 2016Co-Authors: Chun-ron ChiangAbstract:Abstract Green’s function in a cubic piezoelectric crystal is used to find Eshelby’s tensor for an elliptic Inclusion explicitly in terms of material properties and shape ratio of the Inclusion. Inhomogeneity problems are then solved by the Equivalent Inclusion Method and the solutions are specialized for cavity problems. It is found that the medium inside the cavity has a strong influence on the electric response. Explicit formulas are obtained for the stress and electric-displacement concentration factors of elliptic cavities. The relationship between the electromechanical field concentrations of a slender cavity and those of an associated crack is developed and discussed.
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Stress concentration around a triaxial ellipsoidal cavity in transversely isotropic materials
Archive of Applied Mechanics, 2015Co-Authors: Chun-ron ChiangAbstract:The problem of stress concentration around a general triaxial ellipsoidal cavity in transversely isotropic materials is solved by Eshelby’s Equivalent Inclusion Method. The numerical results are found in excellent agreement with known solutions and consistent with the theoretical predictions. Some useful findings are obtained, including a theoretical connection between the stress concentration factors of 2D elliptical cavities and those of strongly prolate ellipsoidal configurations, the stress concentration factor around a strongly oblate ellipsoidal cavity, as well as the stress intensity factor of a flat elliptical crack. Stress concentration factors of ellipsoidal cavities with various shape ratios in different materials (zinc, magnesium, β -quartz, poled barium titanate ceramic and graphite) are determined and tabulated.
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Stress concentration around a strongly oblate cavity in a cubic crystal and its associated crack problems
Engineering Fracture Mechanics, 2010Co-Authors: Chun-ron ChiangAbstract:Abstract The stress distribution around a strongly oblate spheroidal cavity in a cubic crystal is determined by the Equivalent Inclusion Method. The stress concentration factor is shown to be a product of two factors: one factor is purely geometric; the other factor depends on the material properties. By allowing the aspect ratio of the cavity to approach zero, the stress intensity factor of the associated penny-shaped crack is deduced. The energy release rates of cracks on {1 0 0} planes are computed for different growth directions. Theses results are found to be correlated well with Zener’s anisotropy factor.
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Thermal mismatch stress of a cylindrical Inclusion in a cubic crystal
Engineering Fracture Mechanics, 2008Co-Authors: Chun-ron ChiangAbstract:The thermal stress induced in a spherical Inclusion by the difference of the thermal expansion coefficiences of the Inclusion and its embedding matrix is considered. Both the Inclusion and the matrix are assumed to be of cubic symmetry. Eshelby’s Equivalent Inclusion Method is used to solve the problem. A smple expression for the determination of thermal mismatch stress is thus derived. Some numerical examples are provided.
Tomoyuki Kojima - One of the best experts on this subject based on the ideXlab platform.
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Stochastic homogenization analysis for thermal expansion coefficients of fiber reinforced composites using the Equivalent Inclusion Method with perturbation-based approach
Computers & Structures, 2010Co-Authors: Sei-ichiro Sakata, Fumihiro Ashida, Tomoyuki KojimaAbstract:This paper describes a perturbation-based stochastic homogenization analysis Method for a thermal expansion coefficient of a fiber reinforced composite material using the Equivalent Inclusion Method. The proposed Method is formulated for evaluation of the probabilistic characteristics of the homogenized thermal expansion coefficients considering uncertainties in material properties and geometry of a component material. As a numerical example, the probabilistic characteristics of the homogenized thermal expansion coefficients of a unidirectional fiber reinforced plastic are analyzed. With comparison between the results of the proposed Method and the results of the Monte-Carlo simulation, validity, accuracy and effectiveness of the proposed Method are investigated.
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Stochastic homogenization analysis on elastic properties of fiber reinforced composites using the Equivalent Inclusion Method and perturbation Method
International Journal of Solids and Structures, 2008Co-Authors: Sei-ichiro Sakata, Fumihiro Ashida, Tomoyuki KojimaAbstract:Abstract This paper describes a Methodology for evaluation of influence of microscopic uncertainty in material properties and geometry of a microstructure on a homogenized macroscopic elastic property of an inhomogeneous material. For the analysis of the stochastic characteristics of a homogenized elastic property, the first-order perturbation Method is used. In order to analyze the influence of microscopic geometrical uncertainty, the perturbation-based Equivalent Inclusion Method is formulated. In this paper, an analytical form of the perturbation term using the Equivalent Inclusion Method is provided. As a numerical example, macroscopic stochastic characteristics such as an expected value or variance of the homogenized elastic tensor of a unidirectional fiber reinforced plastic, which is caused by microscopic uncertainty in material properties or geometry of a microstructure, are estimated with computing the first order perturbation term of the homogenized elastic tensor. Compared the results of the proposed Method with the results of the Monte-Carlo simulation, validity, effectiveness and a limitation of the perturbation-based homogenization Method is investigated.
Sei-ichiro Sakata - One of the best experts on this subject based on the ideXlab platform.
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Stochastic homogenization analysis for thermal expansion coefficients of fiber reinforced composites using the Equivalent Inclusion Method with perturbation-based approach
Computers & Structures, 2010Co-Authors: Sei-ichiro Sakata, Fumihiro Ashida, Tomoyuki KojimaAbstract:This paper describes a perturbation-based stochastic homogenization analysis Method for a thermal expansion coefficient of a fiber reinforced composite material using the Equivalent Inclusion Method. The proposed Method is formulated for evaluation of the probabilistic characteristics of the homogenized thermal expansion coefficients considering uncertainties in material properties and geometry of a component material. As a numerical example, the probabilistic characteristics of the homogenized thermal expansion coefficients of a unidirectional fiber reinforced plastic are analyzed. With comparison between the results of the proposed Method and the results of the Monte-Carlo simulation, validity, accuracy and effectiveness of the proposed Method are investigated.
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Stochastic homogenization analysis on elastic properties of fiber reinforced composites using the Equivalent Inclusion Method and perturbation Method
International Journal of Solids and Structures, 2008Co-Authors: Sei-ichiro Sakata, Fumihiro Ashida, Tomoyuki KojimaAbstract:Abstract This paper describes a Methodology for evaluation of influence of microscopic uncertainty in material properties and geometry of a microstructure on a homogenized macroscopic elastic property of an inhomogeneous material. For the analysis of the stochastic characteristics of a homogenized elastic property, the first-order perturbation Method is used. In order to analyze the influence of microscopic geometrical uncertainty, the perturbation-based Equivalent Inclusion Method is formulated. In this paper, an analytical form of the perturbation term using the Equivalent Inclusion Method is provided. As a numerical example, macroscopic stochastic characteristics such as an expected value or variance of the homogenized elastic tensor of a unidirectional fiber reinforced plastic, which is caused by microscopic uncertainty in material properties or geometry of a microstructure, are estimated with computing the first order perturbation term of the homogenized elastic tensor. Compared the results of the proposed Method with the results of the Monte-Carlo simulation, validity, effectiveness and a limitation of the perturbation-based homogenization Method is investigated.
Du Shanyi - One of the best experts on this subject based on the ideXlab platform.
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The stiffness and strength of transformation toughening ceramics with misoriented microcracks
Journal of Materials Science, 1994Co-Authors: Li Wenfang, Meng Jilong, Du ShanyiAbstract:Theoretical studies on misoriented transformation particles and microcracks in transformation toughening ceramics are presented using the Eshelby Equivalent Inclusion Method. The stress field, stiffness and strength were calculated. Experiments were done by the three-point bend Method using Al2O3/ZrO2 ceramics and the stiffness and strength were also measured. Comparison between theoretical and test results confirmed the important role of microcracks.
Hossein M. Shodja - One of the best experts on this subject based on the ideXlab platform.
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The electro-elastic scattered fields of an SH-wave by an eccentric two-phase circular piezoelectric sensor in an unbounded piezoelectric medium
Mechanics of Materials, 2014Co-Authors: Hossein M. Shodja, Hamid Jarfi, Ehsan RashidinejadAbstract:The dynamic Equivalent Inclusion Method (DEIM) which was first proposed by Fu and Mura (1983), in its original context has some shortcomings, which were pointed out and remedied by Shodja and Delfani (2009) who introduced the new consistency conditions along with the related micromechanically substantiated notion of eigenstress and eigenbody-force fields. However, these theories are bound to elastic media with isotropic phases. The present work extends the idea of the above-mentioned new DEIM to the dynamic electro-mechanical Equivalent Inclusion Method (DEMEIM) for the treatment of the scattering of SH-waves by a two-phase circular piezoelectric obstacle bonded to a third phase piezoelectric matrix. All the three transversely isotropic media have the same rotational axis of symmetry and the same poling direction which are parallel to the axis of the coated fiber, but perpendicular to the direction of propagation of the incident SH-wave. In general, the nested circular media are considered to be eccentric, i.e., the core fiber has a coating with variable thickness. Realization of the nature of the behavior of the field quantities a priori and its appropriate implementation in to the new extended consistency conditions is a critical step to insure a rigorous mathematical framework. As it will be shown, the expansion of the Green’s function and the eigenelectric, eigenstress, and eigenbody-force fields in terms of the eigenfunctions of the pertinent field equations rather than the commonly considered polynomials in the traditional Equivalent Inclusion Method (EIM) leads to an accurate solution with high convergence rate. The exact analytical expression for the total scattering cross-section which is influenced by the piezoelectric couplings is derived. The effects of the piezoelectric couplings and the properties of the fiber, coating, and the matrix as well as the wave number on the electro-mechanical scattered fields are examined.
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Electroelastic fields in interacting piezoelectric inhomogeneities by the electromechanical Equivalent Inclusion Method
Smart Materials and Structures, 2010Co-Authors: Hossein M. Shodja, M H Kargarnovin, R. HashemiAbstract:Consider two piezoelectric ellipsoidal inhomogeneities of arbitrary size, orientation and material constants, which in turn are surrounded by an infinite isotropic medium. The system under consideration is subjected to far-field non-uniform electromechanical loadings. Based on the extension of the electromechanical Equivalent Inclusion Method (EMEIM), the present paper develops a unified solution for determination of the associated electroelastic fields in the vicinity of interacting inhomogeneities. Accordingly, each of the piezoelectric inhomogeneities is broken down into two Equivalent Inclusions with proper polynomial eigenstrains and eigenelectric fields. The robustness and efficacy of the present solution are demonstrated through consideration of several boundary value problems. As a special case encompassed by the presented formulation, the interaction of a piezoelectric inhomogeneity and a lamellar inhomogeneity for two- and three-dimensional problems is addressed. For a particular case involving interaction of a slit-like crack and a piezoelectric circular fiber, comparison with the other available results in the literature attests to the validity of the proposed Method. Subsequently, the effect of some parameters such as geometry and stiffness of each phase on the quantitative value of stress intensity factors (SIFs) are examined for far-field non-uniform loadings.
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Spectral Equivalent Inclusion Method: Anisotropic cylindrical multi-inhomogeneities
Journal of the Mechanics and Physics of Solids, 2008Co-Authors: B. Shokrolahi-zadeh, Hossein M. ShodjaAbstract:Abstract Consider a set of nested infinitely extended elastic cylindrical bodies possessing general cylindrical anisotropy embedded in an unbounded elastic isotropic medium. For general far-field loading, the nature of the elastic fields inside the inhomogeneities is predicted and a number of pertinent attractive properties is noted and proved. Moreover, the associated Equivalent Inclusion Method (EIM) is concisely formulated. The concepts of the homogenization, spectral consistency conditions, and the so-called Eshelby–Fourier tensor are introduced. As a result the tedious and lengthy algebra encountered in the conventional EIM is circumvented and the corresponding large number of unknowns is reduced remarkably. Interestingly, the proposed theory is proved useful in the study of inhomogeneities with coatings made of functionally graded material (FGM). In addition to the relevance of the present work to multiple coated fiber reinforced composites, it is also of great value in the study of multi-shell quantum wire in electronic devices. The robustness and efficacy of the presented theories are demonstrated through consideration of several boundary value problems and various types of materials.
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A general unified treatment of lamellar inhomogeneities
Engineering Fracture Mechanics, 2007Co-Authors: Hossein M. Shodja, Farzaneh OjaghnezhadAbstract:Abstract Consider a lamellar inhomogeneity embedded in an unbounded isotropic elastic medium. When the elastic moduli of the lamellar inhomogeneity are zero it is a crack, if its elastic moduli are infinite it is an anticrack, and when its elastic moduli are finite it is called a quasicrack. Based on the Eshelby’s Equivalent Inclusion Method (EIM), the present paper develops a unified approach for determination of the exact closed-form expressions for modes I, II, and III stress intensity factors (SIFs) at the tips of lamellar inhomogeneities under a remote applied polynomial loading.
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Interacting cracks and ellipsoidal inhomogeneities by the Equivalent Inclusion Method
Journal of the Mechanics and Physics of Solids, 2003Co-Authors: Hossein M. Shodja, I.z. Rad, Reza SoheilifardAbstract:Based on the Eshelby's Equivalent Inclusion Method (EIM) and Hill's theorem on discontinuities of elastic fields across the interfaces, a theory for the determination of the stress intensity factors (SIFs) of arbitrarily oriented interacting cracks under non-uniform far-field applied stress (strain) is developed. As shown in this investigation the EIM proposed by Moschovidis and Mura can be extended for treatment of such problems, but their formulations are quite cumbersome and computationally inefficient. An alternative analytical approach is proposed that is computationally more efficient, and unlike the Method of Moschovidis and Mura can easily handle complex problems of interacting inhomogeneities and cracks. It is seen that as the interaction between the inhomogeneities becomes stronger, this Method yields results that are closer to the solutions reported in the literature than the solutions obtained using the extended EIM of Moschovidis and Mura, which is developed herein. Problems involving combinations of interacting elliptic and penny shape cracks and inhomogeneities are excellent candidates for demonstration of the accuracy and robustness of the present theory, for which the previous EIM produces less accurate results. Due to the limitations imposed on the existing Methods, every reported treatment has been tailored for a certain category of problems, and only uniform far-field loadings have been remedied. In contrast, the present theory is more general than the previously reported theories and it encompasses interacting cracks having a variety of geometries subjected to non-uniform far-field applied stress (strain); moreover, it is applicable to modes, I, II, III, and mixed mode fracture.