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1
Chang, Hua Jian, and Shu Wen Zhan. "A Method to Evaluate the Elastic Properties of Ceramics-Enhanced Composites Undertaking Interfacial Delamination." Key Engineering Materials 336-338 (April 2007): 2513–16. http://dx.doi.org/10.4028/www.scientific.net/kem.336-338.2513.
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A micromechanical approach is developed to investigate the behavior of composite materials, which undergo interfacial delamination. The main objective of this approach is to build a bridge between the intricate theories and the engineering applications. On the basis of the spring-layer model, which is useful to treat the interfacial debonding and sliding, the present paper proposes a convenient method to assess the effects of delamination on the overall properties of composites. By applying the Equivalent Inclusion Method (EIM), two fundamental tensors are derived in the present model, the modified Eshelby tensor, and the compliance tensor (or stiffness tensor) of the weakened inclusions. Both of them are the fundamental tensors for constructing the overall constitutive law of composite materials. By simply substituting these tensors into an existing constitutive model, for instance, the Mori-Tanaka model, one can easily evaluate the effects of interfacial delamination on the overall properties of composite materials. Therefore, the present method offers a pretty convenient tool. Some numerical results are carried out in order to demonstrate the performance of this model.
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Shodja, H. M., and A. S. Sarvestani. "Elastic Fields in Double Inhomogeneity by the Equivalent Inclusion Method." Journal of Applied Mechanics 68, no. 1 (June 14, 2000): 3–10. http://dx.doi.org/10.1115/1.1346680.
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Consider a double-inhomogeneity system whose microstructural configuration is composed of an ellipsoidal inhomogeneity of arbitrary elastic constants, size, and orientation encapsulated in another ellipsoidal inhomogeneity, which in turn is surrounded by an infinite medium. Each of these three constituents in general possesses elastic constants different from one another. The double-inhomogeneity system under consideration is subjected to far-field strain (stress). Using the equivalent inclusion method (EIM), the double inhomogeneity is replaced by an equivalent double-inclusion (EDI) problem with proper polynomial eigenstrains. The double inclusion is subsequently broken down to single-inclusion problems by means of superposition. The present theory is the first to obtain the actual distribution rather than the averages of the field quantities over the double inhomogeneity using Eshelby’s EIM. The present method is precise and is valid for thin as well as thick layers of coatings, and accommodates eccentric heterogeneity of arbitrary size and orientation. To establish the accuracy and robustness of the present method and for the sake of comparison, results on some of the previously reported problems, which are special cases encompassed by the present theory, will be re-examined. The formulations are easily extended to treat multi-inhomogeneity cases, where an inhomogeneity is surrounded by many layers of coatings. Employing an averaging scheme to the present theory, the average consistency conditions reported by Hori and Nemat-Nasser for the evaluation of average strains and stresses are recovered.
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Zhou, Kun, and Qingbing Dong. "A Three-Dimensional Model of Line-Contact Elastohydrodynamic Lubrication for Heterogeneous Materials with Inclusions." International Journal of Applied Mechanics 08, no. 02 (March 2016): 1650014. http://dx.doi.org/10.1142/s1758825116500149.
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This paper develops a three-dimensional (3D) model for a heterogeneous half-space with inclusions distributed periodically beneath its surface subject to elastohydrodynamic lubrication (EHL) line-contact applied by a cylindrical loading body. The model takes into account the interactions between the loading body, the fluid lubricant and the heterogeneous half-space. In the absence of subsurface inclusions, the surface contact pressure distribution, the half-space surface deformation and the lubricant film thickness profile are obtained through solving a unified Reynolds equation system. The inclusions are homogenized according to Eshelby’s equivalent inclusion method (EIM) with unknown eigenstrains to be determined. The disturbed half-space surface deformations induced by the subsurface inclusions or eigenstrains are iteratively introduced into the lubricant film thickness until the surface deformation finally converges. Both time-independent smooth surface contact and time-dependent rough surface contact are considered for the lubricated contact problem.
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Markenscoff, Xanthippi. "On the dynamic generalization of the anisotropic Eshelby ellipsoidal inclusion and the dynamically expanding inhomogeneities with transformation strain." Journal of Micromechanics and Molecular Physics 01, no. 03n04 (October 2016): 1640001. http://dx.doi.org/10.1142/s2424913016400014.
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The self-similarly dynamically (subsonically) expanding anisotropic ellipsoidal Eshelby inclusion is shown to exhibit the constant stress “Eshelby property” in the interior domain of the expanding inclusion on the basis of dimensional analysis, analytic properties and the proof for the static inclusion alone. As an example of this property and the application of the dynamic Eshelby tensor (constant in the interior domain), it is shown that the Eshelby equivalent inclusion method always allows for the determination of the equivalent transformation strain for a self-similarly dynamically expanding inhomogeneous spherical inclusion when the Poisson's ratio is in the real range (positive definiteness of the strain energy). Thus, the solution of dynamically self-similarly expanding inhomogeneities (chemical phase change) with transformation strain can be obtained, as well as the driving force per unit area of the expanding inhomogeneity.
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Duan, H. L., Xin Yi, Zhu Ping Huang, and J. Wang. "Eshelby Equivalent Inclusion Method for Composites with Interface Effects." Key Engineering Materials 312 (June 2006): 161–66. http://dx.doi.org/10.4028/www.scientific.net/kem.312.161.
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The Eshelby equivalent inclusion method is generalized to calculate the stress fields related to spherical inhomogeneities with two interface conditions depicted by the interface stress model and the linear-spring model. It is found that the method gives the exact results for the hydrostatic loading and very accurate results for a deviatoric loading. The method can be used to predict the effective properties of composites with the interface effects.
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Zhang, Hui, Zong Fu Zhang, and Jia Chu Xu. "Effective Elastic Moduli of Fiber-Reinforced Polymer Matrix Composites Filled with Nanoparticle." Advanced Materials Research 811 (September 2013): 32–38. http://dx.doi.org/10.4028/www.scientific.net/amr.811.32.
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Effective moduli of fiber-reinforced polymer matrix composites filled with nanoparticle considering the effect of linear change of interphase are presented in this paper. The three-phase inclusion problem for matrix-interface-particle is equivalent to the Eshelby two-phase inclusion problem. According to the result of the Eshelby inclusion problem, the effective modulus tensor of unit cell of equivalent particle is derived. The effective moduli of equivalent matrix are given based on Mori-Tanaka method. Using two fundamental equation of micromechanic theory, the three-dimensional bridged formulation of unidirectional composites is derived. The quantitative relationship between the macroscopic elastic parameters and the structural parameters of the fiber-reinforced polymer composites filled with nanoparticles is investigated. Effects of the thickness of interfacial layer, the particle size and the volume fraction of nanoparticles on the effective elastic moduli of the composites are also discussed.
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Yang, Lihong, Qiang Chen, and Zhonghua Li. "Crack–inclusion interaction for mode II crack analyzed by Eshelby equivalent inclusion method." Engineering Fracture Mechanics 71, no. 9-10 (June 2004): 1421–33. http://dx.doi.org/10.1016/s0013-7944(03)00162-0.
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Zhou, Kun, Rongbing Wei, Guijun Bi, Xu Wang, Bin Song, and Xiqiao Feng. "Semi-Analytic Solution of Multiple Inhomogeneous Inclusions and Cracks in an Infinite Space." International Journal of Computational Methods 12, no. 01 (January 23, 2015): 1550002. http://dx.doi.org/10.1142/s0219876215500024.
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This work develops a semi-analytic solution for multiple inhomogeneous inclusions of arbitrary shape and cracks in an isotropic infinite space. The solution is capable of fully taking into account the interactions among any number of inhomogeneous inclusions and cracks which no reported analytic or semi-analytic solution can handle. In the solution development, a novel method combining the equivalent inclusion method (EIM) and the distributed dislocation technique (DDT) is proposed. Each inhomogeneous inclusion is modeled as a homogenous inclusion with initial eigenstrain plus unknown equivalent eigenstrain using the EIM, and each crack of mixed modes I and II is modeled as a distribution of edge climb and glide dislocations with unknown densities. All the unknown equivalent eigenstrains and dislocation densities are solved simultaneously by means of iteration using the conjugate gradient method (CGM). The fast Fourier transform algorithm is also employed to greatly improve computational efficiency. The solution is verified by the finite element method (FEM) and its capability and generality are demonstrated through the study of a few sample cases. This work has potential applications in reliability analysis of heterogeneous materials.
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Zeng, Xian Wei, and Xi Luo. "Analysis of Crack-Inclusion Interaction in an Anisotropic Medium by Eshelby Equivalent Inclusion Method." Advanced Materials Research 268-270 (July 2011): 72–75. http://dx.doi.org/10.4028/www.scientific.net/amr.268-270.72.
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The problem of a semi-infinite crack in anisotropic medium interacting with a near-tip inclusion is analyzed by the Eshelby equivalent inclusion method. The change of mode I stress intensity factor due to crack-inclusion interaction is evaluated using a novel analytical solution for the model I stress intensity factor at the tip of a semi-infinite crack due to near-tip eigenstrains. Numerical results of the mode I stress intensity factor due to the presence of a near-tip circular inclusion are presented to show the influence of the elastic stiffness of an inclusion on the near-tip elastic field. The present scheme can be applied to calculate the stress intensity at a crack-tip in anisotropic media due to the interaction of inclusions with arbitrary shapes.
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Li, Z. "The interaction of a screw dislocation with inclusion analyzed by Eshelby equivalent inclusion method." Scripta Materialia 47, no. 6 (September 16, 2002): 371–75. http://dx.doi.org/10.1016/s1359-6462(02)00113-6.
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Li, Zhonghua, and Lihong Yang. "The Near-Tip Stress Intensity Factor for a Crack Partially Penetrating an Inclusion." Journal of Applied Mechanics 71, no. 4 (July 1, 2004): 465–69. http://dx.doi.org/10.1115/1.1651539.
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When a crack is lodged in an inclusion, the difference between the elastic modulus of the inclusion and matrix material will cause the near-tip stress intensity factor to be greater or less than that prevailing in a homogeneous material. A method is derived for calculation of the near-tip stress intensity factor for the inclusion with arbitrary shape. The derivation of the fundamental formula is based on the transformation toughening theory. The equivalent transformation strain contributed from modulus difference between inclusion and matrix is calculated from Eshelby equivalent inclusion approach. As validated by numerical examples, the developed formula has excellent accuracy.
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Ma, Hang, Cheng Yan, and Qing-hua Qin. "Eigenstrain Boundary Integral Equations with Local Eshelby Matrix for Stress Analysis of Ellipsoidal Particles." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/947205.
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Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.
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Wu, Jun. "Uniaxial Compression Creep Prediction of Asphalt Mixture Using the Eshelby Equivalent Inclusion Method." Advanced Materials Research 1061-1062 (December 2014): 410–13. http://dx.doi.org/10.4028/www.scientific.net/amr.1061-1062.410.
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Asphalt mixture was simply treated as a two-phase composite, in which coarse aggregates are embedded into asphalt mastic matrix. According to the elastic-viscoelastic correspondence principle, an elastic micromechanical method is extended for predicting viscoelastic properties of asphalt mixture, which is simply treated as elastic coarse aggregate inclusions periodically and isotropically embedded into viscoelastic asphalt mastic matrix. The Burgers model is adopted for characterizing the matrix mechanical behavior, so that the homogenized relaxation modulus of asphalt mixture in compression creep is derived. After a series of uniaxial compression creep tests are performed on asphalt mastic in different stress conditions in order to determine the matrix constitutive parameters, the presented framework is validated by comparison with the experiment, and then some predictions to uniaxial compression creep behavior of asphalt mixture in different stress conditions are given.
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Wu, Jun. "Thermal Expansion Coefficient Prediction of Asphalt Mixture with the Eshelby Equivalent Inclusion Theory." Applied Mechanics and Materials 584-586 (July 2014): 1071–75. http://dx.doi.org/10.4028/www.scientific.net/amm.584-586.1071.
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Asphalt mixture was considered as a two-phase composite, in which coarse aggregates are embedded into asphalt mastic matrix, namely a mix of fine aggregates and asphalt, so that a theoretical framework was proposed to correlate its effective thermal expansion coefficient with its components and microstructures based on the Eshelby equivalent inclusion theory. A four-parameter model with the experimentally determined parameters was used to characterize the viscoelastic constitutive behavior of asphalt mastic. The thermal expansion coefficient prediction of asphalt mixture was conducted and compared with the predictions by the sparse method and the self-consistent method. It was revealed that the prediction from the proposed theoretical framework is reasonable.
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Liu, Wen Lian, and Li De Wei. "Study on Statistical Damage Constitutive Model of Rock Basing on Thermdynamics." Advanced Materials Research 217-218 (March 2011): 220–25. http://dx.doi.org/10.4028/www.scientific.net/amr.217-218.220.
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Statistics models are effective to describe the relation of strain-stress of rock. But the constitutive relations in the statistical models are too simple for rock. Using the Eshelby equivalent inclusion method, a Helmholtz free energy for e damage rock is set up in the present paper. A constitutive model for damage rock is set up . The presented model is verified as reasonable and practical with comparion to the experiment data.
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Li, Zhonghua, and Lihong Yang. "The application of the Eshelby equivalent inclusion method for unifying modulus and transformation toughening." International Journal of Solids and Structures 39, no. 20 (October 2002): 5225–40. http://dx.doi.org/10.1016/s0020-7683(02)00420-1.
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Zhong, Z., and S. A. Meguid. "On the Imperfectly Bonded Spherical Inclusion Problem." Journal of Applied Mechanics 66, no. 4 (December 1, 1999): 839–46. http://dx.doi.org/10.1115/1.2791787.
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An exact solution is developed for the problem of a spherical inclusion with an imperfectly bonded interface. The inclusion is assumed to have a uniform eigenstrain and a different elastic modulus tensor from that of the matrix. The displacement discontinuity at the interface is considered and a linear interfacial condition, which assumes that the displacement jump is proportional to the interfacial traction, is adopted. The elastic field induced by the uniform eigenstrain given in the imperfectly bonded inclusion is decomposed into three parts. The first part is prescribed by a uniform eigenstrain in a perfectly bonded spherical inclusion. The second part is formulated in terms of an equivalent nonuniform eigenstrain distributed over a perfectly bonded spherical inclusion which models the material mismatch between the inclusion and the matrix, while the third part is obtained in terms of an imaginary Somigliana dislocation field which models the interfacial sliding and normal separation. The exact form of the equivalent nonuniform eigenstrain and the imaginary Somigliana dislocation are fully determined using the equivalent inclusion method and the associated interfacial condition. The elastic fields are then obtained explicitly by means of the superposition principle. The resulting solution is then used to evaluate the average Eshelby tensor and the elastic strain energy.
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Chalon, F., and F. Montheillet. "The Interaction of Two Spherical Gas Bubbles in an Infinite Elastic Solid." Journal of Applied Mechanics 70, no. 6 (November 1, 2003): 789–98. http://dx.doi.org/10.1115/1.1629110.
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The elastic strain and stress fields between two bubbles of different sizes and different pressures were estimated by using the fundamental result of Eshelby. The equivalent inclusion method was extended to the case of two inclusions in an infinite elastic solid. This approach, which remains totally analytical, was compared successfully to finite element calculations. The mean stress provides information about gas diffusion between the bubbles: according to the results, the bubbles are likely to progressively equalize their sizes. Moreover, the derivation of the von Mises equivalent stress showed that its value, in the vicinity of the bubbles, is larger than the elasticity limit. Therefore, for a complete mechanical description of the problem, plasticity should be taken into account. In spite of its simplicity, this method nevertheless leads to results, which are very close to the prediction of numerical calculations.
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Wang, Man. "Calculation and Measurement of Elastic Modulus of Nano BaTiO3 Enhanced IPMC." Key Engineering Materials 793 (January 2019): 53–57. http://dx.doi.org/10.4028/www.scientific.net/kem.793.53.
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The Mechanical parameters of elastic modulus about the preparation technology of BaTiO3/IPMC (Ionic Polymer Metal Composite) were studied. In order to get the relationship between the elastic modulus and the different content of BaTiO3/IPMC the Mori-Tanaka method based on Eshelby equivalent inclusion theory was used. In order to verify the correctness of the model, Solution casting method was used to prepare different content of BaTiO3/IPMC (100:1,100:3,100:5,100:7). The elastic modulus of IPMC was texted by tensile testing and the bending test of cantilever. The result shows that: The elastic modulus of IPMC film increased by 6.3% ~ 84.7% with addition of BaTiO3. It was proved that the reinforced fillers could greatly improve the elasticity modulus of IPMC.
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Yuan, Min, Dan Zhou, Jian Chen, Xia Hua, and Sheng Qiang. "Study on the Calculation Method of Stress in Strong Constraint Zones of the Concrete Structure on the Pile Foundation Based on Eshelby Equivalent Inclusion Theory." Materials 13, no. 17 (August 29, 2020): 3815. http://dx.doi.org/10.3390/ma13173815.
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In view of the strong constraint zones of the concrete structure on the pile foundation, there are some differences between the calculation results of the isotropic equivalent pile foundation by the volume replacement ratio method and the actual engineering. In this paper, referring to the relevant algorithm of rock mass with anchor, the anchor and rock mass are, respectively, compared to pile and surrounding soil foundation. Eshelby equivalent inclusion theory is introduced into the equivalent mechanical model of soil foundation with pile, and a new equivalent pile foundation algorithm considering anisotropic elastic constant is compiled by Fortran. Three kinds of calculation methods are used to calculate the stress field of the concrete structure of the large pump station on the pile foundation during the construction period, and the stress in the strong constraint zones of the concrete structure are mainly analyzed. It is found that the calculation accuracy of Algorithm 3 is the highest, and the calculation results of Algorithm 2 can be modified by the coefficients to achieve the calculation accuracy of Algorithm 3 and the calculation efficiency is actually improved. Finally, the accuracy of the proposed method is verified by the engineering measured data.
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Wang, Yao Mian, Huan Ping Yang, and Cong Hui Zhang. "Modeling of the Tensile Deformation Behavior of SiCp/Fe Composites." Applied Mechanics and Materials 217-219 (November 2012): 79–85. http://dx.doi.org/10.4028/www.scientific.net/amm.217-219.79.
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A combined model taking account of the dislocation strengthening effects and particle cracking during tensile straining based on Eshelby equivalent inclusion method is presented to model the deformation behavior of SiCp/Fe composites. Stress-strain curves of the composites were simulated and it is found that the curves vary obviously with the volume fraction and particle size. The yield stress is increased significantly by increasing the volume fraction and decreasing the particle size. Stress in particles is very high during straining and the fraction of cracked particles increased obviously with increasing the particle size. These results indicate that higher volume fraction and finer particles can give better mechanical properties of the composites attributed to the increased load sharing effect and dislocation strengthening effects of the matrix.
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Chen, Xiao, Hongfa Xu, Hansheng Geng, Lu Dong, and Jixiang Zhang. "A New Equivalent Statistical Damage Constitutive Model on Rock Block Mixed Up with Fluid Inclusions." Mathematical Problems in Engineering 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/3080173.
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So far, there are few studies concerning the effect of closed “fluid inclusions” on the macroscopic constitutive relation of deep rock. Fluid-matrix element (FME) is defined based on rock element in statistical damage model. The properties of FME are related to the size of inclusions, fluid properties, and pore pressure. Using FME, the equivalent elastic modulus of rock block containing fluid inclusions is obtained with Eshelby inclusion theory and the double M-T homogenization method. The new statistical damage model of rock is established on the equivalent elastic modulus. Besides, the porosity and confining pressure are important influencing factors of the model. The model reflects the initial damage (void and fluid inclusion) and the macroscopic deformation law of rock, which is an improvement of the traditional statistical damage model. Additionally, the model can not only be consistent with the rock damage experiment date and three-axis compression experiment date of rock containing pore water but also describe the locked-in stress experiment in rock-like material. It is a new fundamental study of the constitutive relation of locked-in stress in deep rock mass.
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Chang, Julius C., and Samuel M. Allen. "Elstic energy changes accompanying gamma-prime rafting in nickel-base superalloys." Journal of Materials Research 6, no. 9 (September 1991): 1843–55. http://dx.doi.org/10.1557/jmr.1991.1843.
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Eshelby's equivalent inclusion method is applied to the case of a single, inhomogeneous, ellipsoidal precipitate in an infinite matrix to study the morphological changes of the gamma-prime precipitates in nickel-base superalloys due to the influence of lattice constant misfit, elastic inhomogeneity and anisotropy, applied stress, and interfacial energy. The energy-minimizing inclusion shapes depend very sensitively on the degree of elastic inhomogeneity, on the sense and magnitude of the applied stress, and on the sense of the lattice constant misfit. The interfacial energy contribution can dominate that of elastic strain energy for small precipitate sizes, elastically compliant systems, nearly homogeneous alloys, and/or nearly isotropic materials. Calculations are carried out for two well-characterized nickel-base alloys: a Ni–13.5Al alloy (positive misfit, elastically hard inclusions) studied by Miyazaki et al. and CMSX-3 (negative misfit, elastically soft inclusions) studied by Pollock. The Eshelby energy calculations correctly predict the precipitate morphologies observed by Miyazaki et al. and by Pollock.
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Song, Xiaoqi, Yukio Takahashi, Weiming He, and Tohru Ihara. "Analytical Model for Studying the Influence of Thickness on the Protective Effect." International Journal of Automation Technology 15, no. 4 (July 5, 2021): 431–47. http://dx.doi.org/10.20965/ijat.2021.p0431.
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This paper presents an analytical model to study the influence of the thickness of the built-up layer (BUL) / built-up edge (BUE) on its protective effect during cutting. A new elastic-plastic contact model at the tool-chip interface is proposed to analyze the sliding contact problem with a layer of adhesion (including the BUL and BUE). The equivalent inclusion method (EIM) is utilized to analyze the stress disturbance caused by the adhesion and to evaluate the protective effect of the adhesion. In this method, the adhesion is considered as an equivalent elliptical inclusion at the tool-chip interface. The protective effect of the adhesion and the influence of the adhesion thickness on its protective effect can be evaluated. The proposed analytical model was verified based on experimental data obtained from dry cutting of SUS304 stainless steel. From the results, it can be confirmed that BUL/BUE can protect the cutting tool by affecting the stress distributions in the tool, the positions of yield initiation, and the tangential force acting on the tool. It can also be concluded that a greater thickness improves the protective effect of the BUL/BUE. Furthermore, the proposed model can also provide a clear understanding of the BUL/BUE formation phenomenon.
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Wei, Tao, Wei Liu, Wenxuan Gou, and Junqiang Kou. "Effective Modulus Estimation Method of QT400-18 Cast Iron with Repair Welding." Mathematical Problems in Engineering 2019 (September 19, 2019): 1–9. http://dx.doi.org/10.1155/2019/5737029.
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Repair welding is an important remediation process for castings with slight defects. In this paper, the tensile behaviors of the QT400-18 nodular cast iron with different repair welding sizes were experimentally analyzed. Specimens with different diameters of the filler region were prepared by the same welding process. The fracture initiated in the filler region under uniaxial tensile loading. The modulus, strength, and ductility decreased with the weld diameter increase. The postyield hardening phenomenon was not observed in the repaired specimen. The repair region ratio was defined as the proportion of the repair welding area to the cross-sectional area of the structure. The effective modulus of the repaired specimens decreased with the repair region ratio increase, and the relationship between them was fitted by a negative exponential function. The repair welding region was treated as an inclusion in the matrix of castings, and the volume fraction of inclusion was applied to characterize the repair welding size. Based on the theories of Eshelby tensor and Mori–Tanaka equivalent method, a method for estimating macroscopic effective modulus of repair welding castings was established. The theoretical solutions were in good agreement with the experimental results. The method will be helpful in estimating the safe service limit of repair welded castings.
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Basista, M., and W. Weglewski. "Micromechanical modeling of sulphate corrosion in concrete: Influence of ettringite forming reaction." Theoretical and Applied Mechanics 35, no. 1-3 (2008): 29–52. http://dx.doi.org/10.2298/tam0803029b.
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Two micromechanical models are developed to simulate the expansion of cementitious composites exposed to external sulphate attack. The difference between the two models lies in the form of chemical reaction of the ettringite formation (through-solution vs. topochemical). In both models the Fick's second law with reaction term is assumed to govern the transport of the sulphate ions. The Eshelby solution and the equivalent inclusion method are used to determine the eigenstrain of the expanding ettringite crystals in microcracked hardened cement paste. The degradation of transport properties is studied in the effective medium and the percolation regime. An initial-boundary value problem (2D) of expansion of a mortar specimen immersed in a sodium sulphate solution is solved and compared with available test data. The obtained results indicate that the topochemical mechanism is the one capable of producing the experimentally observed amount of expansion.
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Takashima, Shuji, Noriyuki Miyazaki, Toru Ikeda, and Michihiko Nakagaki. "Elastic-Plastic Constitutive Equation Accounting for Microstructure." Key Engineering Materials 340-341 (June 2007): 1037–42. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.1037.
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In this study, we focus on the modeling of solid structures that include microstructures observed in particle-dispersed composites. The finite element modeling can be used to clarify how the macroscopic behaviors of solid structures are influenced by the microstructures. In such a case, if the whole structure including the microstructures is modeled by the finite elements, an enormous number of finite elements and enormous amount of computational time are required. To overcome such difficulties, we propose a new method for modeling microstructures. In this method, an explicit form of the stress-strain relation covering both elastic and elastic-plastic regions is derived from the equivalent inclusion method proposed by Eshelby that provides mathematical solutions for stress and strain at an arbitrary point inside and outside the inclusion. The derived elastic-plastic constitutive equation takes account of the microstructures, so that the effect of microstructures on the macroscopic behaviors can be obtained from the conventional finite element method by using such a constitutive equation without modeling microstructures in the finite element analysis. The effectiveness of the proposed constitutive equation is verified for a simple problem by comparing the results of the one-element finite element analyses using the proposed constitutive equation with those of the detailed finite element analyses using multi-element finite element modeling.
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Thuinet, Ludovic, and Alexandre Legris. "Zêta Hydride Precipitation in Zirconium Alloys: an Example of Elastically Driven Morphology of Coherent Trigonal Precipitates inside a Сlose-Packed Hexagonal Matrix." Solid State Phenomena 172-174 (June 2011): 248–53. http://dx.doi.org/10.4028/www.scientific.net/ssp.172-174.248.
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The influence of a crystallographic symmetry break on the morphology of precipitates during the coherent precipitation of a trigonal phase in a close packed hexagonal matrix is analyzed. It is pointed out that in spite of the isotropy of the stress free strain of the precipitate in the basal plane, the existence of an extra elastic constant in the precipitate (associated to the loss of symmetry) induces a morphological evolution from a shape having a symmetry of revolution around the threefold axis to a needle-like one oriented along the compact directions in the basal plane. These general considerations are applied to the case of zêta zirconium hydrides the crystallography of which has been recently identified to be coherent with that of the alpha Zr matrix. The influence of symmetry break and elastic heterogeneity on precipitation morphology has been numerically addressed by using different approaches. An analytical approximation to the elastic energy based on Eshelby equivalent inclusion method allows obtaining a qualitative criterion to determine the occurrence of a shape bifurcation of zêta hydrides.
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Zhi, Chao, Mingjuan Du, Zhaoling Sun, Mengjie Wu, Xiaoyi He, Jiaguang Meng, and Lingjie Yu. "Warp-Knitted Spacer Fabric Reinforced Syntactic Foam: A Compression Modulus Meso-Mechanics Theoretical Model and Experimental Verification." Polymers 12, no. 2 (February 1, 2020): 286. http://dx.doi.org/10.3390/polym12020286.
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In this study, a new type ternary composite, called warp-knitted spacer fabric reinforced syntactic foam (WKSF-SF), with the advantages of high mechanical properties and a lower density, was proposed. Then, a meso-mechanics theoretical model based on the Eshelby–Mori–Tanaka equivalent inclusion method, average stress method and composite hybrid theory was established to predict the compression modulus of WKSF-SF. In order to verify the validity of this model, compression modulus values of theoretical simulations were compared with the quasi-static compression experiment results. The results showed that the addition of suitable WKSF produces at least 15% improvement in the compressive modulus of WKSF-SF compared with neat syntactic foam (NSF). Meanwhile, the theoretical model can effectively simulate the values and variation tendency of the compression modulus for different WKSF-SF samples, and is especially suitable for the samples with smaller wall thickness or a moderate volume fraction of microballoons (the deviations is less than 5%). The study of the meso-mechanical properties of WKSF-SF will help to increase understanding of the compression properties of this new type composite deeply. It is expected that WKSF-SF can be used in aerospace, marine, transportation, construction, and other fields.
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Budagosky, Jorge A., and Alberto García-Cristóbal. "Multiscale Kinetic Monte Carlo Simulation of Self-Organized Growth of GaN/AlN Quantum Dots." Nanomaterials 12, no. 17 (September 2, 2022): 3052. http://dx.doi.org/10.3390/nano12173052.
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A three-dimensional kinetic Monte Carlo methodology is developed to study the strained epitaxial growth of wurtzite GaN/AlN quantum dots. It describes the kinetics of effective GaN adatoms on an hexagonal lattice. The elastic strain energy is evaluated by a purposely devised procedure: first, we take advantage of the fact that the deformation in a lattice-mismatched heterostructure is equivalent to that obtained by assuming that one of the regions of the system is subjected to a properly chosen uniform stress (Eshelby inclusion concept), and then the strain is obtained by applying the Green’s function method. The standard Monte Carlo method has been modified to implement a multiscale algorithm that allows the isolated adatoms to perform long diffusion jumps. With these state-of-the art modifications, it is possible to perform efficiently simulations over large areas and long elapsed times. We have taylored the model to the conditions of molecular beam epitaxy under N-rich conditions. The corresponding simulations reproduce the different stages of the Stranski–Krastanov transition, showing quantitative agreement with the experimental findings concerning the critical deposition, and island size and density. The influence of growth parameters, such as the relative fluxes of Ga and N and the substrate temperature, is also studied and found to be consistent with the experimental observations. In addition, the growth of stacked layers of quantum dots is also simulated and the conditions for their vertical alignment and homogenization are illustrated. In summary, the developed methodology allows one to reproduce the main features of the self-organized quantum dot growth and to understand the microscopic mechanisms at play.
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Zhou, Qinghua, Lechun Xie, Xiaoqing Jin, Zhanjiang Wang, Jiaxu Wang, Leon M. Keer, and Qian Wang. "Numerical Modeling of Distributed Inhomogeneities and Their Effect on Rolling-Contact Fatigue Life." Journal of Tribology 137, no. 1 (September 24, 2014). http://dx.doi.org/10.1115/1.4028406.
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The present work proposes a new efficient numerical solution method based on Eshelby's equivalent inclusion method (EIM) to study the influence of distributed inhomogeneities on the contact of inhomogeneous materials. Benchmark comparisons with the results obtained with an existing numerical method and the finite element method (FEM) demonstrate the accuracy and efficiency of the proposed solution method. An effective influence radius is defined to quantify the scope of influence for inhomogeneities, and the biconjugate gradient stabilized method (Bi-CGSTAB) is introduced to determine the eigenstrains of a large number of inclusions efficiently. Integrated with a rolling-contact fatigue (RCF) life prediction model, the proposed numerical solution is applied to investigate the RCF life of (TiB + TiC)/Ti-6Al-4V composites, and the results are compared with those of a group of RCF tests, revealing that the presence of the reinforcements causes reduction in the RCF lives of the composites. The comparison illustrates the capability of the proposed solution method on RCF life prediction for inhomogeneous materials.
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Amuzuga, Kwassi Vilevo, Thibaut Chaise, Arnaud Duval, and Daniel Nelias. "Fully Coupled Resolution of Heterogeneous Elastic–Plastic Contact Problem." Journal of Tribology 138, no. 2 (February 15, 2016). http://dx.doi.org/10.1115/1.4032072.
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The recent development of semi-analytical methods (SAM) has led to numerous improvements in their capabilities in terms of phenomena that can be accounted for and numerical efficiency. They now allow to perform fast and robust simulations of contact between inelastic—with either elastic–plastic or viscoelastic behavior—and anisotropic or heterogeneous materials. All effects may be combined, with either coating, inclusions, cavities, or fibers as inhomogeneities. The coupling between local and global scales remains numerically difficult. A framework is proposed here for contact problems considering the effect of elastic heterogeneities within an elastic–plastic matrix. The mutual interactions among heterogeneities and their surrounding plastic zone as well as the interactions between them and the contact surface through which the load is transmitted should be accounted for. These couplings are outside the validity domain of the Eshelby’s equivalent inclusion method (EIM) that assumes a uniform stress field in an infinite space far from the inhomogeneity. In the presence of heterogeneities close to the surface or located at the Hertzian depth, the yield stress can be reached locally due to the additional stress it generates, whereas the stress and strain state would remain purely elastic for a matrix without inclusion. It is well known that for rolling element bearing and gear applications, the ruin of components is often linked to cracks initiated in the vicinity of large or hard inclusions that act as stress raisers. It turned out that plastic strains tend to reduce the stress generated by the contact pressure while hard heterogeneities will increase it. As plastic strain accumulation can provide the basis for fatigue damage criteria, the second half of the paper will illustrate how the method can be used to identify and rank geometrical and material parameters that influence the location and magnitude of the maximal plastic strain.
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Wu, Chunlin, and Huiming Yin. "The effects of boundary and inhomogeneities on the delamination of a bi-layered material system." International Journal of Damage Mechanics, November 25, 2023. http://dx.doi.org/10.1177/10567895231216008.
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The inclusion-based boundary element method (iBEM) is developed to calculate the elastic fields of a bi-layered composite with inhomogeneities in one layer. The bi-material Green’s function has been applied to obtain the elastic field caused by the domain integral of the source fields on inclusions and the boundary integral of the applied loads on the surface. Using Eshelby’s equivalent inclusion method (EIM), the material mismatch between the particle and matrix phases is simulated with a continuously distributed source field, namely eigenstrain, on inhomogeneities so that the iBEM can calculate the local field. The stress singularity along the interface leads to the delamination of the bimaterials under a certain load. The crack’s energy release rate ( J) is obtained through the J-integral, which predicts the stability of the delamination. When the stiffness of one layer increases, the J-integral increases with a higher gradient, leading to lower stability. Particularly, the effect of the boundary and inhomogeneity on the J-integral is illustrated by changing the crack length and inhomogeneity configuration, which shows the crack is stable at the beginning stage and becomes unstable when the crack tip approaches the boundary; a stiffer inhomogeneity in the neighborhood of a crack tip decreases J and improves the fracture resistance. For the stable cracking phase, the J-integral increases with the volume fraction of inhomogeneity are evaluated. The model is applied to a dual-glass solar module with air bubbles in the encapsulant layer. The stress distribution is evaluated with the iBEM, and the J-integral is evaluated to predict the delamination process with the energy release rate, which shows that the bubbles significantly increase the J-integral. The effect of the bubble size, location, and number on the J-integral is also investigated. The present method provides a powerful tool for the design and analysis of layered materials and structures.
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Ahmadi, Masoud, and Prashant Saxena. "Analytical modeling of the electrical conductivity of CNT-filled polymer nanocomposites." Mathematics and Mechanics of Solids, February 8, 2024. http://dx.doi.org/10.1177/10812865231225483.
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Electrical conductivity of most polymeric insulators can be drastically enhanced by introducing a small volume fraction [Formula: see text] of conductive nanofillers. These nanocomposites find wide-ranging engineering applications from cellular metamaterials to strain sensors. In this work, we present a mathematical model to predict the effective electrical conductivity of carbon nanotubes (CNTs)/polymer nanocomposites accounting for the conductivity, dimensions, volume fraction, and alignment of the CNTs. Eshelby’s classical equivalent inclusion method (EIM) is generalized to account for electron-hopping—a key mechanism of electron transport across CNTs, and is validated with experimental data. Two measurements, namely, the limit angle of filler orientation and the probability distribution function, are used to control the alignment of CNTs within the composites. Our simulations show that decreasing the angle from a uniformly random distribution to a fully aligned state significantly reduces the transverse electrical conductivity, while the longitudinal conductivity shows less sensitivity to angle variation. Moreover, it is observed that distributing CNTs with non-uniform probability distribution functions results in an increase in longitudinal conductivity and a decrease in transverse conductivity, with these differences becoming more pronounced as the volume fraction of CNTs is increased. A reduction in CNT length decreases the effective electrical conductivity due to the reduced number of available conductive pathways while reducing CNT diameter increases the conductivity.
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Wang, Tengxiang, Chunlin Wu, Liangliang Zhang, and Huiming Yin. "The Green's Function Based Thermal Analysis of a Spherical Geothermal Tank in a Semi-infinite Domain." Journal of Applied Mechanics, May 16, 2022, 1–29. http://dx.doi.org/10.1115/1.4054568.
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Abstract The Green's function of a bi-material infinite domain with a plane interface is applied to thermal analysis of a spherical underground heat storage tank. The heat transfer from a spherical source is derived from the integral of the Green's function over the spherical domain. Because the thermal conductivity of the tank is generally different from soil, the Eshelby's equivalent inclusion method (EIM) is used to simulate the thermal conductivity mismatch of the tank from the soil. For simplicity, the ground with an approximately uniform temperature on the surface is simulated by a bi-material infinite domain which is perfectly conductive above the ground. The heat conduction in the ground is investigated for two scenarios: Firstly, a steady-state uniform heat flux from surface into the ground is considered, and the heat flux is disturbed by the existence of the tank due to the conductivity mismatch. A prescribed temperature gradient, or an eigen-temperature gradient, is introduced to investigate the local temperature field in the neighborhood of the tank. Secondly, when a temperature difference exists between the water in the tank and soil, the heat transfer between the tank and soil depends on the tank size, conductivity and temperature difference, which provide a guideline for heat exchange design for tank size. The modeling framework can be extended to two-dimensional cases, periodic or transient heat transfer problems for geothermal well operations. The corresponding Green's functions are provided for those applications.
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Jin, Xiaoqing, Leon M. Keer, and Qian Wang. "A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion." Journal of Applied Mechanics 78, no. 3 (February 15, 2011). http://dx.doi.org/10.1115/1.4003238.
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From the analytical formulation developed by Ju and Sun [1999, “A Novel Formulation for the Exterior-Point Eshelby’s Tensor of an Ellipsoidal Inclusion,” ASME Trans. J. Appl. Mech., 66, pp. 570–574], it is seen that the exterior point Eshelby tensor for an ellipsoid inclusion possesses a minor symmetry. The solution to an elliptic cylindrical inclusion may be obtained as a special case of Ju and Sun’s solution. It is noted that the closed-form expression for the exterior-point Eshelby tensor by Kim and Lee [2010, “Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion,” ASME Trans. J. Appl. Mech., 77, p. 024503] violates the minor symmetry. Due to the importance of the solution in micromechanics-based analysis and plane-elasticity-related problems, in this work, the explicit analytical solution is rederived. Furthermore, the exterior-point Eshelby tensor is used to derive the explicit closed-form solution for the elastic field outside the inclusion, as well as to quantify the elastic field discontinuity across the interface. A benchmark problem is used to demonstrate a valuable application of the present solution in implementing the equivalent inclusion method.
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Sun, L. G., K. Y. Xu, and E. Pan. "Irregular Inhomogeneities in an Anisotropic Piezoelectric Plane." Journal of Applied Mechanics 79, no. 2 (February 24, 2012). http://dx.doi.org/10.1115/1.4005557.
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This paper presents an analytical solution for the Eshelby problem of polygonal inhomogeneity in an anisotropic piezoelectric plane. By virtue of the equivalent body-force concept of eigenstrain, the induced elastic and piezoelectric fields in the corresponding inclusion are first expressed in terms of the line integral along its boundary with the integrand being the Green’s functions, which is carried out analytically. The Eshelby inhomogeneity relation for the elliptical shape is then extended to the polygonal inhomogeneity, with the final induced field involving only elementary functions with small steps of iteration. Numerical solutions are compared to the results obtained from other methods, which verified the accuracy of the proposed method. Finally, the solution is applied to a triangular and a rectangular quantum wire made of InAs within the semiconductor GaAs full-plane substrate.
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Zhou, Ye, Caichao Zhu, Xiaojin Chen, and Wei Ye. "Numerical study on butterfly wings around inclusion based on damage evolution and semi-analytical method." Friction, September 15, 2021. http://dx.doi.org/10.1007/s40544-021-0540-2.
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AbstractButterfly wings are closely related to the premature failure of rolling element bearings. In this study, butterfly formation is investigated using the developed semi-analytical three-dimensional (3D) contact model incorporating inclusion and material property degradation. The 3D elastic field introduced by inhomogeneous inclusion is solved by using numerical approaches, which include the equivalent inclusion method (EIM) and the conjugate gradient method (CGM). The accumulation of fatigue damage surrounding inclusions is described using continuum damage mechanics. The coupling between the development of the damaged zone and the stress field is considered. The effects of the inclusion properties on the contact status and butterfly formation are discussed in detail. The model provides a potential method for quantifying material defects and fatigue behavior in terms of the deterioration of material properties.
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Shi, Xiujiang, Liqin Wang, Qinghua Zhou, and Qian Wang. "A Fast Approximate Method for Heat Conduction in an Inhomogeneous Half-Space Subjected to Frictional Heating." Journal of Tribology 140, no. 4 (February 9, 2018). http://dx.doi.org/10.1115/1.4038953.
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This paper reports a new three-dimensional model for heat conduction in a half-space containing inhomogeneities, applicable to frictional heat transfer, together with a novel combined algorithm of the equivalent inclusion method (EIM) and the imaging inclusion approach for building this model. The influence coefficients (ICs) for temperature and heat flux are obtained via converting the frequency response function (FRF) and integrating Green's function. The model solution is based on the discrete convolution and fast Fourier transform (DC-FFT) algorithm using the ICs, convenient for solving problems involving multiple elliptical inhomogeneities with arbitrary orientations. A group of parametric studies are conducted for understanding the thermal fields in the inhomogeneous half-space due to surface frictional heating, influenced by the properties of the inhomogeneity, its depth, and orientation.
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"Elastic inclusions and inhomogeneities in transversely isotropic solids." Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 444, no. 1920 (January 8, 1994): 239–52. http://dx.doi.org/10.1098/rspa.1994.0014.
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A method that introduces a new stress vector function ( the hexagonal stress vector ) is applied to obtain, in closed form, the elastic fields due to an inclusion in transversely isotropic solids. The solution is an extension of Eshelby’s solution for an ellipsoidal inclusion in isotropic solids. The Green’s functions for double forces and double forces with moment are derived and these are then used to solve the inclusion problem. The elastic field inside the inclusion is expressed in terms of the newtonian and biharmonic potential functions, which are similar to those needed for the solution in isotropic solids. Two more harmonic potential functions are introduced to express the solution outside the inclusion. The constrained strain inside the inclusion is uniform and the relation between the constrained strain and the misfit strain has the same characteristics as those of the Eshelby tensor for isotropic solids, namely, the coefficients coupling an extension to a shear or one shear to another are zero. The explicit closed form expression of this tensor is given. The inhomogeneity problem is then solved by using Eshelby’s equivalent inclusion method. The solution for the thermoelastic displacements due to thermal inhomogeneities is also presented.
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Shengguang, Zhang, Wang Wenzhong, and Zhao Ziqiang. "Elastohydrodynamic Lubrication Analysis of Point Contacts With Consideration of Material Inhomogeneity." Journal of Tribology 136, no. 4 (June 19, 2014). http://dx.doi.org/10.1115/1.4027750.
Full textAbstract:
Inhomogeneities in matrix may significantly affect the performance of mechanical elements, such as possible fatigue life reduction for rolling bearing due to stress concentration induced by inhomogeneities; on the other hand, most components operate under lubrication environment. So far the numerical algorithms to solve lubrication problems without the consideration of inhomogeneities or inclusions are well developed. In this paper, the combination of elastohydrodynamic lubrication (EHL) and inclusion problem is realized to consider the effect of material inhomogeneity on the lubrication performance and subsurface stress distribution, etc. The matrix inhomogeneity will induce disturbed displacement, which will modify the film thickness and consequently result in the change of lubricated contact pressure distribution, etc. The matrix inhomogeneity is treated as the homogeneous inclusion with equivalent eigenstrain according to equivalent inclusion method (EIM), and the disturbed displacement is calculated by semi-analytical method (SAM). While the pressure and film thickness distributions are obtained by solving Reynolds equation. The iterative process is realized to consider the interaction between lubrication behavior and material response. The results show the inhomogeneity in contacting body will greatly influence the lubricated contact performance. The influences are different between compliant and stiff inhomogeneity. It is also found that different sizes and positions of inhomogeneity can significantly affect the contact characteristic parameters.
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Fu, Yao, Xiangning Zhang, and Xiaomin Zhou. "A Computational Scheme for Evaluating the Stress Field of Thermally and Pressure Induced Unconventional Reservoir." Lithosphere 2021, Special 1 (September 21, 2021). http://dx.doi.org/10.2113/2021/1164947.
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Abstract The fluid flow connecting the hydraulic fracture and associated unconventional gas or oil reservoir is of great importance to explore such unconventional resource. The deformation of unconventional reservoir caused by heat transport and pore pressure fluctuation may change the stress field of surrounding layer. In this paper, the stress distribution around a penny-shaped reservoir, whose shape is more versatile to cover a wide variety of special case, is investigated via the numerical equivalent inclusion method. Fluid production or hydraulic injection in a subsurface resource caused by the change of pore pressure and temperature within the reservoir may be simulated with the help of the Eshelby inclusion model. By employing the approach of classical eigenstrain, a computational scheme for solving the disturbance produced by the thermally and pressure induced unconventional reservoir is coded to study the effect of Biot coefficient and some other important factors. Moreover, thermo-poro transformation strain and arbitrarily orientated reservoir existing within the surrounding layer are also considered.
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Wang, Chao, and Jili Feng. "Fracture criteria and initiation mechanism of concrete based on material configurational mechanics." Fatigue & Fracture of Engineering Materials & Structures, April 2024. http://dx.doi.org/10.1111/ffe.14287.
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AbstractIn this study, the interaction force between an in‐plane elliptical inclusion and a crack is evaluated using the Eshelby equivalent inclusion and material configurational force method. The toughening effect of coarse aggregates on concrete is investigated. The fracture criteria for mixed‐mode cracks based on the characteristics of the crack‐tip plastic zone assessed by the principal configurational stress difference are proposed and verified by experimental results in the literature. The fracture probability is then used to improve the fracture criteria, and the dimensionless factor associated with stress intensity factors is introduced to determine the fracture probability. Additionally, the volume fraction of coarse aggregates, the age and fatigue life of concrete are considered in the present fracture criteria. Theoretical studies show that the interaction between a crack and a hard or soft inclusion exhibits mutual repulsion and attraction. The size and shape of the crack‐tip plastic zones assessed by the Mises stress and the principal configurational stress difference are essentially the same. The fracture load envelopes increase with the increase in the volume fraction of coarse aggregates and the age of concrete and shrink with the increase in the life ratio.
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He, Junzhao, Yunan Li, Yuling Jin, Anming Wang, Yumin Zhang, Jinchao Jia, Hei Song, and Dong Liang. "Study on Mechanical Problems of Complex Rock Mass by Composite Material Micromechanics Methods: A Literature Review." Frontiers in Earth Science 9 (January 13, 2022). http://dx.doi.org/10.3389/feart.2021.808161.
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The mechanical analysis of complex rock mass is a difficult problem, which often occurs in scientific research and practical engineering. Many achievements have been made in the study of rock mass composite problems by composite material micromechanics method, but it has not been well summarized so far. This paper summarizes in detail the research status of complex rock mass problems by composite material micromechanics method at home and abroad, including the application of the Eshelby equivalent inclusion theory and self-consistent model in rock mass composite problems, and the application of the homogenization method in jointed rock mass and other rock mass composite problems such as anchored rock mass, layered rock mass, and salt rock mass with impurities. It is proposed that the structural similarity and mechanical analysis similarity should be satisfied when the composite material micromechanics method is used to study the complex rock mass. Finally, the problems that need to be further studied are put forward. The research results provide a valuable reference for the study of complex rock mass by the composite material micromechanics method.
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Zhang, Mengqi, and Zhiqiang Yan. "Effects of Near-surface Composites on Frictional Rolling Contact Solved by a Semi-analytical Model." Journal of Tribology, September 2, 2021, 1–23. http://dx.doi.org/10.1115/1.4052330.
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Abstract A semi-analytical model (SAM) to tackle the steady-state elastic frictional rolling contact problem involving composites is presented. Specifically, the frictional rolling contact is categorized into two subtypes, namely normal and tangential problems, and the conjugate gradient method (CGM) is used to figure out the normal pressure and tangential traction. In SAM, the equivalent inclusion method (EIM) is applied to analyze the influence of composites on the matrix, and the displacement disturbance resulting from such composites is added to the total surface displacement, which implements the coupling between surface contact and composites. The accuracy of the proposed model is verified by the finite element model. The effects of composites on the frictional rolling contact behavior are investigated. The results indicate that Young's modulus, as well as the size and location of the composites, are correlated with the distributions of tangential traction, subsurface stresses and the sizes of stick and sliding zones.
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Huang, Yezeng, Peng Yan, Junbo Wang, Leiting Dong, and Satya N. Atluri. "Eshelby tensors and overall properties of nano-composites considering both interface stretching and bending effects." Journal of Micromechanics and Molecular Physics, January 28, 2022, 1–11. http://dx.doi.org/10.1142/s2424913021420091.
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In this study, analytical micromechanical models are developed for nanocomposites with both interface stretching and bending effects. First, the interior and exterior Eshelby tensors for a spherical nano-inclusion, with an interface defined by the Steigmann–Ogden (S–O) model, subjected to an arbitrary uniform eigenstrain are derived. Correspondingly, the stress/strain concentration tensors for a spherical nano-inhomogeneity subjected to arbitrary uniform far-field stress/strain loadings are also derived. Using the obtained concentration tensors, the effective bulk and shear moduli are derived by employing the dilute approximation and the Mori–Tanaka method, respectively, which can be used for both nano-composites and nano-porous materials. An equivalent interface curvature parameter reflecting the influence of the interface bending resistance is found, which can significantly simplify the complex expressions of the effective properties. In addition to size-dependency, the closed form expressions show that the effective bulk modulus is invariant to interface bending resistance parameters, in contrast to the effective shear modulus. We also put forward a characteristic interface curvature parameter, near which the effective shear modulus is affected significantly. Numerical results show that the effective shear moduli of nano-composites and nano-porous materials can be greatly improved by an appropriate surface modification. Finally, the derived effective modulus with the S–O interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.
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Serre, Rémy, Carole Nadot-Martin, and Philippe Bocher. "Equivalent Inclusion Method (EIM) for isotropic and anisotropic spatially oriented spheroidal inhomogeneities: A unified calculation module validated via comparisons to Finite Element (FE) simulations." Mechanics of Materials, November 2024, 105194. http://dx.doi.org/10.1016/j.mechmat.2024.105194.
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Cetraro, Marek, Walter Lacarbonara, and Giovanni Formica. "Nonlinear Dynamic Response of Carbon Nanotube Nanocomposite Microbeams." Journal of Computational and Nonlinear Dynamics 12, no. 3 (December 5, 2016). http://dx.doi.org/10.1115/1.4034736.
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The nonlinear dynamic response of nanocomposite microcantilevers is investigated. The microbeams are made of a polymeric hosting matrix (e.g., epoxy, polyether ether ketone (PEEK), and polycarbonate) reinforced by longitudinally aligned carbon nanotubes (CNTs). The 3D transversely isotropic elastic constitutive equations for the nanocomposite material are based on the equivalent inclusion theory of Eshelby and the Mori–Tanaka homogenization approach. The beam-generalized stress resultants, obtained in accordance with the Saint-Venant principle, are expressed in terms of the generalized strains making use of the equivalent constitutive laws. These equations depend on both the hosting matrix and CNTs elastic properties as well as on the CNTs volume fraction, geometry, and orientation. The description of the geometry of deformation and the balance equations for the microbeams are based on the geometrically exact Euler–Bernoulli beam theory specialized to incorporate the additional inextensibility constraint due to the relevant boundary conditions of microcantilevers. The obtained equations of motion are discretized via the Galerkin method retaining an arbitrary number of eigenfunctions. A path following algorithm is then employed to obtain the nonlinear frequency response for different excitation levels and for increasing volume fractions of carbon nanotubes. The fold lines delimiting the multistability regions of the frequency responses are also discussed. The volume fraction is shown to play a key role in shifting the linear frequencies of the beam flexural modes to higher values. The CNT volume fraction further shifts the fold lines to higher excitation amplitudes, while it does not affect the backbones of the modes (i.e., oscillation frequency–amplitude curves).
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Malekmotiei, Leila, Farzam Farahmand, Hossein M. Shodja, and Aref Samadi-Dooki. "An Analytical Approach to Study the Intraoperative Fractures of Femoral Shaft During Total Hip Arthroplasty." Journal of Biomechanical Engineering 135, no. 4 (April 1, 2013). http://dx.doi.org/10.1115/1.4023699.
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An analytical approach which is popular in micromechanical studies has been extended to the solution for the interference fit problem of the femoral stem in cementless total hip arthroplasty (THA). The multiple inhomogeneity problem of THA in transverse plane, including an elliptical stem, a cortical wall, and a cancellous layer interface, was formulated using the equivalent inclusion method (EIM) to obtain the induced interference elastic fields. Results indicated a maximum interference fit of about 210 μm before bone fracture, predicted based on the Drucker–Prager criterion for a partially reamed section. The cancellous layer had a significant effect on reducing the hoop stresses in the cortical wall; the maximum press fit increased to as high as 480 μm for a 2 mm thick cancellous. The increase of the thickness and the mechanical quality, i.e., stiffness and strength, of the cortical wall also increased the maximum interference fit before fracture significantly. No considerable effect was found for the implant material on the maximum allowable interference fit. It was concluded that while larger interference fits could be adapted for younger patients, care must be taken when dealing with the elderly and those suffering from osteoporosis. A conservative reaming procedure is beneficial for such patients; however, in order to ensure sufficient primary stability without risking bone fracture, a preoperative analysis might be necessary.
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Liu, Jia, and Deluan Feng. "A multiscale finite element method for soil-rock mixture." Frontiers in Materials 10 (March 6, 2023). http://dx.doi.org/10.3389/fmats.2023.1116544.
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Soil-rock mixture is a complex multi-phase composite geotechnical material, and its strength is determined by the physical properties of constituent multi-phase materials and their coupling mechanical response between different phases of materials. Based on the Eshelby-Mori-Tanaka equivalent inclusion average stress principle, a theoretical model of multi-scale coupled shear strength of soil-rock mixture considering the interaction effect of rock block and soil is established, and the rotational freedom reflecting the microscopic motion details of rock block is introduced. Moreover, a multi-scale coupled constitutive relationship of soil-rock mixture is derived and compiled into a multi-scale finite element program. Based on the large-scale direct shear test of soil-rock mixture, the model parameters of the multi-scale finite element method are determined, and then the multi-scale finite element program is used to simulate and predict the cross-scale deformation process of the soil-rock mixture slope. The results show that the multi-scale finite element method can effectively describe the influence of the mechanism of the micro motion characteristics of the soil-rock mixture on the macro mechanical response, and can effectively overcome the pathological mesh-dependency of the classical finite element method; the rotation displacement of the rock block is mainly concentrated within the shear zone of the slope. The maximum rotational displacement of rock blocks inside the soil-rock mixture slope is 40.7°, and the rotational displacement of rock blocks outside the shear zone is about 0°. The physical mechanism of the cross scale evolution of the shear band of the soil-rock mixture slope is that: the rotation of the rock blocks weakens the strain transmission ability between the rock block and the matrix soil, thus forming the concentration and development of the plastic strain, and finally leading to the penetration of the shear bands of the slope and the overall sliding failure.