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Journal articles on the topic 'Equivalent materials'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

SHIROTANI, Takashi. "Progress of tissue equivalent materials." Journal of the Atomic Energy Society of Japan / Atomic Energy Society of Japan 28, no. 11 (1986): 1015–20. http://dx.doi.org/10.3327/jaesj.28.1015.

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2

Chialina, Silvano, Matteo Cicuttin, Lorenzo Codecasa, Giovanni Solari, Ruben Specogna, and Francesco Trevisan. "Modeling of Anechoic Chambers With Equivalent Materials and Equivalent Sources." IEEE Transactions on Electromagnetic Compatibility 58, no. 4 (August 2016): 956–63. http://dx.doi.org/10.1109/temc.2016.2547327.

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3

Schoenfeld, Andreas A., Dietrich Harder, Björn Poppe, and Ndimofor Chofor. "Water equivalent phantom materials for192Ir brachytherapy." Physics in Medicine and Biology 60, no. 24 (November 18, 2015): 9403–20. http://dx.doi.org/10.1088/0031-9155/60/24/9403.

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4

Elayyan, H. S. B., and S. N. Al-Refaie. "Equivalent network characterization for dielectric materials." Journal of Materials Science 31, no. 5 (March 1996): 1199–204. http://dx.doi.org/10.1007/bf00353098.

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5

Odegard, G. "Equivalent-continuum modeling of nano-structured materials." Composites Science and Technology 62, no. 14 (November 2002): 1869–80. http://dx.doi.org/10.1016/s0266-3538(02)00113-6.

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6

Al-Refaie, S. N., and H. S. B. Elayyan. "The a.c. equivalent circuit of dielectric materials." Journal of Materials Science 28, no. 8 (January 1, 1993): 2233–37. http://dx.doi.org/10.1007/bf00367589.

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7

Hagmann, M. J., R. L. Levin, L. Calloway, A. J. Osborn, and K. R. Foster. "Muscle-equivalent phantom materials for 10-100 MHz." IEEE Transactions on Microwave Theory and Techniques 40, no. 4 (April 1992): 760–62. http://dx.doi.org/10.1109/22.127527.

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8

Pilon, Dominic, and Raymond Panneton. "An equivalent solid (u) formulation for poroelastic materials." Journal of the Acoustical Society of America 111, no. 5 (2002): 2404. http://dx.doi.org/10.1121/1.4778190.

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9

Nicolet, A., F. Zolla, Y. Ould Agha, and S. Guenneau. "Geometrical transformations and equivalent materials in computational electromagnetism." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 27, no. 4 (July 11, 2008): 806–19. http://dx.doi.org/10.1108/03321640810878216.

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PurposeThis paper aims to review various techniques used in computational electromagnetism such as the treatment of open problems, helicoidal geometries and the design of arbitrarily shaped invisibility cloaks. This seemingly heterogeneous list is unified by the concept of geometrical transformation that leads to equivalent materials. The practical set‐up is conveniently effected via the finite element method.Design/methodology/approachThe change of coordinates is completely encapsulated in the material properties.FindingsThe most significant examples are the simple 2D treatment of helicoidal geometries and the design of arbitrarily shaped invisibility cloaks.Originality/valueThe paper provides a unifying point of view, bridging several techniques in electromagnetism.

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10

Smith, K. R., and D. F. Jackson. "New tissue-equivalent phantom materials for negative pions." Physics in Medicine and Biology 32, no. 2 (February 1, 1987): 237–41. http://dx.doi.org/10.1088/0031-9155/32/2/008.

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11

Kitis, G., C. Furetta, M. Prokic, and V. Prokic. "Kinetic parameters of some tissue equivalent thermoluminescence materials." Journal of Physics D: Applied Physics 33, no. 11 (May 16, 2000): 1252–62. http://dx.doi.org/10.1088/0022-3727/33/11/302.

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12

Glushikhin, F. P., M. F. Shklyarskii, and M. S. Zlotnikov. "Modeling rheologic processes in rocks with equivalent materials." Soviet Mining Science 22, no. 1 (January 1986): 71–75. http://dx.doi.org/10.1007/bf02504117.

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13

Zhou, Zhen Yu, and Qi Wen Xue. "Research on Homogenization of Composite Materials." Advanced Materials Research 663 (February 2013): 426–30. http://dx.doi.org/10.4028/www.scientific.net/amr.663.426.

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A numerical model is given to identify equivalent parameters of composite materials, using BP neural network algorithm. Taking Filament-wound composite pressure vessels as the research object, finite element models are first constructed .Getting node displacements as network training samples, the mechanical parameters as output information of network for effective training, the equivalent material parameters can be obtained. The satisfactory numerical validation is given and results show that the proposed method can identify the equivalent modulus and the equivalent Poisson’s ratio of the Filament-wound composite pressure vessels with precision. The computational efficiency is improved with BP neural network.

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14

Yu, Chen, Wen Yu-Mei, and Li Ping. "Equivalent circuit with complex physical constants and equivalent-parameters-expressed dissipation factors of piezoelectric materials." Chinese Physics 15, no. 6 (May 31, 2006): 1356–63. http://dx.doi.org/10.1088/1009-1963/15/6/038.

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15

Poletti, M. E., and O. D. Gonçalves. "Scattering investigation on the suitability of hydrophilic materials as breast-equivalent materials." Radiation Physics and Chemistry 71, no. 3-4 (October 2004): 973–74. http://dx.doi.org/10.1016/j.radphyschem.2004.05.006.

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16

Tello, V. M., R. C. Tailor, and W. F. Hanson. "How water equivalent are water-equivalent solid materials for output calibration of photon and electron beams?" Medical Physics 22, no. 7 (July 1995): 1177–89. http://dx.doi.org/10.1118/1.597613.

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17

Nissen, Shawn L., Richard W. Harris, Ron W. Channell, Brooke Conklin, Misty Kim, and Lena Wong. "The development of psychometrically equivalent Cantonese speech audiometry materials." International Journal of Audiology 50, no. 3 (February 14, 2011): 191–201. http://dx.doi.org/10.3109/14992027.2010.542491.

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18

Alva-Sánchez, H., C. Quintana-Bautista, A. Martínez-Dávalos, M. A. Ávila-Rodríguez, and M. Rodríguez-Villafuerte. "Positron range in tissue-equivalent materials: experimental microPET studies." Physics in Medicine and Biology 61, no. 17 (August 5, 2016): 6307–21. http://dx.doi.org/10.1088/0031-9155/61/17/6307.

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19

Cieszko, Mieczyslaw, Radoslaw Drelich, and Michal Pakula. "Acoustic wave propagation in equivalent fluid macroscopically inhomogeneous materials." Journal of the Acoustical Society of America 132, no. 5 (November 2012): 2970–77. http://dx.doi.org/10.1121/1.4756949.

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20

Soderkvist, J. "Electric equivalent circuit for flexural vibrations in piezoelectric materials." IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 37, no. 6 (November 1990): 577–86. http://dx.doi.org/10.1109/58.63116.

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21

TANIR, Ayşe Güneş, Fatma Serap KETENCİ, and Mustafa Hicabi BÖLÜKDEMİR. "Usage of attenuation coefficients of some tissue-equivalent materials." TURKISH JOURNAL OF PHYSICS 39 (2015): 69–74. http://dx.doi.org/10.3906/fiz-1406-10.

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22

Holloway, C. L., M. S. Sarto, and M. Johansson. "Analyzing Carbon-Fiber Composite Materials With Equivalent-Layer Models." IEEE Transactions on Electromagnetic Compatibility 47, no. 4 (November 2005): 833–44. http://dx.doi.org/10.1109/temc.2005.854101.

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23

Li, Lang, Mingyang Wang, Pengxian Fan, Haiming Jiang, Yihao Cheng, and Derong Wang. "Strain Rockbursts Simulated by Low-Strength Brittle Equivalent Materials." Advances in Materials Science and Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/5341904.

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This paper presents experimental study on rockbursts that occur in deep underground excavations. To begin with, the boundary conditions for excavation in deep underground engineering were analysed and elastic adaptive boundary is an effective way to minimize the boundary effect of geomechanical model test. Then, in order to simulate an elastic adaptive loading boundary, Belleville springs were used to establish this loading boundary. With the aforementioned experimental set-ups and fabrication of similarity models for test, the phenomena of strain mode rockbursts were satisfactorily reproduced in laboratory. The internal stress, strain, and convergences of the openings of the model were instrumented by subtly preembedded sensors and transducers. Test results showed that, with an initial state of high stress from both upper layers’ gravitational effects and in situ stress due to tectonic movements, the excavation brings a dramatic rise in the hoop stress and sharp drop in radial stress, which leads to the splitting failure of rock mass. Finally a rockburst occurred associated with the release of strain energy stored in highly stressed rock mass. In addition, the failure of the surrounding rock demonstrated an obvious hysteresis effect which supplies valuable guide and reference for tunnel support. Not only do these results provide a basis for further comprehensive experiments, but also the data can offer assisting aids for further theoretical study of rockbursts.

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24

Qin, Zhuang, Yaosheng Hu, Yu Ma, Wei Lin, Xianping Luo, Wenhui Zhao, Weimin Sun, et al. "Water-equivalent fiber radiation dosimeter with two scintillating materials." Biomedical Optics Express 7, no. 12 (November 3, 2016): 4919. http://dx.doi.org/10.1364/boe.7.004919.

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25

Solymar, L. "An equivalent circuit for spatial variations in photorefractive materials." Optics Communications 63, no. 6 (September 1987): 413–14. http://dx.doi.org/10.1016/0030-4018(87)90335-x.

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26

Messner, Mark C., Matthew I. Barham, Mukul Kumar, and Nathan R. Barton. "Wave propagation in equivalent continuums representing truss lattice materials." International Journal of Solids and Structures 73-74 (November 2015): 55–66. http://dx.doi.org/10.1016/j.ijsolstr.2015.07.023.

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27

Finke, E., G. Geske, H. Greupner, K. Groche, and R. Rittwag. "Development of solid water-equivalent radioactive certified reference materials." International Journal of Radiation Applications and Instrumentation. Part A. Applied Radiation and Isotopes 42, no. 6 (January 1991): 587–89. http://dx.doi.org/10.1016/0883-2889(91)90168-z.

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28

Pyshkina, M. D., A. V. Vasilyev, A. A. Ekidin, E. I. Nazarov, M. A. Romanova, V. I. Gurinovich, D. I. Komar, and V. A. Kozhemyakin. "Neutron dosimetry at workplaces of JC “Institute of Nuclear Materials”." Radiatsionnaya Gygiena = Radiation Hygiene 14, no. 2 (June 27, 2021): 89–99. http://dx.doi.org/10.21514/1998-426x-2021-14-2-89-99.

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If the neutron fields at personnel workplaces differ from the neutron fields in which individual dosimeters are verified, there is a possibility of additional errors in the assessment of such dosimetric quantities as ambient dose equivalent, individual dose equivalent or effective dose. To take into account the energy distribution of the neutron radiation flux density and the geometry of the irradiation of workers, it is necessary to study the characteristics of the fields of neutron radiation at the workplaces of the personnel. In order to obtain conditionally true levels of personnel exposure to neutron radiation at nuclear facilities, studies of the energy and angular distribution of the neutron radiation flux density were carried out at the workplaces of the Institute of Reactor Materials JSC, Zarechny. The energy distribution of the neutron radiation flux density was obtained using an MKS-AT1117M multi-sphere dosimeter-radiometer with a BDKN-06 detection unit and a set of polyethylene spheres-moderators. The angular distribution of the neutron radiation flux density was estimated from the results of measurements of the accumulated dose of neutron radiation by individual thermoluminescent dosimeters placed on four vertical planes of a heterogeneous human phantom. The results of measurements of the energy and angular distribution of the neutron radiation flux density made it possible to estimate the conditionally true values of the ambient and individual dose equivalents. The calculated conventionally true values differ from the measured values from 0.7 to 8.9 times for the ambient dose equivalent and from 6 to 50 times for the individual dose equivalent. In order to reduce the error in assessing the effective dose of personnel using personal dosimeters, correction factors were determined. For different workplaces and types of personal dosimeters, correction factors are in the range of values from 0.02 to 0.16.

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29

Ahmadi, G., and I. I. Orabi. "Equivalence of single-term Wiener-Hermite and equivalent linearization techniques." Journal of Sound and Vibration 118, no. 2 (October 1987): 307–11. http://dx.doi.org/10.1016/0022-460x(87)90528-1.

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30

Labidi, Mondher, and Fethi Choubani. "Electrical equivalent model of meta-materials based on circular SRR." International Journal of Microwave and Wireless Technologies 8, no. 6 (April 20, 2015): 909–13. http://dx.doi.org/10.1017/s1759078715000604.

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This work focuses on the circuit modeling and full-wave analysis behavior of circular split ring resonator (SRR). We investigate an equivalent circuit model that allows calculating the resonant frequency from the geometric parameters. Equivalent LC parameters of inductance and capacitance are derived using conformal mapping and constitutive equations. Lumped element equivalent circuit models of resonator are investigated highlighting the behavior of inductance and capacitance. In order to validate our proposed analytical LC model, a comparison of theoretical and simulation results has been performed and a good agreement is achieved with a maximum error of 4.23% and a minimum error of 0.52%, which supports the validity of the equivalent model.

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31

Kamm, Jochen, Michael Becken, and Rafael Abreu. "Electromagnetic modelling with topography on regular grids with equivalent materials." Geophysical Journal International 220, no. 3 (December 13, 2019): 2021–38. http://dx.doi.org/10.1093/gji/ggz563.

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SUMMARY Maxwell’s equations are valid regardless of the choice of the coordinate system. By this property a change of coordinates can be equivalently expressed as a change of the material parameters. This idea opens a new approach to the problem of accurate electromagnetic modelling in the vicinity of steep topography or bathymetry. Via a change of coordinates, any earth model with complicated layer interfaces can be represented by an equivalent model where those interfaces are flat, but with its materials correspondingly altered. This new model could then be discretized on a regular mesh and fields could be computed by an appropriate finite difference or integral equation code. Unfortunately, this is not straightforward because both the new electric and magnetic materials are fully anisotropic. By instead applying a finite element secondary field approach to the equivalent model, we can completely account for the topography interface in the planar layered background model. The only modification required to existing finite element formulations is a slightly more complicated right-hand side of the linear system of equations, whereas the system matrix is unchanged in any coordinate system. In a numerical modelling experiment we confirm that our technique gives increased accuracy when compared with a recently published technique for dealing with topography in a secondary field formulation for the case of a magnetotelluric source field. In turn, in the vicinity of conductivity anomalies, accuracy can also be negatively affected.

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32

Yohannes, Indra, Daniel Kolditz, and Willi A. Kalender. "Semiempirical analysis of materials' elemental composition to formulate tissue-equivalent materials: a preliminary study." Physics in Medicine and Biology 56, no. 10 (April 13, 2011): 2963–77. http://dx.doi.org/10.1088/0031-9155/56/10/005.

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33

Nascimento, Bruna C., Audrew Frimaio, Ramon M. M. Barrio, Ana C. A. Sirico, and Paulo R. Costa. "Comparative analysis of the transmission properties of tissue equivalent materials." Radiation Physics and Chemistry 167 (February 2020): 108300. http://dx.doi.org/10.1016/j.radphyschem.2019.04.050.

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34

ARAKI, Shigetoshi, Hironori YAMASHITA, and Aki MINAMI. "Study on Equivalent Expressions for Composite Materials Containing Incompressible Constituent." Transactions of the Japan Society of Mechanical Engineers Series A 71, no. 701 (2005): 157–64. http://dx.doi.org/10.1299/kikaia.71.157.

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35

HIRAYAMA, Hideo, and Shun-ichi TANAKA. "Investigation of 1cm dose equivalent for photons behind shielding materials." Journal of the Atomic Energy Society of Japan / Atomic Energy Society of Japan 31, no. 7 (1989): 841–51. http://dx.doi.org/10.3327/jaesj.31.841.

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36

Ding, Kun, Yuan Shen, Jack Ng, and Lei Zhou. "Equivalent-medium theory for metamaterials made by planar electronic materials." EPL (Europhysics Letters) 102, no. 2 (April 1, 2013): 28005. http://dx.doi.org/10.1209/0295-5075/102/28005.

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37

Bero, M. A., and I. Abukassem. "Detection of ultraviolet radiation using tissue equivalent radiochromic gel materials." Journal of Physics: Conference Series 164 (May 1, 2009): 012064. http://dx.doi.org/10.1088/1742-6596/164/1/012064.

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38

de Vera, Pablo, Isabel Abril, and Rafael Garcia-Molina. "Water equivalent properties of materials commonly used in proton dosimetry." Applied Radiation and Isotopes 83 (January 2014): 122–27. http://dx.doi.org/10.1016/j.apradiso.2013.01.023.

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39

Vignjevic, Rade, Nenad Djordjevic, Tom De Vuyst, and Simone Gemkow. "Modelling of strain softening materials based on equivalent damage force." Computer Methods in Applied Mechanics and Engineering 335 (June 2018): 52–68. http://dx.doi.org/10.1016/j.cma.2018.01.049.

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40

Zheng, Qing, and Hualin Fan. "Equivalent continuum method of plane-stress dominated plate-lattice materials." Thin-Walled Structures 164 (July 2021): 107865. http://dx.doi.org/10.1016/j.tws.2021.107865.

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41

Lin, Y. K., and G. Q. Cai. "Equivalent Stochastic Systems." Journal of Applied Mechanics 55, no. 4 (December 1, 1988): 918–22. http://dx.doi.org/10.1115/1.3173742.

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Equivalent stochastic systems are defined as randomly excited dynamical systems whose response vectors in the state space share the same probability distribution. In this paper, the random excitations are restricted to Gaussian white noises; thus, the system responses are Markov vectors, and their probability densities are governed by the associated Fokker-Planck equations. When the associated Fokker-Planck equations are identical, the equivalent stochastic systems must share both the stationary probability distribution and the transient nonstationary probability distribution under identical initial conditions. Such systems are said to be stochastically equivalent in the strict (or strong) sense. A wider class, referred to as the class of equivalent stochastic systems in the wide (or weak) sense, also includes those sharing only the stationary probability distribution but having different Fokker-Planck equations. Given a stochastic system with a known probability distribution, procedures are developed to identify and construct equivalent stochastic systems, both in the strict and in the wide sense.

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42

Won Kim, Jae, Jae Ung Cho, Chan Ki Cho, and Jin Oh Kim. "A study on damage to mechanical seat cushion made from different materials of extension frame." International Journal of Engineering & Technology 7, no. 3.3 (June 8, 2018): 315. http://dx.doi.org/10.14419/ijet.v7i2.33.14176.

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Background/Objectives: : Automotive seat is a very important component to prevent accidents by reducing passenger’s tiredness, thus, this study worked on analyzing damage with different materials of extension frames of mechanical seat cushions.Methods/Statistical analysis: In this study, we performed an experiment on cushion extension frames by splitting it into two parts. We studied about the damage prediction of slave body for each material property of ABS, PP, PLA, and PA6.6. For analyzing the condition, we assigned the side part of the master body for fixed support, and we progressed on analysis by applying with 690N on the entire part of the slave body.Findings: This research worked on the study of damage to different materials of extension frames of seat cushions. After confirming the stress equivalence of the entire model for each material, PP showed the highest equivalent stress of 180.88MPa, and ABS showed the lowest equivalent stress of 151.73MPa. Overall, we could see that in the order of ABS, PA6.6, PLA, PP have a higher tendency to be broken. In addition, when confirming equivalent stress of master body depending on materials of slave body, PA6.6 showed the highest equivalent stress of 166.3MPa, and ABS showed the lowest equivalent stress of 124.06MPa. Overall, we could see that in the order of ABS, PP, PLA and PP6.6 have a higher tendency to be broken. In comparing shear stress on the gear part, which has the highest tendency to be broken in among the entire model, depending on the material of the slave body, PLA showed the greatest shear stress of 88.945MPa, and ABS showed the lowest shear stress of 69.766MPa.Improvements/Applications: This study worked for the improvements and applications of cushion extension frames as the securement of material by investigating these factors.

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43

Hua, Guang Jun, Yong Xie, Peng Tian, and Ming Wang. "Research on Equivalent Cushioning Property and Design Idea of Overlay Combination Cushion." Applied Mechanics and Materials 200 (October 2012): 22–26. http://dx.doi.org/10.4028/www.scientific.net/amm.200.22.

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Based on the research on application and design method of combination cushion, the equivalent cushioning coefficient formula of overlay combination cushion made by different cushioning material were derived, and the relevant cushion design method was proposed. The work provides a theory basis for the combination cushion design. The equivalent cushioning coefficient formula can be used conveniently as it is expressed by the material’s property parameters. The research can help to play the advantages of different materials, promote the integrated use of different materials, and carry out economic packaging, green packaging ultimately.

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44

Zypman, F. R., and J. Ferrante. "Gradient equivalent crystal theory." Journal of Physics: Condensed Matter 18, no. 26 (June 19, 2006): 6095–99. http://dx.doi.org/10.1088/0953-8984/18/26/027.

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45

Lai, Jin Xing, and Qian Zhang. "Analytical Method to Equivalent Modulus of Entrainment Multiphase Composite." Applied Mechanics and Materials 52-54 (March 2011): 1757–61. http://dx.doi.org/10.4028/www.scientific.net/amm.52-54.1757.

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Energy equivalent modulus medium of entrainment multiphase composite body is one of main methods, Those methods study frangible materials damage in micromechanics. Through studying the physical and mechanical process of microstructure varity, we can introduce some kind averaging method to find the material’s macroscopic property. It has not been studied as yet that we study entrainment composite body’s damage trough introducing continous field variable of every exponent tensor from macrophenomenology angle. This paper regards entrainment multiphase composite body as the micropolar medium of introducing inner structure. It provides analytic formula to describe equivalent modus of entrainment multiphase composite body damage, through the stress in micropolar theory of elasticity,couple-stresses tensor and Helmhoetz degrees of freedom density.

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46

Koutsenko, Timur, Nikolay Shelihov, and Svetlana Kutsenko. "Calculation of the durability of sealing and awning materials." E3S Web of Conferences 274 (2021): 04001. http://dx.doi.org/10.1051/e3sconf/202127404001.

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The article discusses the hypotheses for determining the equivalent laboratory modes for assessing the durability of sealing and awning materials, and evaluates the accuracy of the proposed method. Qualitative research of operational factors influence (UV, temperature) on sealing and awning materials durability was conducted. Purpose of the study: a method for predicting the durability of sealing and awning materials. Methods: Methods for fast assessment of durability and methods of equivalent factors. Results: Based on the obtained regularities of the behavior of sealing and awning materials under conditions of repeated loading and ultraviolet radiation, as well as the accepted hypotheses about the summation of damage and irreversibility of the destruction process, a laboratory test mode was determined that was equivalent in terms of the level of introduced destruction to the operating mode, including the action of multiple loads and ultraviolet radiation. Based on the equivalent accelerated test mode and the characteristics of the operating mode of loading and irradiation, a method for assessing the durability of sealing and awning materials is proposed.

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47

Pandey, Lakshman, O. M. Parkash, Rajesh K. Katare, and Devendra Kumar. "Equivalent circuit models for electronic ceramics." Bulletin of Materials Science 18, no. 5 (September 1995): 563–76. http://dx.doi.org/10.1007/bf02744842.

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48

Kolyada, L. G., E. V. Tarasyuk, and S. A. Krylova. "Modern Packaging Materials for Steel Products." Solid State Phenomena 265 (September 2017): 1040–47. http://dx.doi.org/10.4028/www.scientific.net/ssp.265.1040.

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The paper investigates structural, physical, deformation, strength, barrier, and corrosion resistance properties of domestic packaging papers in comparison with Fislage's foreign equivalent. It studies packaging paper protection of cold-rolled steel under different relative humidity, periodic humidity concentration, and available chloride ion conditions. The corrosion resistance properties of BLIK paper with UNI inhibitor are proven to match those of the foreign equivalent previously used. The EuroBum's packaging paper has poorer protective properties possibly due to the lower corrosion inhibitor content. The competitive recovery of domestic combined packaging materials for metal products can be improved by changing their production processes: increasing inhibitor content, creeping ratio of the paper base and reinforcement in order to obtain better deformation and strength properties.

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49

Nakai, Hiroaki, Hiromasa Tomioka, Tetsusei Kurashiki, and Masaru Zako. "A Proposal of Calculation Method for Equivalent Property of Composite Materials." Key Engineering Materials 334-335 (March 2007): 241–44. http://dx.doi.org/10.4028/www.scientific.net/kem.334-335.241.

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To predict the mechanical properties of composite materials by using computer is complicated, because it is difficult to model directly by ordinary FEM. A calculation method by using the mesh superposition method and periodic boundary condition has been proposed in order to obtain the equivalent mechanical properties of composite materials easily. The numerical results by proposed method have shown good agreement with ones by the traditional procedure. The proposed method is efficient for the materials with complicated structure like woven fabric composites etc.

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50

Qiulin, Fan, Xiao Xingcheng, Hu Xingfang, and Guo Jingkun. "Calculating method of the equivalent thermal conductivity of functionally gradient materials." Materials Science and Engineering: A 261, no. 1-2 (March 1999): 84–88. http://dx.doi.org/10.1016/s0921-5093(98)01052-1.

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