How to cite this paper
Patiño, I & Isaza, C. (2022). Mori-Tanaka-based statistical methodology to compute the effective Young modulus of polymer matrix nano-composites considering the experimental quantification of nanotubes dispersion and alignment degree.Engineering Solid Mechanics, 10(1), 79-98.
Refrences
Ahmed, S., & Jones, F. (1990). A review of particulate reinforcement theories for polymer composites. Journal of Materials Science, 25(12), 4933-4942.
Aragh, B. S., Barati, A. N., & Hedayati, H. (2012). Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels. Composites Part B: Engineering, 43(4), 1943-1954.
Armbrister, C. E., Okoli, O. I., & Shanbhag, S. (2015). Micromechanics predictions for two-phased nanocomposites and three-phased multiscale composites: A review. Journal of Reinforced Plastics and Composites, 34(8), 605-623.
Barati, M. R., & Zenkour, A. M. (2019). Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions. Mechanics of Advanced Materials and Structures, 26(18), 1580-1588.
Brodnyan, J. G. (1959). The concentration dependence of the Newtonian viscosity of prolate ellipsoids. Transactions of the Society of Rheology, 3(1), 61-68.
Coleman, J. N., Khan, U., Blau, W. J., & Gun’ko, Y. K. (2006). Small but strong: a review of the mechanical properties of carbon nanotube–polymer composites. Carbon, 44(9), 1624-1652.
Cox, H. (1952). The elasticity and strength of paper and other fibrous materials. British Journal of Applied Physics, 3(3), 72.
Chen, Z., Wu, Y., Yang, Y., Li, J., Xie, B., Li, X., . . . Zhou, Q. (2018). Multilayered carbon nanotube yarn based optoacoustic transducer with high energy conversion efficiency for ultrasound application. Nano Energy, 46, 314-321.
Choi, H., Shin, J., Min, B., Park, J., & Bae, D. (2009). Reinforcing effects of carbon nanotubes in structural aluminum matrix nanocomposites. Journal of Materials Research, 24(8), 2610-2616.
Christensen, R., & Waals, F. (1972). Effective stiffness of randomly oriented fibre composites. Journal of Composite Materials, 6(4), 518-532.
De Villoria, R. G., & Miravete, A. (2007). Mechanical model to evaluate the effect of the dispersion in nanocomposites. Acta Materialia, 55(9), 3025-3031.
Dervishi, E., Li, Z., Xu, Y., Saini, V., Biris, A. R., Lupu, D., & Biris, A. S. (2009). Carbon nanotubes: synthesis, properties, and applications. Particulate Science and Technology, 27(2), 107-125.
Desai, A., & Haque, M. (2005). Mechanics of the interface for carbon nanotube–polymer composites. Thin-walled structures, 43(11), 1787-1803.
Diez-Pascual, A., Naffakh, M., Gómez, M., Marco, C., Ellis, G., Gonzalez-Dominguez, J., . . . Simard, B. (2009a). The influence of a compatibilizer on the thermal and dynamic mechanical properties of PEEK/carbon nanotube composites. Nanotechnology, 20(31), 315707.
Díez-Pascual, A. M., Naffakh, M., Gómez, M. A., Marco, C., Ellis, G., Martínez, M. T., . . . Simard, B. (2009b). Development and characterization of PEEK/carbon nanotube composites. Carbon, 47(13), 3079-3090.
Dunn, M., & Ledbetter, H. (1995). Elastic moduli of composites reinforced by multiphase particles.
Ebrahimi, F., & Dabbagh, A. (2019). A comprehensive review on modeling of nanocomposite materials and structures. Journal of Computational Applied Mechanics, 50(1), 197-209.
Enqvist, E., Ramanenka, D., Marques, P. A., Gracio, J., & Emami, N. (2016). The effect of ball milling time and rotational speed on ultra high molecular weight polyethylene reinforced with multiwalled carbon nanotubes. Polymer Composites, 37(4), 1128-1136.
Feng, W., Bai, X., Lian, Y., Liang, J., Wang, X., & Yoshino, K. (2003). Well-aligned polyaniline/carbon-nanotube composite films grown by in-situ aniline polymerization. Carbon, 41(8), 1551-1557.
Gao, J., He, Y., & Gong, X. (2018). Effect of electric field induced alignment and dispersion of functionalized carbon nanotubes on properties of natural rubber. Results in Physics, 9, 493-499.
Gao, X.-L., & Li, K. (2005). A shear-lag model for carbon nanotube-reinforced polymer composites. International Journal of Solids and Structures, 42(5-6), 1649-1667.
García-Macías, E., Rodríguez-Tembleque, L., Castro-Triguero, R., & Sáez, A. (2017). Eshelby-Mori-Tanaka approach for post-buckling analysis of axially compressed functionally graded CNT/polymer composite cylindrical panels. Composites Part B: Engineering, 128, 208-224.
Ghorbanpour Arani, A., Baba Akbar Zarei, H., & Haghparast, E. (2016). Application of Halpin-Tsai Method in Modelling and Size-dependent Vibration Analysis of CNTs/fiber/polymer Composite Microplates. Journal of Computational Applied Mechanics, 47(1), 45-52.
Guo, J., Briggs, N., Crossley, S., & Grady, B. P. (2018). A new finding for carbon nanotubes in polymer blends: Reduction of nanotube breakage during melt mixing. Journal of Thermoplastic Composite Materials, 31(1), 110-118.
Halpin, J. (1969). Stiffness and expansion estimates for oriented short fiber composites. Journal of Composite Materials, 3(4), 732-734.
Halpin, J. C., & Kardos, J. (1976). The Halpin-Tsai equations: a review. Polymer Engineering and Science, 16(5), 344-352.
Hashin, Z. (1966). Viscoelastic fiber reinforced materials. AIAA journal, 4(8), 1411-1417.
Hashin, Z. (1983). Analysis of composite materials—a survey. Journal of Applied Mechanics, 50(3), 481-505.
Hashin, Z., & Rosen, B. W. (1964). The elastic moduli of fiber-reinforced materials.
Hashin, Z., & Shtrikman, S. (1963). A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids, 11(2), 127-140.
Hill, R. (1965). Theory of mechanical properties of fibre-strengthened materials—III. Self-consistent model. Journal of the Mechanics and Physics of Solids, 13(4), 189-198.
Hone, J., Llaguno, M., Biercuk, M., Johnson, A., Batlogg, B., Benes, Z., & Fischer, J. (2002). Thermal properties of carbon nanotubes and nanotube-based materials. Applied physics A, 74(3), 339-343.
Hu, H., Onyebueke, L., & Abatan, A. (2010). Characterizing and modeling mechanical properties of nanocomposites-review and evaluation. Journal of Minerals and Materials Characterization and Engineering, 9(04), 275.
Hu, Z., Arefin, M. R. H., Yan, X., & Fan, Q. H. (2014). Mechanical property characterization of carbon nanotube modified polymeric nanocomposites by computer modeling. Composites Part B: Engineering, 56, 100-108.
Huang, Z.-M., Zhang, Y.-Z., Kotaki, M., & Ramakrishna, S. (2003). A review on polymer nanofibers by electrospinning and their applications in nanocomposites. Composites Science and Technology, 63(15), 2223-2253.
Hui, C., & Shia, D. (1998). Simple formulae for the effective moduli of unidirectional aligned composites. Polymer Engineering & Science, 38(5), 774-782.
Huong, P. V., Cavagnat, R., Ajayan, P., & Stephan, O. (1995). Temperature-dependent vibrational spectra of carbon nanotubes. Physical review B, 51(15), 10048.
Hyer, M. W., & White, S. R. (2009). Stress analysis of fiber-reinforced composite materials: DEStech Publications, Inc.
Iijima, S. (1991). Helical microtubules of graphitic carbon. Nature, 354(6348), 56.
Isaza M, C. A., Herrera Ramírez, J., Ledezma Sillas, J., & Meza, J. (2018). Dispersion and alignment quantification of carbon nanotubes in a polyvinyl alcohol matrix. Journal of Composite Materials, 52(12), 1617-1626.
Kim, M., Okoli, O., Jack, D., Park, Y.-B., & Liang, Z. (2011). Characterisation and modelling of CNT–epoxy and CNT–fibre–epoxy composites. Plastics, Rubber and Composites, 40(10), 481-490.
Kumar, J. P., & Srinivas, J. (2018). Three phase composite cylinder assemblage model for analyzing the elastic behavior of MWCNT-reinforced polymers. Computers Materials and Continua, 54(1), 1-20.
Kundalwal, S. I. (2018). Review on micromechanics of nano‐and micro‐fiber reinforced composites. Polymer Composites, 39(12), 4243-4274.
Lin, J. H., Lin, Z. I., Pan, Y. J., Hsieh, C. T., Huang, C. L., & Lou, C. W. (2016). Thermoplastic polyvinyl alcohol/multiwalled carbon nanotube composites: preparation, mechanical properties, thermal properties, and electromagnetic shielding effectiveness. Journal of Applied Polymer Science, 133(21).
Lourie, O., & Wagner, H. (1998). Evaluation of Young's modulus of carbon nanotubes by micro-Raman spectroscopy. Journal of Materials Research, 13(9), 2418-2422.
Luo, Z., & Koo, J. (2007). Quantifying the dispersion of mixture microstructures. Journal of Microscopy, 225(2), 118-125.
Mallick, P. K. (2007). Fiber-reinforced composites: materials, manufacturing, and design: CRC press.
Martínez-Morlanes, M., Castell, P., Martínez-Nogués, V., Martinez, M., Alonso, P. J., & Puértolas, J. (2011). Effects of gamma-irradiation on UHMWPE/MWNT nanocomposites. Composites Science and Technology, 71(3), 282-288.
Mooney, M. (1951). The viscosity of a concentrated suspension of spherical particles. Journal of Colloid Science, 6(2), 162-170.
Mori, T., & Tanaka, K. (1973). Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21(5), 571-574.
Noor, N., Razak, J., Ismail, S., Mohamad, N., Tee, L., Munawar, R., & Junid, R. (2018). Review on Carbon Nanotube based Polymer Composites and Its Applications. Journal of Advanced Manufacturing Technology (JAMT), 12(1), 311-326.
Odegard, G. M., Gates, T., Wise, K., Park, C., & Siochi, E. (2003). Constitutive modeling of nanotube–reinforced polymer composites. Composites Science and Technology, 63(11), 1671-1687.
Pharr, G., & Oliver, W. (1992). Measurement of thin film mechanical properties using nanoindentation. Mrs Bulletin, 17(7), 28-33.
Qiu, Y., & Weng, G. (1990). On the application of Mori-Tanaka's theory involving transversely isotropic spheroidal inclusions. International Journal of Engineering Science, 28(11), 1121-1137.
Rafiee, M. A., Rafiee, J., Wang, Z., Song, H., Yu, Z.-Z., & Koratkar, N. (2009). Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano, 3(12), 3884-3890.
Rathi, A., & Kundalwal, S. I. (2020). Mechanical and fracture behavior of MWCNT/ZrO2/epoxy nanocomposite systems: Experimental and numerical study. Polymer Composites.
Reddy, J. N. (2003). Mechanics of laminated composite plates and shells: theory and analysis: CRC press.
Reuss, A. (1929). Berechnung der Flieggrenze yon Mischkristallen auf Grund der Plastizithtsbedingung fiir Einkristalle. Z. Angew. Math. Mech, 9.
Ruan, S., Gao, P., Yang, X. G., & Yu, T. (2003). Toughening high performance ultrahigh molecular weight polyethylene using multiwalled carbon nanotubes. Polymer, 44(19), 5643-5654.
Sadeghpour, E., Guo, Y., Chua, D., & Shim, V. P. (2020). A Modified Mori-Tanaka Approach Incorporating Filler-Matrix Interface Failure to Model Graphene/Polymer Nanocomposites. International Journal of Mechanical Sciences, 105699.
Schaufele, a., & Shimanouchi, T. (1967). Longitudinal acoustical vibrations of finite polymethylene chains. The Journal of Chemical Physics, 47(9), 3605-3610.
Seidel, G. D., & Lagoudas, D. C. (2006). Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites. Mechanics of Materials, 38(8-10), 884-907.
Shang, Y., Wu, X., Liu, Y., Jiang, Z., Wang, Z., Jiang, Z., & Zhang, H. (2019). Preparation of PEEK/MWCNTs composites with excellent mechanical and tribological properties. High Performance Polymers, 31(1), 43-50.
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Aragh, B. S., Barati, A. N., & Hedayati, H. (2012). Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels. Composites Part B: Engineering, 43(4), 1943-1954.
Armbrister, C. E., Okoli, O. I., & Shanbhag, S. (2015). Micromechanics predictions for two-phased nanocomposites and three-phased multiscale composites: A review. Journal of Reinforced Plastics and Composites, 34(8), 605-623.
Barati, M. R., & Zenkour, A. M. (2019). Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions. Mechanics of Advanced Materials and Structures, 26(18), 1580-1588.
Brodnyan, J. G. (1959). The concentration dependence of the Newtonian viscosity of prolate ellipsoids. Transactions of the Society of Rheology, 3(1), 61-68.
Coleman, J. N., Khan, U., Blau, W. J., & Gun’ko, Y. K. (2006). Small but strong: a review of the mechanical properties of carbon nanotube–polymer composites. Carbon, 44(9), 1624-1652.
Cox, H. (1952). The elasticity and strength of paper and other fibrous materials. British Journal of Applied Physics, 3(3), 72.
Chen, Z., Wu, Y., Yang, Y., Li, J., Xie, B., Li, X., . . . Zhou, Q. (2018). Multilayered carbon nanotube yarn based optoacoustic transducer with high energy conversion efficiency for ultrasound application. Nano Energy, 46, 314-321.
Choi, H., Shin, J., Min, B., Park, J., & Bae, D. (2009). Reinforcing effects of carbon nanotubes in structural aluminum matrix nanocomposites. Journal of Materials Research, 24(8), 2610-2616.
Christensen, R., & Waals, F. (1972). Effective stiffness of randomly oriented fibre composites. Journal of Composite Materials, 6(4), 518-532.
De Villoria, R. G., & Miravete, A. (2007). Mechanical model to evaluate the effect of the dispersion in nanocomposites. Acta Materialia, 55(9), 3025-3031.
Dervishi, E., Li, Z., Xu, Y., Saini, V., Biris, A. R., Lupu, D., & Biris, A. S. (2009). Carbon nanotubes: synthesis, properties, and applications. Particulate Science and Technology, 27(2), 107-125.
Desai, A., & Haque, M. (2005). Mechanics of the interface for carbon nanotube–polymer composites. Thin-walled structures, 43(11), 1787-1803.
Diez-Pascual, A., Naffakh, M., Gómez, M., Marco, C., Ellis, G., Gonzalez-Dominguez, J., . . . Simard, B. (2009a). The influence of a compatibilizer on the thermal and dynamic mechanical properties of PEEK/carbon nanotube composites. Nanotechnology, 20(31), 315707.
Díez-Pascual, A. M., Naffakh, M., Gómez, M. A., Marco, C., Ellis, G., Martínez, M. T., . . . Simard, B. (2009b). Development and characterization of PEEK/carbon nanotube composites. Carbon, 47(13), 3079-3090.
Dunn, M., & Ledbetter, H. (1995). Elastic moduli of composites reinforced by multiphase particles.
Ebrahimi, F., & Dabbagh, A. (2019). A comprehensive review on modeling of nanocomposite materials and structures. Journal of Computational Applied Mechanics, 50(1), 197-209.
Enqvist, E., Ramanenka, D., Marques, P. A., Gracio, J., & Emami, N. (2016). The effect of ball milling time and rotational speed on ultra high molecular weight polyethylene reinforced with multiwalled carbon nanotubes. Polymer Composites, 37(4), 1128-1136.
Feng, W., Bai, X., Lian, Y., Liang, J., Wang, X., & Yoshino, K. (2003). Well-aligned polyaniline/carbon-nanotube composite films grown by in-situ aniline polymerization. Carbon, 41(8), 1551-1557.
Gao, J., He, Y., & Gong, X. (2018). Effect of electric field induced alignment and dispersion of functionalized carbon nanotubes on properties of natural rubber. Results in Physics, 9, 493-499.
Gao, X.-L., & Li, K. (2005). A shear-lag model for carbon nanotube-reinforced polymer composites. International Journal of Solids and Structures, 42(5-6), 1649-1667.
García-Macías, E., Rodríguez-Tembleque, L., Castro-Triguero, R., & Sáez, A. (2017). Eshelby-Mori-Tanaka approach for post-buckling analysis of axially compressed functionally graded CNT/polymer composite cylindrical panels. Composites Part B: Engineering, 128, 208-224.
Ghorbanpour Arani, A., Baba Akbar Zarei, H., & Haghparast, E. (2016). Application of Halpin-Tsai Method in Modelling and Size-dependent Vibration Analysis of CNTs/fiber/polymer Composite Microplates. Journal of Computational Applied Mechanics, 47(1), 45-52.
Guo, J., Briggs, N., Crossley, S., & Grady, B. P. (2018). A new finding for carbon nanotubes in polymer blends: Reduction of nanotube breakage during melt mixing. Journal of Thermoplastic Composite Materials, 31(1), 110-118.
Halpin, J. (1969). Stiffness and expansion estimates for oriented short fiber composites. Journal of Composite Materials, 3(4), 732-734.
Halpin, J. C., & Kardos, J. (1976). The Halpin-Tsai equations: a review. Polymer Engineering and Science, 16(5), 344-352.
Hashin, Z. (1966). Viscoelastic fiber reinforced materials. AIAA journal, 4(8), 1411-1417.
Hashin, Z. (1983). Analysis of composite materials—a survey. Journal of Applied Mechanics, 50(3), 481-505.
Hashin, Z., & Rosen, B. W. (1964). The elastic moduli of fiber-reinforced materials.
Hashin, Z., & Shtrikman, S. (1963). A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids, 11(2), 127-140.
Hill, R. (1965). Theory of mechanical properties of fibre-strengthened materials—III. Self-consistent model. Journal of the Mechanics and Physics of Solids, 13(4), 189-198.
Hone, J., Llaguno, M., Biercuk, M., Johnson, A., Batlogg, B., Benes, Z., & Fischer, J. (2002). Thermal properties of carbon nanotubes and nanotube-based materials. Applied physics A, 74(3), 339-343.
Hu, H., Onyebueke, L., & Abatan, A. (2010). Characterizing and modeling mechanical properties of nanocomposites-review and evaluation. Journal of Minerals and Materials Characterization and Engineering, 9(04), 275.
Hu, Z., Arefin, M. R. H., Yan, X., & Fan, Q. H. (2014). Mechanical property characterization of carbon nanotube modified polymeric nanocomposites by computer modeling. Composites Part B: Engineering, 56, 100-108.
Huang, Z.-M., Zhang, Y.-Z., Kotaki, M., & Ramakrishna, S. (2003). A review on polymer nanofibers by electrospinning and their applications in nanocomposites. Composites Science and Technology, 63(15), 2223-2253.
Hui, C., & Shia, D. (1998). Simple formulae for the effective moduli of unidirectional aligned composites. Polymer Engineering & Science, 38(5), 774-782.
Huong, P. V., Cavagnat, R., Ajayan, P., & Stephan, O. (1995). Temperature-dependent vibrational spectra of carbon nanotubes. Physical review B, 51(15), 10048.
Hyer, M. W., & White, S. R. (2009). Stress analysis of fiber-reinforced composite materials: DEStech Publications, Inc.
Iijima, S. (1991). Helical microtubules of graphitic carbon. Nature, 354(6348), 56.
Isaza M, C. A., Herrera Ramírez, J., Ledezma Sillas, J., & Meza, J. (2018). Dispersion and alignment quantification of carbon nanotubes in a polyvinyl alcohol matrix. Journal of Composite Materials, 52(12), 1617-1626.
Kim, M., Okoli, O., Jack, D., Park, Y.-B., & Liang, Z. (2011). Characterisation and modelling of CNT–epoxy and CNT–fibre–epoxy composites. Plastics, Rubber and Composites, 40(10), 481-490.
Kumar, J. P., & Srinivas, J. (2018). Three phase composite cylinder assemblage model for analyzing the elastic behavior of MWCNT-reinforced polymers. Computers Materials and Continua, 54(1), 1-20.
Kundalwal, S. I. (2018). Review on micromechanics of nano‐and micro‐fiber reinforced composites. Polymer Composites, 39(12), 4243-4274.
Lin, J. H., Lin, Z. I., Pan, Y. J., Hsieh, C. T., Huang, C. L., & Lou, C. W. (2016). Thermoplastic polyvinyl alcohol/multiwalled carbon nanotube composites: preparation, mechanical properties, thermal properties, and electromagnetic shielding effectiveness. Journal of Applied Polymer Science, 133(21).
Lourie, O., & Wagner, H. (1998). Evaluation of Young's modulus of carbon nanotubes by micro-Raman spectroscopy. Journal of Materials Research, 13(9), 2418-2422.
Luo, Z., & Koo, J. (2007). Quantifying the dispersion of mixture microstructures. Journal of Microscopy, 225(2), 118-125.
Mallick, P. K. (2007). Fiber-reinforced composites: materials, manufacturing, and design: CRC press.
Martínez-Morlanes, M., Castell, P., Martínez-Nogués, V., Martinez, M., Alonso, P. J., & Puértolas, J. (2011). Effects of gamma-irradiation on UHMWPE/MWNT nanocomposites. Composites Science and Technology, 71(3), 282-288.
Mooney, M. (1951). The viscosity of a concentrated suspension of spherical particles. Journal of Colloid Science, 6(2), 162-170.
Mori, T., & Tanaka, K. (1973). Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21(5), 571-574.
Noor, N., Razak, J., Ismail, S., Mohamad, N., Tee, L., Munawar, R., & Junid, R. (2018). Review on Carbon Nanotube based Polymer Composites and Its Applications. Journal of Advanced Manufacturing Technology (JAMT), 12(1), 311-326.
Odegard, G. M., Gates, T., Wise, K., Park, C., & Siochi, E. (2003). Constitutive modeling of nanotube–reinforced polymer composites. Composites Science and Technology, 63(11), 1671-1687.
Pharr, G., & Oliver, W. (1992). Measurement of thin film mechanical properties using nanoindentation. Mrs Bulletin, 17(7), 28-33.
Qiu, Y., & Weng, G. (1990). On the application of Mori-Tanaka's theory involving transversely isotropic spheroidal inclusions. International Journal of Engineering Science, 28(11), 1121-1137.
Rafiee, M. A., Rafiee, J., Wang, Z., Song, H., Yu, Z.-Z., & Koratkar, N. (2009). Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano, 3(12), 3884-3890.
Rathi, A., & Kundalwal, S. I. (2020). Mechanical and fracture behavior of MWCNT/ZrO2/epoxy nanocomposite systems: Experimental and numerical study. Polymer Composites.
Reddy, J. N. (2003). Mechanics of laminated composite plates and shells: theory and analysis: CRC press.
Reuss, A. (1929). Berechnung der Flieggrenze yon Mischkristallen auf Grund der Plastizithtsbedingung fiir Einkristalle. Z. Angew. Math. Mech, 9.
Ruan, S., Gao, P., Yang, X. G., & Yu, T. (2003). Toughening high performance ultrahigh molecular weight polyethylene using multiwalled carbon nanotubes. Polymer, 44(19), 5643-5654.
Sadeghpour, E., Guo, Y., Chua, D., & Shim, V. P. (2020). A Modified Mori-Tanaka Approach Incorporating Filler-Matrix Interface Failure to Model Graphene/Polymer Nanocomposites. International Journal of Mechanical Sciences, 105699.
Schaufele, a., & Shimanouchi, T. (1967). Longitudinal acoustical vibrations of finite polymethylene chains. The Journal of Chemical Physics, 47(9), 3605-3610.
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