Within the frame work of a piecewise homogeneous body model, with the use of the three-dimensional geometrically nonlinear exact equations of elasticity theory, a method is developed for determining the stress distribution in unidirectional fibrous composites with periodically curved fibers. The distribution of the normal and shear stresses acting on interfaces for the case where there exists a bond covering cylinder of constant thickness between the fiber and matrix is considered. The concentration of fibers in the composite is assumed to be low, and the interaction between them is neglected. Numerous numerical results related to the stress distribution in the body considered are obtained, and the influence of geometrical nonlinearity on this distribution is analyzed.
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References
S. D. Akbarov and A. N. Guz, Mechanics of Curved Composites, Kluwer Academic Publishers (2000).
S. D. Akbarov and A. N. Guz’, “Continuum approaches in the mechanics of curved composites and related problems for members of constructions,” Int. Appl. Mech, 38, No.11, 3-31 (2002).
S. D. Akbarov and A. N. Guz, “Mechanics of curved composites and some related problems for structural members,” Mech. Adv. Mater. Struct., 11, 445-515 (2004).
V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilayer Structures [in Russian], Mashinostroenie, Moscow (1980).
S. D. Akbarov, T. Sisman, and N. Yahnio?lu, “On the fracture of unidirectional composites in compression,” Int. J. Eng. Sci, 35, Nos. 12/13, 1115-1136 (1997).
S. D. Akbarov, A. Cilli, and A. N. Guz, “The theoretical strength limit in compression of viscoelastic layered composite materials,” Composites, Pt. B: Engineering, 30, 465-472 (1999).
S. D. Akbarov, N. Yahnioglu, and Z. Kutug, “On the three dimensional stability loss problem of a viscoelastic composite plate,” Int. J. Eng. Sci., 39, 1443-1457 (2001).
S. D. Akbarov and A. N. Guz’, “Mechanics of curved composites (piecewise homogeneous body model),” Int. Appl. Mech., 38, No. 12, 1415-1439 (2002).
S. D. Akbarov and A. N. Guz’, “Stress state of a fiber composite with curved structures with a low fiber concentration,” Sov. Appl. Mech., 21, No. 6, 560-565 (1985).
S. D. Akbarov and A. N. Guz’, “Method of solving problems in the mechanics of fiber composites with curved structures,” Sov. Appl. Mech., 20, No. 9, 777-790 (1985).
S. D. Akbarov, “On the three-dimensional stability loss problems of elements of structures of viscoelastic composite materials,” Mech. Compos. Mater., 34, No. 6, 537-544 (1998).
S. D. Akbarov and R. Kosker, “Fiber buckling in a viscoelastic matrix,” Mech. Com pos. Mater., 37, No. 4, 299-306 (2001).
S. D. Akbarov, R. Kosker, and K. Simsek, “Stress distribution in an in finite elastic body with a locally curved fiber in a geometrically nonlinear statement,” Mech. Compos. Mater., 41, No. 4, 291-302 (2005).
S. D. Akbarov and R. Kosker, “On a stresses analysis in the infinite elastic body with two neighbouring curved fibers,” Composites, Pt. B, 34, 143-150 (2003).
S. D. Akbarov and R. Kosker, “Influence of the interaction of two neighbouring curved fibers,” Composites. Part B, 34, No. 2, 143-150 (2003).
S. D. Akbarov and R. Kosker, “Stress distribution caused by anti-phase periodical curving of two neighbouring fibers in a composite materials,” Eur. J. Mech., A/Sol ids, No. 22, 243-256 (2003).
S. D. Akbarov, A. N. Guz’, and M. A. Cherekov, “Stability of two fibers in a matrix under finite subcritical strains,” Mech. Com pos. Ma ter., 18, No. 1, 34-41 (1982).
S. D. Akbarov and R. Kosker, “Internal stability loss of two neighboring fibers in a viscoelastic matrix,” Int. J. Eng. Sci., No. 42, 1847-1873 (2004).
S. D. Akbarov, R. Kosker, and Y. Ucan, “Stress distribution in an elastic body with a periodically curved row of fibers,” Mech. Com pos. Mater., 40, No. 3, 191-202 (2004).
S. D. Akbarov, R. Kosker, and Y. Ucan, “Stress distribution in a composite material with the row of anti-phase periodically curved fibres,” Int. Appl. Mech., 42, No. 4, 486-493 (2006).
A. N. Guz’, “Constructing the three-dimensional theory of stability of de formable bodies,” Int. Appl. Mech., 37, No. 1, 1-37 (2001).
I. Yu. Babich, A. N. Guz’, and V. N. Chekhov, “The three-dimensional theory of stability of fibrous and laminated materials,” Int. Appl. Mech., 37, No. 9, 1103-1141 (2001).
S. D. Akbarov, “Three-dimensional stability loss problems of the viscoelastic composite materials and structural members,” Int. Appl. Mech., 43, No. 10, 3-27 (2007).
A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of De form able Bodies, Springer (1999).
A. N. Guz’, J. J. Rushchitsky, and I. A. Guz’, “Establishing fundamentals of the mechanics of nanocomposites,” Int. Appl. Mech., 43, No. 3 (2007).
A. N. Guz’ and V. N. Chekhov, “Problems of folding in the earth’s stratified crust,” Int. Appl. Mech., 43, No. 2 (2007).
K. Q. Xiao, L. C. Zhang, and I. Zarudi, “Mechanical and rheological properties of carbon nanotube-reinforced poly ethylene composites”, Compos. Sci. Technol., 67, 77-182 (2007).
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Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 269-288, March-April, 2009.
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Kosker, R., Dikbas, D.M. Stress distribution in an infinite elastic body with a covered periodically curved fiber. Mech Compos Mater 45, 183–198 (2009). https://doi.org/10.1007/s11029-009-9070-0
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DOI: https://doi.org/10.1007/s11029-009-9070-0