Source: http://journals.uran.ua/eejet/article/view/143406
Timestamp: 2019-04-24 00:42:53+00:00

Document:
When solving problems on the mechanics of composites, it is convenient to use a composite model in the form of a continuous homogeneous medium with effective constants, which adequately reflect its most essential characteristics. Modern engineering and construction commonly use the composites, reinforced with hollow fibers. Unknown for today are the analytical dependences for the effective elastic constants of such composite materials with transtropic components. The task on constructing such dependences is resolved in this paper.
We have derived analytical dependences for the effective longitudinal modulus of elasticity and the Poisson’s coefficient in the unidirectional fiber composite, consisting of a transtropic matrix and hollow fiber. The composite is simulated by a solid uniform transtropic material. The conditions for a perfect connection are satisfied at the interphase surfaces. In order to obtain the analytical dependences, we have solved two boundary problems: on the longitudinal elongation of a composite cylinder, whose components are the transtropic matrix and hollow fiber, and a solid homogeneous cylinder that models the transtropic composite. The application of conditions for displacements alignment and stresses, found by solving these problems, provided an opportunity to derive formulae for the effective longitudinal modulus of elasticity and Poisson’s coefficient. These formulae reflect the dependences of effective characteristics of a composite on elastic characteristics of the matrix, fibers, and volumetric shares of the fiber and the cavity inside it.
Klastorny, M., Konderla, P., Piekarskiy, R. (2009). An exact stiffness theory of unidirectional xFRP composites. Mekhanika kompozitnyh materialov, 45 (1), 109–144.
Grebenyuk, S. N. (2011). Elastic characteristics of composite material with transversaly isotropic matrix and fiber. Methods of solving applied problems of mechanics of a deformable solid, 12, 62–68.
Tang, T. (2008). Variational Asymptotic Micromechanics Modeling of Composite Materials. Logan: Utah State University, 280.
Bol'shakov, V. I., Andrianov, I. V., Danishevskiy, V. V. (2008). Asimptoticheskie metody rascheta kompozitnyh materialov s uchetom vnutrenney struktury. Dnepropetrovsk: «Porogi», 196.
Francevich, I. N., Karpinos, D. M. (Eds.) (1970). Kompozicionnye materialy voloknistogo stroeniya. Kyiv, 403.
Van Fo Fy, G. A., Klyavlin, V. V. (1972). Ob effektivnosti ispol'zovaniya kompozicionnyh materialov, orientirovanno armirovannyh polymi voloknami. Problemy prochnosti, 4, 10–13.
Vanin, G. A. (1985). Mikromekhanika kompozicionnyh materialov. Kyiv: Naukova dumka, 304.
Grebenyuk, S. M. (2012). Determination of the elastic constants of composite with transtropic matrix and fiber based on the kinematic consistency condition. Visnyk Zaporizkoho natsionalnoho universytetu, 1, 62–76.
Vasil'ev, V. V., Tarnopol'skiy, Yu. M. (Eds.) (1990). Kompozicionnye materialy. Moscow: Mashinostroenie, 512.
Klastorny M., Konderla P., Piekarskiy R. An exact stiffness theory of unidirectional xFRP composites // Mekhanika kompozitnyh materialov. 2009. Vol. 45, Issue 1. P. 109–144.
Grebenyuk S. N. Elastic characteristics of composite material with transversaly isotropic matrix and fiber // Methods of solving applied problems of mechanics of a deformable solid. 2011. Issue 12. P. 62–68.
Tang T. Variational Asymptotic Micromechanics Modeling of Composite Materials. Logan: Utah State University, 2008. 280 p.
Bol'shakov V. I., Andrianov I. V., Danishevskiy V. V. Asimptoticheskie metody rascheta kompozitnyh materialov s uchetom vnutrenney struktury: monografiya. Dnepropetrovsk: «Porogi», 2008. 196 p.
Kompozicionnye materialy voloknistogo stroeniya / I. N. Francevich, D. M. Karpinos (Eds.). Kyiv, 1970. 403 p.
Van Fo Fy G. A., Klyavlin V. V. Ob effektivnosti ispol'zovaniya kompozicionnyh materialov, orientirovanno armirovannyh polymi voloknami // Problemy prochnosti. 1972. Issue 4. P. 10–13.
Vanin G. A. Mikromekhanika kompozicionnyh materialov: monografiya. Kyiv: Naukova dumka, 1985. 304 p.
Grebenyuk S. M. Determination of the elastic constants of composite with transtropic matrix and fiber based on the kinematic consistency condition // Visnyk Zaporizkoho natsionalnoho universytetu. 2012. Issue 1. P. 62–76.
Kompozicionnye materialy: spravochnik / V. V. Vasil'ev, Yu. M. Tarnopol'skiy (Eds.). Moscow: Mashinostroenie, 1990. 512 p.

References: V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V.