The Viscoelastic Response of Fiber-Reinforced Composite Material
Xu Zhenyu,Zhang Ruojing,He Wei
(The Key Laboratory of Solid Mechanics of Ministry of Education, Tongji University, Shanghai, 200092)

Abstract: Under some circumstances, metal-based or polymer-based composite may behave viscoelasticaly. In the present paper, the fractional derivative mod el in Riemann-Liouville form is adopted to describe the viscous property of the matrix. Then the global constitutive relationship of fiber reinforced composite is formaluted, based on the asymptotic homogenization method. An application of the method is given when the matrix is of Makris's viscoelastic relation. The case of rectangular arrangement and staggered arrangement of fibers with circular cross-section are cited, the curves of global elastic constants and global viscous constants vs volume ratio of fibers are calculated. It can be concluded that, such composite is also viscoelastic, with the global elastic part is made up of the elasticity of both fibers and matrix, while global viscous part solely comes from matrix. The compoiste has the same viscous coefficient and fractional derivative as the matrix. In order to determine the microstructural parameters in global constitutive relations, two types of local problems have to be solved. A t the same volume ratio of fibers, the global elastic constants of rectangular arrangement are greater than that of staggered arrangement, while the viscous constants behave counter to them.
Keywords: composite material, viscoelastic, asymptotic homogenization, fractiona l derivative model, the arrangement of fibers.