A HOMOGENIZATION THEORY FOR TIME-DEPENDENT DEFORMATION OF COMPOSITES WITH PERIODIC INTERNAL STRUCTURES

A homogenization theory for time-dependent deformation such as creep a nd viscoplasticity of composites with periodic internal structures is developed. The deviation of microscopic displacement rate from macrosc opic one in the macroscopically uniform case, i.e., the first order pe rturbation of displacement rate in the macroscopically nonuniform case is decomposed into elastic and viscous parts. Thus, the constitutive relation between macroscopic stress and strain rates and the evolution equation of microscopic stress are derived using Y-periodic functions introduced into the elastic and viscous parts, and two unit cell prob lems to determine the Y-periodic functions are formulated. The theory is described first in the macroscopically uniform case in a rate form, and then it is extended to the macroscopically nonuniform case in an incremental form using the asymptotic expansion of field variables. As an application of the theory, transverse creep of metal matrix compos ites reinforced unidirectionally with continuous fibers is analyzed nu merically to discuss the effect of fiber arrays on the anisotropy in s uch creep.