A homogenization theory for time-dependentnonlinear composites with periodic internal structures

A homogenization theory for time!dependent deformation such as creep and viscoplasticity of nonlinear composites with periodic internal structures is developed[ To begin with\ in the macroscopically uniform case\ a rate!type macroscopic constitutive relation between stress and strain and an evolution equation of microscopic stress are derived by introducing two kinds of Y!periodic functions\ which are determined by solving two unit cell problems[ Then\ the macroscopically nonuniform case is discussed in an incremental form using the two!scale asymptotic expansion of _eld variables[ The resulting equations are shown to be e}ective for computing incrementally the time!dependent deformation for which the history of either macroscopic stress or macroscopic strain is prescribed[ As an application of the theory\ transverse creep of metal matrix composites reinforced undirectionally with continuous _bers is analyzed numerically to discuss the e}ect of _ber arrays on the anisotropy in such creep