A homogenization theory for time-dependent nonlinear composites with periodic internal structures (Q1302787)

This paper describes a homogenization theory for time-dependent deformations (such as creep and viscoplasticity) of nonlinear composites with periodic internal structure, within the framework of infinitesimal strain. The theory is firstly developed in the macroscopically uniform case in a rate form, without resort to any asymptotic expansion, and then it is extended to the macroscopically nonuniform case in an incremental form, using an asymptotic expansion. Thus a macroscopic constitutive equation and a microscopic stress evolution equation are derived in rate and incremental forms by introducing two kinds of Y-periodic functions, which are determined by solving two unit cell problems. The resulting equations are shown to be effective for computing incrementally the time-dependent deformations for which the history of either macroscopic stress or macroscopic strain is prescribed. An application is considered to the transverse creep of metal matrix composites reinforced undirectionally with continuous fibers.