Homogenized properties of elastic–viscoplastic composites with periodic internal structures

A homogenization theory for elastic–viscoplastic composites with periodic internal structures is developed in rate and incremental forms by considering unit cells subjected to macroscopically uniform stress and strain. The theory enables us to incrementally compute the macroscopic as well as the microscopic stress and strain states in nonlinear time-dependent periodic composites. The theory is effective for problems in which the history of either macro-strain or macro-stress, or a combination of them, is prescribed as a function of time. As applications of the theory, transverse and off-axial deformation problems of metal matrix composites reinforced unidirectionally with continuous fibers are analyzed to discuss the effects of fiber arrangement and orientation on the macroscopic deformation behavior.