THE FINITE DEFORMATION OF NONLINEAR COMPOSITE-MATERIALS .1. INSTANTANEOUS CONSTITUTIVE RELATIONS

This work deals with the development of effective constitutive models for two-phase nonlinearly viscous and rigid-perfectly plastic composit es subjected to finite deformations. The main new feature of the model is the ability to account approximately for the evolution of the micr ostructure resulting from the finite changes in geometry during a give n deformation process. The model is formulated in terms of instantaneo us constitutive relations for the composites, which depend on appropri ate variables characterizing the state of the microstructure, together with evolution equations for these state variables. This first part o f the work is concerned with the development of the instantaneous cons titutive relations for classes of microstructures that are sufficientl y broad to capture the changes in microstructure associated with gener al triaxial finite-deformation histories. Simple formulae are given fo r the effective potentials and stress-strain rate relations of power-l aw viscous composites made of aligned ellipsoidal inclusions of one ph ase dispersed in a matrix of a second phase. In addition, effective yi eld surfaces are computed for the special case of two-phase rigid-perf ectly plastic composites with aligned spheroidal inclusions. The effec ts of the phase volume fractions, inclusion shape and yield strength r atio on these effective yield surfaces are considered. These effects w ill turn out to be important in the understanding of the effective res ponse of the composites with evolving microstructures, which is consid ered in Part II of this work.