Pp. Castaneda et M. Zaidman, THE FINITE DEFORMATION OF NONLINEAR COMPOSITE-MATERIALS .1. INSTANTANEOUS CONSTITUTIVE RELATIONS, International journal of solids and structures, 33(9), 1996, pp. 1271-1286
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.