M. Kailasam et al., THE EFFECT OF PARTICLE-SIZE, SHAPE, DISTRIBUTION AND THEIR EVOLUTION ON THE CONSTITUTIVE RESPONSE OF NONLINEARLY VISCOUS COMPOSITES .1. THEORY, Philosophical transactions-Royal Society of London. Physical sciences and engineering, 355(1730), 1997, pp. 1835-1852
This work deals with the development of constitutive models for two-ph
ase nonlinearly viscous and perfectly plastic composites with evolving
microstructures. The work builds on the earlier models of Ponte Casta
neda & Zaidman (1994) for composites with particulate microstructures
subjected to finite deformation, where the influence of the evolution
of the average shape and size of the inclusions (or voids) on the over
all anisotropic response of the composites was considered. The present
model additionally takes into account the effect of independent chang
es in the random distribution of the inclusions as the deformation pro
gresses. Thus, appropriate 'internal variables' characterizing the sta
te of the microstructure are incorporated into the 'instantaneous' con
stitutive equations for the composite and 'evolution laws' for these v
ariables are proposed. The first part of this work deals with the deve
lopment of the instantaneous constitutive relations for a sufficiently
broad class of microstructures to be able to consider the evolution p
roblem under general triaxial loading conditions (with fixed loading a
xes). The 'aspect ratios' of the two-point distribution function are i
ntroduced as new microstructural variables, along with the aspect rati
os and the volume fraction of the inclusions as proposed in the earlie
r models. Evolution laws are then developed for all these variables, w
hich-when integrated together with the instantaneous constitutive rela
tions-serve to determine the effective anisotropic response of the com
posite under the prescribed loading conditions. Part II of this work i
s concerned with the application of the model to some specific classes
of two-phase composite materials subjected to axisymmetric loading co
nditions.