THE EFFECT OF PARTICLE-SIZE, SHAPE, DISTRIBUTION AND THEIR EVOLUTION ON THE CONSTITUTIVE RESPONSE OF NONLINEARLY VISCOUS COMPOSITES .1. THEORY

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.