The effect of particle size, shape, distribution and their evolution on the constitutive response of nonlinearly viscous composites. I. Theory

Abstract
This work deals with the development of constitutive models for two–phase nonlinearly viscous and perfectly plastic composites with evolving microstructures. The work builds on the earlier models of Ponte Castañeda and 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 overall anisotropic response of the composites was considered. The present model additionally takes into account the effect of independent changes in the random distribution of the inclusions as the deformation progresses. Thus, appropriate ‘internal variables’ characterizing the state of the microstructure are incorporated into the ‘instantaneous’ constitutive equations for the composite and ‘evolution laws’ for these variables are proposed. The first part of this work deals with the development of the instantaneous constitutive relations for a sufficiently broad class of microstructures to be able to consider the evolution problem under general triaxial loading conditions (with fixed loading axes). The ‘aspect ratios’ of the two–point distribution function are introduced as new microstructural variables, along with the aspect ratios and the volume fraction of the inclusions as proposed in the earlier models. Evolution laws are then developed for all these variables, which–when integrated together with the instantaneous constitutive relations–serve to determine the effective anisotropic response of the composite under the prescribed loading conditions. Part II of this work is concerned with the application of the model to some specific classes of two–phase composite materials subjected to axisymmetric loading conditions.

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