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

Abstract

Part I of this work was concerned with the development of constitutive models for nonlinearly viscous and perfectly plastic composites, which are capable of accounting for the evolution of microstructure when the composites are subjected to finite deformation. This involved the derivation of instantaneous constitutive relations for the composites depending on appropriate microstructural variables, as well as of evolution equations for these variables. As an application of the general theory, in this part of the work, use is made of the models to analyse the response of porous materials and of two–phase composites with perfectly plastic phases under axisymmetric loading conditions (with fixed axes). Attention is focused on the effect of the evolution of the distribution of the inclusions (or voids) on the overall response of the composites. It is found that for porous materials, or for more general classes of composites where the inclusions are softer than the matrix, the effect of changes in the distribution of the inclusions is not very significant relative to the effect of changes in the size and shape of the inclusions. On the other hand, for composites with inclusions that are sufficiently harder than the matrix, the deformation is concentrated in the matrix, and the effect of changes in the distribution function of the inclusions can become quite significant.