A GENERAL CONSTITUTIVE THEORY FOR LINEAR AND NONLINEAR PARTICULATE MEDIA WITH MICROSTRUCTURE EVOLUTION

This work is concerned with the development of a constitutive theory f or composite materials with particulate microstructures, which is capa ble of predicting approximately, the evolution of the microstructure a nd its influence on the effective response of composites under general three-dimensional finite-strain loading conditions, such as those pre sent in metal-forming operations. In its present form, the theory is g eneral enough to be used for linearly viscous, nonlinearly viscous and perfectly plastic composites with randomly oriented and distributed e llipsoidal inclusions (or pores), which, in the most general case, can change size, shape and orientation. In addition, the ''shape'' and '' orientation'' of their center-to-center statistical distribution funct ions can also evolve with the deformation. To illustrate the key featu res of the new theory in the context of a simple example, an applicati on is carried out for plane-strain loading of two-phase systems consis ting of random distributions of aligned rigid particles in a power-law matrix phase. The results show that the evolution of the relevant mic rostructural variables, as well as the effective response, depend in a complex fashion on the initial state of the microstructure, as well a s on the specific boundary conditions. In particular, it is found that the changes in orientation of the particles provide a mechanism analo gous to ''geometric softening'' in ductile single crystals, which can lead to significant changes in the instantaneous hardening rate of the composite. This is shown to have important consequences for the possi ble onset of shear localization in the composite. (C) 1998 Elsevier Sc ience Ltd. All rights reserved.