M. Kailasam et Pp. Castaneda, A GENERAL CONSTITUTIVE THEORY FOR LINEAR AND NONLINEAR PARTICULATE MEDIA WITH MICROSTRUCTURE EVOLUTION, Journal of the mechanics and physics of solids, 46(3), 1998, pp. 427-465
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.