M. Zaidman et Pp. Castaneda, THE FINITE DEFORMATION OF NONLINEAR COMPOSITE-MATERIALS .2. EVOLUTIONOF THE MICROSTRUCTURE, International journal of solids and structures, 33(9), 1996, pp. 1287-1303
This work deals with the development of constitutive models for two-ph
ase nonlinearly viscous and rigid-perfectly plastic composites with ev
olving microstructures. Part I of the work was concerned with the esti
mation of instantaneous constitutive relations for the class of partic
ulate microstructures with aligned ellipsoidal inclusions. This second
part deals with the identification of appropriate variables character
izing the state of the microstructure, and with the development of evo
lution equations for these variables. Under the assumption of triaxial
loading conditions, it is argued that aligned ellipsoidal inclusions
deform-in some average sense-into ellipsoidal inclusions with differen
t size and shape. The appropriate state variables are thus the current
values of the volume fractions of the phases and the aspect ratios of
the inclusions. The pertinent evolution laws then follow from well-kn
own kinematical relations, together with appropriate estimates for the
average strain rate in the inclusion and matrix phase. The resulting
constitutive models take the form of standard homogenized stress-strai
n rate relations, supplemented by evolution equations for the above-me
ntioned state variables. Although the ultimate goal of this study is t
o be able to model complex forming processes, illustrative results are
given here only for axisymmetric and plane strain deformations of com
posites with rigid-perfectly plastic phases. The main conclusion is th
at effective behavior of these composites will not be perfectly plasti
c, but may exhibit hardening, or even softening, depending on the spec
ific nature of the applied loading conditions.