THE FINITE DEFORMATION OF NONLINEAR COMPOSITE-MATERIALS .2. EVOLUTIONOF THE MICROSTRUCTURE

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.