ABSTRACT
CHAPTER 13
MICRO-TO-MACRO TRANSITION
Some fundamental aspects of the transition in the constitutive description
of the material response from microlevel to macrolevel are discussed in this
chapter. The analysis is aimed toward the derivation of the constitutive
equations for polycrystalline aggregates based on the known constitutive
equations for elastoplastic single crystals. The theoretical framework for this
study was developed by Bishop and Hill (1951a,b), Hill (1963,1967,1972),
Mandel (1966), Bui (1970), Rice (1970,1971,1975), Hill and Rice (1973),
Havner (1973,1974), and others. The presentation in this chapter follows
the large deformation formulation of Hill (1984,1985). The representative
macroelement is dened, and the macroscopic measures of stress and strain,
and their rates, are introduced. The corresponding elastoplastic moduli
and pseudomoduli tensors, the macroscopic normality and the macroscopic
plastic potentials are then discussed.
