Effect of a Third Invariant on the Effective Reaction of Plastic Porous Bodies. Part 1. Behavior of a Porous Material Unit Cell and a Generalized Rule of Normality

This work is devoted to deriving in general form definitive equations for plastic flow of porous bodies whose behavior is sensitive to a third strain rate invariant. Use of a micromechanical approach, including analysis of the behavior of a unit cell, and also such concepts as energy dissipation and an associated flow rule, make it possible to obtain the structure of macroscopic definitive equations in a general form. However, analysis of them and application gives rise to difficulties since they contain elliptical integrals and they cannot be expressed by means of elementary functions. Therefore the general definitive equations serve as a basis for subsequent analysis, i.e. determination of the lower and upper boundary approximations for the macroscopic stress tensor components and also formulation of macroscopic flow conditions in a convenient and compact form.