The effect of third invariant on the effective reaction of plastic porous bodies - I: the behavior of the elementary cell of porous material and generalized normality rule

摘要

The given paper is aimed on the general form definition of the constitutive law for third invariant dependent plastic porous bodies. Analysis based on micromechanical consideration involving the Unit Cell analysis, the notion of energy dissipation and normality rule leads to the general set of the macroscopic constitutive equations. However their analysis and use are difficulty because the expressions include elliptic integrals and can not be expressed by means of elementary functions. Therefore general constitutive equations serve as a basis for the subsequent analysis, that leads to the lower and upper boundary approximation for the macroscopic stress tensor components and allows to formulate the macroscopic yield condition in the convenient and compact form.