Microscopic thermodynamic basis of normality structure of inelastic constitutive relations

The essential content of plasticity theory is the normality of plastic strain increments to the yield or flow potential surface at smooth points. The corresponding microscopic thermodynamic mechanism has been explored by Rice [Rice, J.R., 1971. Inelastic constitutive relations for solids: an integral variable theory and its application to metal plasticity. Journal of the Mechanics and Physics of Solids 19, 433; Rice, J.R., 1975. Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms, in: Argon, A.S. (Ed.), Constitutive Equations in Plasticity. MIT Press, Cambridge, MA, p. 23] in his thermodynamic framework with internal variables. Rice's kinetic rate laws of local internal variables, with each rate being stress dependent only via its conjugate thermodynamic force, directly lead to a unifying normality structure and represent a wide class of inelastic behaviors. The aim of this paper is to reveal the underlying physical mechanism and basis of Rice's kinetic rate laws. It is shown that Onsager fluxes which satisfy the so-called non-linear Onsager reciprocal relations Edelen [Edelen, D.G.B., 1972. A non-linear Onsager theory of irreversibility. International Journal of Engineering Science 10, 481; 1973. Asymptotic stability, Onsager fluxes and reaction kinetics, International Journal of Engineering Science 11, 819], can ensure the existence of the flow potential function and lead to the normality structure, and Rice's kinetic rate laws of local internal variables are just certain specific Onsager fluxes. It is also shown that the convexity of the entropy production rate can ensure the convexity of the flow potential function based on homogeneous Onsager fluxes.