Relationship between normality structure and orthogonality condition

Abstract

The nonlinear generalization of the phenomenological equations along with Onsager [Reciprocal relations in irreversible processes, I, II. Physical Review 37 (1931) 405] reciprocal relations includes the normality structure of Rice [Inelastic constitutive relations for solids: an integral variable theory and its application to metal plasticity. Journal of the Mechanics and Physics of Solids 19 (1971) 433; 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, 1975, pp. 23–79] and the orthogonality condition of Ziegler [An Introduction to Thermomechanics. North-Holland, Amsterdam, 1977] and Ziegler and Wehrli [The derivation of constitutive relations from the free-energy and the dissipation function. Advances in Applied Mechanics 25 (1987a) 183–238; On a principle of maximal rate of entropy production. Journal of Non-Equilibrium Thermodynamics 12 (1987b) 229–243]. The normality structure is generally not consistent with the orthogonality condition due to the different potential functions. The aim of this paper is to examine whether or not the two theories conflict with each other and to establish the consistency condition between the two theories. It is shown in this paper that monotonic increasing and homogeneous kinetic rate laws of local internal variables are thermo-dynamically admissible within the normality structure. The homogeneity property of the kinetic rate laws is the necessary and sufficient consistency condition between the normality structure and orthogonality condition. The thermodynamic processes obeying the orthogonality condition belong to a subset of these processes covered by the normality structure, so the normality structure possesses much more generality than the orthogonality condition.