Multiscale Thermodynamic Basis of Plastic Potential Theory

Abstract

In this paper, the multiscale thermodynamic basis of the plastic potential theory is addressed within the irreversible thermodynamic framework with internal variables by (1971, “ Inelastic Constitutive Relations for Solids: An Integral Variable Theory and Its Application to Metal Plasticity,” J. Mech. Phys. Solids, 19, pp. 433–455). It is shown that the condition of free or complementary energy equivalence leads to the full equivalence of the microscale and macroscale thermodynamic formulations as soon as the multiscale kinematic relation is prescribed. The condition of dissipation equivalence by Rice is not an independent condition. The thermodynamic significance and counterparts of plastic potentials and multipliers, Koiter’s and Mises’ flow rules, the intrinsic time in the work of (1975, “ On the Foundations of the Endochronic Theory of Viscoplasticity,” Arch. Mech., 27, pp. 857–868), the viscoplasticity, and the J2 plasticity can all be revealed and recovered within the multiscale thermodynamic framework.