Enriched by the nonlinear Onsager reciprocal relations and thermodynamic equilibrium points (Onsager, Phys. Rev., 37, pp. 405–406; 38, pp. 2265–2279), an extended normality structure by Rice (1971, J. Mech. Phys. Solids, 19, pp. 433–455) is established in this paper as a unified nonlinear thermodynamic theory of solids. It is revealed that the normality structure stems from the microscale irrotational thermodynamic fluxes. Within the extended normality structure, this paper focuses on the microscale thermodynamic mechanisms and significance of the convexity of flow potentials and yield surfaces. It is shown that the flow potential is convex if the conjugate force increment cannot not oppose the increment of the rates of local internal variables. For the Rice fluxes, the convexity condition reduces to the local rates being monotonic increasing functions with respect to their conjugate forces. The convexity of the flow potential provides the thermodynamic system a capability against the disturbance of the thermodynamic equilibrium point. It is proposed for time-independent behavior that the set of plastically admissible stresses determined by yield conditions corresponds to the set of thermodynamic equilibrium points. Based on that viewpoint, the intrinsic dissipation inequality is just the thermodynamic counterpart of the principle of maximum plastic dissipation and requires the convexity of the yield surfaces.

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