On the incremental plastic work and related aspects of invariance: Part II

Summary Presuming that the incremental free energy is invariant under a change of the Lagrangean finite strain measure and/or the reference configuration Hill’s transformation rules for the basic quantities occurring in mechanics of elastic–plastic solids are recasted in general 3D situation. On this background the invariant incremental plastic work is defined. The basic connections between Hill–Rice theoretical framework and Eckart–Mandel approach, involving the mobile stress-free configuration, are discussed both in generalized coordinates and in the tensorial notation. To this end the selected fundamentals of solid mechanics including the work-conjugacy are recalled. The structure of the updated Lagrangean plastic increment of the total strain is exhibited accounting for the deformation and stress effects due to possible damage and pressure sensitivity of a solid. Special simple approximate relations are derived for the situations when non-dilatational elastic strains are small. The merits of using the logarithmic elastic strain as a state variable are also discussed.