On the yield functionals in Lagrangian stress space of elastic-plastic materials with internal constraints

In the present paper it is shown that the elastic range in the second Piola-Kirchhoff stress space can be chosen in a hyperplane perpendicular to the direction related to the simple internal constraint if the determinate stress response of the elastic-plastic material with simple internal constraints with the condition (2.30) is correctly chosen, otherwise, it is in general in a hypersurface and the normal flow rule by Il’yushin’s postulate will have an indeterminate part( [8]). The choice of determinate stress response is probable because of its indeterminacy ([1]). Therefore the yield functional should be a function of the second Piola-Kirchhoff stress lying in the hyperplane so that it is more simple and the back stress as the geometric center of the elastic range in general is inside the elastic range. Finally some examples are concerned.