Extremal paths and holonomic constitutive laws in elastoplasticity

Extremal stress paths between any two stresses are investigated for elastic-plastic materials, extending existing results which hold for the case when one of the stress points is at the origin. Assumptions about the differentiability of the various work and complementary work functions are relaxed, and it is shown that the maximum complementary work $\hat U$ is a potential for the strain in the sense that the strain lies in the subdifferential of $\hat U$. In the same way the minimum work $\hat W$ is a potential for stress. Parallel investigations with respect to maximum complementary plastic work and plastic work show that these quantities are potentials for stress and plastic strain increment, respectively. A holonomic constitutive law based on the relations between stress and strain, obtained when the stress history follows an extremal path, is constructed.