On the non-oscillation criterion for multiplicative anisotropic plasticity at large simple shear deformation

The criterion for non-oscillatory stresses under monotonic large simple shear deformation in the context of multiplicative anisotropic plasticity is discussed. In particular, evolving anisotropy combined with a Hill type of yield criterion is considered. It is shown that a sufficient, but not necessary, criterion for a non-oscillatory stress is ellipticity of the first Piola–Kirchhoff stress. Loss of ellipticity corresponds to a critical value h_cr of the generalized plastic modulus. Similarly, the absence of limit points on the stress–strain relation motivates an alternative criterion in terms of a critical value h_sh  h_cr. Finally, this criterion is demonstrated analytically as well as numerically for an important class of models with evolving anisotropy of the saturation type.