On rotational hardening in soil elastic-plasticity

In this paper, a new approach for rotational hardening in elastic-plasticity is formulated. After discussing the standard yield criteria employed for geomaterials and the rotational hardening models proposed in the past, the authors introduce the concept of pure rotational hardening, that is a rigid rotation of the yield surface not implying any distortion of it. In the second part of the paper, a new approach for rotational hardening, based on Householder transformations, is proposed. The method, that allows to reflect vectors with respect to a given hyper-plane, is briefly described since not usually employed in geomechanics. Moreover, the authors clarify that any yield surface or plastic potential rotation, not being a rolling, is a transformation keeping unaltered first and second invariants, but not the third. As a consequence, when rotational hardening is introduced, the use of the third mixed invariant, for defining in the deviatoric plane the yield surface shape, is not appropriate. Finally, the application of the proposed approach in the formulation of anisotropic elastic-plastic strain hardening constitutive models is briefly discussed for the classes of uncoupled and hybrid yield criteria that include a dependence of the yield surface on Lode angle.