We consider rate-independent models of static and quasistatic plasticity with hardening. These models are usually stated in terms of variational inequalities of the first or second kind, for the primal and dual formulations, respectively. In the static case, the dual variational inequality can be interpreted as the necessary and sufficient optimality conditions for an underlying optimization pr...

This paper derives kinematic admissible bending moment – axial force (M-P) interaction relations for mild steel by considering strain hardening idealisations. Two models for strain hardening – Linear and parabolic have been considered, the parabolic model being closer to the experiments. The interaction relations can predict strains, which is not possible in a rigid, perfectly plastic idealizat...

Hardening plasticity has a long history in constitutive modelling, with many applications in geomechanics. Mathematical models of non-hardening plasticity involve the definition of a single stationary yield surface in stress-space. Examples include the conventional models of elasto-plasticity, often based on the yield criteria of Tresca, von Mises, and Mohr-Coulomb. Within the yield surface the...

In this paper we consider an optimal control problem governed by a time-dependent variational inequality arising in quasistatic plasticity with linear kinematic hardening. We address certain continuity properties of the forward operator, which imply the existence of an optimal control. Moreover, a discretization in time is derived and we show that every local minimizer of the continuous problem...

In this paper, an elastoplastic constitutive model is presented for predicting sandy soil behavior under monotonic and cyclic loadings. The model is based on the CJS3 model that takes into account deviatoric and isotropic mechanisms of plasticity. The flow rule in deviatoric mechanism is non-associated and a kinematic hardening law controls the evolution of the yield surface. In the present s...