Analytical results for a linear hardening elasto-plastic spring investigated via a hemivariational formulation

We investigate the linear hardening phenomena with a method that is not standard in the literature, i.e. with a hemivariational method. As a result, we do not introduce any flow rules, and the number of assumptions is reduced to the generalized variational principle with proper definition of a new set of kinematic descriptors and, as a function of them, with a new definition of the energy functional. The variational framework guarantees the rationality of the deduction. Analytical derivation of the force displacement hysteretic loop is also derived and, finally, the dissipation energy is furnished with respect to either the final value of the dissipation energy potential or the corresponding area of the hysteretic loop.