Comparison of the solutions of the elastic and elastoplastic boundary value problems - Lang, Holger; Dreßler, Klaus; Pinnau, René; Speckert, Michael (Zeitschrift für Angewandte Mathematik und Physik, 2009)
We consider the quasistatic boundary value problems of linear elasticity and nonlinear elastoplasticity, with linear Hooke’s law in the elastic regime for both problems and with the linear kinematic hardening law for the plastic regime in the latter problem. In particular, we derive expressions and estimates for the difference of the solutions of both models, i.e. for the stresses, the strains and the displacements. To this end, we use a description in the language of stop and play operators. We give an explicit example of a homotopy between the solutions of both problems. Further, it is shown that the stress of the elastic model can be estimated by a constant times the stress of the elastoplastic model in L2-norm.
Keywords: Elastic BVP; Elastoplastic BVP; Variational inequalities; Rate-independence; Hysteresis; Linear kinematic hardening; Linear kinematic plus isotropic hardening; Stop- and play-operator.