Analysis of transfer procedures in elastoplasticity based on the error in the constitutive equations: Theory and numerical illustration

The aim of this work is to illustrate a methodology for the assessment of adaptive strategies for the solution of associative rate-independent plasticity problems solved by employing the incremental displacement conforming finite element method. This is the first step towards a more rational definition of transfer operators in terms of the ensuing error. The motivating idea is the observation that change of data and/or finite element mesh from one time interval to the other can be both related to a discontinuity jump of the approximate solution across the time instant tn. Thus, reliable a posteriori estimates will have to depend not only on the time step and finite element mesh size but also on the value of the jump. A new error estimate based on the error in the constitutive equations is developed which allows characterization of the discontinuity jump