Some extremum properties of finite-step solutions inelastoplasticity

For the nonholonomic elastic plastic problem under a given external action history over a time intervalan extremal formulation is given in terms of the complete solution over the whole interval[ The assumed elastic plastic behaviour is of the associated type with piecewise linearized yield surface and linear hardening[ When the loading history is reduced to an in_nitesimal increment of the external actions "incremental problem# or when the material behaviour is assumed to be of the holonomic type " _nite holonomic step# problem\ the functional of the extremal formulation may be split into the sum of two other simpler functionals "previously introduced# whose minimum\ for both of them\ gives the problem solution under less constraints than in the original problem[ For general non!holonomic loading histories the above splitting is shown to be still possible when a particular change of the complementarity condition of the constitutive law is considered\ which leads to a new class of holonomic problems[ It is shown that some problems of this new class\ together with a suitable time discretization\ represent the schematization of the original problem corresponding to well known numerical integration schemes[ 0887 Elsevier Science Ltd[ All rights reserved[