A modified implicit-explicit integration scheme: an application to elastoplasticity problems

In this paper, a novel modified version of the implicit-explicit integration scheme (IMPL-EX) proposed by Oliver (Comput Methods Appl Mech Eng 197:1865-1889, 2008) is presented. This modified approach has as its main difference with respect to the standard IMPL-EX the choice of internal variables to be updated. In the modified approach what is updated are the plastic strain tensor components, instead of the plastic multiplier. This choice of update, as will be shown, has the advantage of making the algorithm stiffness matrix constant, while keeping all the advantages that comes with the standard IMPL-EX already pointed out by Oliver in (Comput Methods Appl Mech Eng 197:1865-1889, 2008) and (Comput Methods Appl Mech Eng 195:7093-7114, 2006). The scope of the paper will be restricted to the application of the proposed scheme to elastoplasticity problems. Due to what is exposed above the authors named the proposed method by Modified IMPL-EX. To assess the algorithm proposed, a few verification examples, with closed-form solutions, for elastoplasticity problems are presented and the Modified IMPL-EX results are compared with the results obtained by the implicit integration scheme.