1. Introduction

Many mechanical problems require the consideration, at the material level, of damaging behaviors: reinforced concrete structures, soil models, etc.

The behavioral relationship can then be softened and the known implicit quasistatic resolution methods have difficulty in converging (the tangent stiffness operator becomes singular). In some cases, even the use of highly efficient strategies such as mixed linear research or management is insufficient.

In order to be able to overcome these limitations, there are alternative strategies based on methods inspired by the tools of direct transitory analysis [bib1].

It is clear that there is no question here of wanting to simulate a dynamic response of the vibratory type or with wave propagation: we seek to obtain solutions that evolve slowly, and therefore in coherence with the hypothesis of virtual staticity. The usual dynamic methods must therefore be adapted to this framework and the solution thus obtained must verify the hypotheses of sufficiently slow evolution.

Finally, it should be borne in mind that these transitional approaches, due to their specificities, should be used as a last resort, when all the remedies available in STAT_NON_LINE have failed.

The prerequisite for using the methods presented in this documentation is therefore to have already developed and comprehensively tested the options available in STAT_NON_LINE for the application in question. It goes without saying that a good knowledge of STAT_NON_LINE and DYNA_NON_LINE is also strongly recommended as well as reading the corresponding documentation: R5.03.01, R5.05.05 and especially U2.06.13.

In particular, the general advice for using the DYNA_NON_LINE operator given in the U2.06.13 documentation remains valid and they are therefore an essential prerequisite for the proper implementation of the methods that are the subject of this documentation.