In Structural Mechanics, nearly all the present computations for time dependent non-linear problems (e.g. plasticity, viscoplasticity or damage) use the step-by-step methods. For small displacement problems, the LArge Time INcremental (LATIN) method, introduced by LADEVEZE, contrasts with these step-by-step procedures. It is an iterative method which accounts for the whole loading process in a single time increment which is not a priori limited. To give an idea of the step length, several loading cycles (or even several thousand) can be simulated in a single time increment. The performances of the method are remarkable for large degrees of freedom problems and when the load is complex. A first extension for large displacement problems has been presented and applied to deep drawing simulation.

This work concerns another extension, suitable for material models described with internal variables, whose principle has been given by LADEVEZE. The objective of this paper is to describe the main ideas of the method, and to show the first numerical applications for tension-bending elastic beams. Essentially, we have studied the behaviour of the method when a loading interval includes a critical point. For buckling and post-buckling problems, the method allows to get the pre and post-buckling critical response of the structure simultaneously without any continuation technique; less than ten iterations are necessary.

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