On numerical simulation of cyclic viscoplastic and viscoelastic constitutive laws with the large time increment method

Computations on structures having a strongly non-linear time-dependent behavior, even nowadays, require considerable computational times. The reduction of the computational costs is crucial for the use of simulations in industrial areas. The large time increment method, which breaks completely with traditional methods, is developed for this purpose. This method is based on a two-stage iterative procedure, which takes into account the whole load in one increment time, irrespective of the loading time. The aim of this paper is to show and understand how this algorithm works, and to assess its performance, for several classes of constitutive laws. This algorithm is tested on one-dimensional periodic loading problems. The theory is developed for a simple viscoelastic model and for one viscoplastic model using material state variables, and constructed in the framework of thermodynamics of irreversible processes. The numerical experiments allowed us to confirm the theoretical basis of this algorithm. The results are remarkable since the computing time is reduced by a factor between 3 and 15 according to the loading, in comparison to other classical methods. Furthermore, the algorithm corrects rapidly perturbations due to a bad initialisation. On the one hand we show that the Large Time Increment Method can be adapted to a wide range of models. On the other hand the efficiency has been measured in several loading cases and for different constitutive laws. This opens new research perspectives such as the adaptation of this algorithm to a finite elements code, in order to achieve three-dimensional computations.