On Numerical Simulation of Cyclic Viscoplastic and Viscoelastic Constitutive Laws with the Large Time Increment Method

Abstract

Computations on structures having a strongly non-linear time-dependentbehavior, even nowadays, require considerable computational times. Thereduction of the computational costs is crucial for the use ofsimulations in industrial areas. The large time increment method, whichbreaks completely with traditional methods, is developed for thispurpose. This method is based on a two-stage iterative procedure, whichtakes into account the whole load in one increment time, irrespective ofthe loading time. The aim of this paper is to show and understand how this algorithmworks, and to assess its performance, for several classes ofconstitutive laws. This algorithm is tested on one-dimensional periodicloading problems. The theory is developed for a simple viscoelasticmodel and for one viscoplastic model using material state variables, andconstructed in the framework of thermodynamics of irreversibleprocesses. The numerical experiments allowed us to confirm the theoreticalbasis of this algorithm. The results are remarkable since the computingtime is reduced by a factor between 3 and 15 according to the loading,in comparison to other classical methods. Furthermore, the algorithmcorrects rapidly perturbations due to a bad initialisation. On the one hand we show that the Large Time Increment Method can beadapted to a wide range of models. On the other hand the efficiency hasbeen measured in several loading cases and for different constitutivelaws. This opens new research perspectives such as the adaptation ofthis algorithm to a finite elements code, in order to achievethree-dimensional computations.