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Communication Dans Un Congrès Année : 2016

Towards a stochastic time homogenization method

Karam Sab

Résumé

The question of predicting the long-term evolution of a structure in operation, such as fatigue, faces the associated issue of computational cost, particularly when the problem is intended to be numerically solved in the time domain (e.g. to account for the history of loads applied on the structure). Indeed, if fast phenomena have to be described for a very long time interval, it could be useful to apply homogenization methods relatively to the time variable in order to reduce the computational cost as much as possible. Typically, a so-called periodic time homogenization scheme has been proposed in [1], and its application on various cases of study detailed in [2,3]. However, the main associated hypothesis consists in assuming periodicity with respect to fast-time phenomena, hence implying studies with cyclic loading only. Therefore the goal of this paper is to extend this method to the stochastic case, when fast loads can be described by stochastic processes: the idea thus consists in adapting what exists in stochastic space homogenization [4] to define a so-called stochastic time homogenization method. First results are shown on the simple academic example of a beam with nonlinear viscoplastic behavior, submitted to loads modeled as ergodic stationary stochastic processes. Beside other points, the question of time averaging will be particularly addressed: Figure 1 shows how viscoplastic strain varies for different choices of duration concerning the time integral involved in the homogenization process. This case of study is a first step towards the definition of a more general stochastic time homogenization scheme.
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Dates et versions

hal-01862085 , version 1 (26-08-2018)

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  • HAL Id : hal-01862085 , version 1

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Guillaume Puel, Karam Sab. Towards a stochastic time homogenization method. VII European Congress on Computational Methods in Applied Sciences and Engineering - ECCOMAS 2016, Jun 2016, Hersonissos, Greece. ⟨hal-01862085⟩
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