A time multiscale based data-driven approach in cyclic elasto-plasticity
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The simulation of nonlinear fatigue problems using classical solvers imposes high computational costs, especially when the time domain under study is large. Additionally, this limitation is exacerbated if parametric studies must be performed. Due to the above, in the present work an efficient nonlinear solver using the model-order reduction technique Proper Generalized Decomposition (PGD) is proposed, in where time evolution is addressed by means of a temporal multiscale PGD. In this sense, the time evolution is approach in terms of micro-macro scales for both the time response of the system and the evaluation of the nonlinearities. Specifically, the temporal micro-macro characterization is exploited together with data-driven techniques to efficiently evaluate the considered nonlinear behaviours. The proposed strategy is tested for the resolution of a 2D solid mechanics problem where a long-time mono-periodic excitation and an elasto-plastic behaviour are considered. The drastic reduction of the computational cost in nonlinear problems defined over large time intervals opens the doors to fatigue analyses at low-cost.
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