A4.: Multi-Scale Methods in Time and Space for Random Fatigue Simulation

Fatigue is a major issue in structural engineering systems. The model-based prediction of fatigue and failure under uncertain conditions via physical based computation methods, e.g. FEM, is still a challenging task. First steps in that direction have been done previously [1,2,3] in our own group. This project is intended for further improvement of these methods. Sophisticated and goal-oriented model order reduction schemes will be developed to predict high cycle fatigue based on continuum damage mechanics concepts implemented in Finite Element Methods (high-fidelity models), which perhaps can be treated as a black-box. Besides the material properties, the loading conditions as well as the damage evolution itself will be assumed to be uncertain (e.g. random-fields or random-processes). Besides scales in space, e.g. heterogeneous meso-structures, scales in time, e.g. few random load cycles up to 10^x-load cycles will be considered.

In this project, besides the physical modelling of fatigue damage in the framework of Finite Element Methods, sophisticated model order reduction techniques will be further developed in a goal-oriented manner.

[1] Mainak Bhattacharyya, Amélie Fau, Rodrigue Desmorat, Shadi Alameddin, David Néron, Pierre Ladevèze, Udo Nackenhorst, A kinetic two-scale damage model for high-cycle fatigue simulation using multi-temporal Latin framework, European Journal of Mechanics - A/Solids, Volume 77, 2019, 103808, ISSN 0997-7538, https://doi.org/10.1016/j.euromechsol.2019.103808.

[2] Alameddin, S., Fau, A., Néron, D., Ladevèze, P., & Nackenhorst, U. (2019). Toward optimality of proper generalised decomposition bases. Mathematical and computational applications, 24(1), 30.

[3] Zhang, W., Fau, A., Nackenhorst, U., Desmorat, R. (2020). Stochastic Material Modeling for Fatigue Damage Analysis. In: Wriggers, P., Allix, O., Weißenfels, C. (eds) Virtual Design and Validation. Lecture Notes in Applied and Computational Mechanics, vol 93. Springer, Cham. doi.org/10.1007/978-3-030-38156-1_17

Supervision: Prof. Dr.-Ing. Udo Nackenhorst (LUH), NN (ENS)