Coupled systems mechanics

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Viscoplasticity model stochastic parameter identification: Multi-scale approach and Bayesian inference

  • Nguyen, Cong-Uy (Royallieu Center of Research, University of Technology of Compiègne/Sorbonne University Alliance) ;
  • Hoang, Truong-Vinh (Chair of Mathematics for Uncertainty Quantification, RWTH Aachen University) ;
  • Hadzalic, Emina (Faculty of Civil Engineering, University of Sarajevo) ;
  • Dobrilla, Simona (Royallieu Center of Research, University of Technology of Compiègne/Sorbonne University Alliance) ;
  • Matthies, Hermann G. (Institute of Scientific Computing, Technical University of Braunschweig) ;
  • Ibrahimbegovic, Adnan (Royallieu Center of Research, University of Technology of Compiègne/Sorbonne University Alliance)
  • Received : 2022.04.01
  • Accepted : 2022.06.26
  • Published : 2022.10.25
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Abstract

In this paper, we present the parameter identification for inelastic and multi-scale problems. First, the theoretical background of several fundamental methods used in the upscaling process is reviewed. Several key definitions including random field, Bayesian theorem, Polynomial chaos expansion (PCE), and Gauss-Markov-Kalman filter are briefly summarized. An illustrative example is given to assimilate fracture energy in a simple inelastic problem with linear hardening and softening phases. Second, the parameter identification using the Gauss-Markov-Kalman filter is employed for a multi-scale problem to identify bulk and shear moduli and other material properties in a macro-scale with the data from a micro-scale as quantities of interest (QoI). The problem can also be viewed as upscaling homogenization.

Keywords

Acknowledgement

This work is financially supported under the research project MS3C by Agence Nationale de la Recherche (ANR-20-CE46-0012-01), MEAE (project CESPA), IUF (project MS1479) and the research fund from the Institute of Scientific Computing, Technical University of Braunschweig. All this support is gratefully acknowledged. These sources of funding are gratefully acknowledged.

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