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

Cong-Uy Nguyen , Truong-Vinh Hoang , Emina Hadzalic , Simona Dobrilla , Hermann G. Matthies , Adnan Ibrahimbegovic

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.

Key Words

Bayesian update; Gauss-Markov-Kalman filter; inelastic and multi-scale problems; parameter identification

Address

Cong-Uy Nguyen — Royallieu Center of Research, University of Technology of Compiègne/Sorbonne University Alliance, France; Institute of Scientific Computing, Technical University of Braunschweig, Germany
Truong-Vinh Hoang — Chair of Mathematics for Uncertainty Quantification, RWTH Aachen University, Germany
Emina Hadzalic — Faculty of Civil Engineering, University of Sarajevo, Bosnia and Herzegovina
Simona Dobrilla — Royallieu Center of Research, University of Technology of Compiègne/Sorbonne University Alliance, France; Institute of Scientific Computing, Technical University of Braunschweig, Germany
Hermann G. Matthies — Institute of Scientific Computing, Technical University of Braunschweig, Germany
Adnan Ibrahimbegovic — Royallieu Center of Research, University of Technology of Compiègne/Sorbonne University Alliance, France; Institut Universitaire de France, France

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