Year: 2026
Type: article
Abstract: This paper introduces the idea of stochastic upscaling, with the aim of clarifying how to handle uncertainty at each scale by describing mechanical system parameters through random quantities or spatially varying stochastic fields. We intend to demonstrate the essential role played by small-scale material heterogeneities and to formulate a new stochastic upscaling framework, capable of capturing their influence on macroscopic fracture behavior. The results for concrete show that the Bayesian updating method produces posterior distributions consistent with the deterministic homogenization method with a Gaussian distribution for elastic parameters, whereas, for the inelastic parameters, the distribution is no longer a simple Gaussian. Comparing two proposed methods for Bayesian inference, we find that the Gauss-Markov-Kalman filter achieves posterior estimates equivalent to the Markov chain Monte Carlo method, but at a much lower computational cost. For fracture parameters, the micro-scale spatial variation is preserved as a non-normal posterior distribution at the macro-scale with a probability distribution reflecting the sensitivity of fracture to initial or induced defects. Accordingly, the stochastic upscaling in the proposed multiscale framework is an essential component for scale laws, allowing one to move beyond homogenization in order to properly incorporate epistemic uncertainties in system parameters as well as the stochastic character of fracture.
Author: Adnan Ibrahimbegovic
Institutions: Université de Technologie de Compiègne, Sorbonne Université
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7225429175