An inverse Mean-Field-Homogenization-based micro-mechanical model for stochastic multiscale simulations of unidirectional composites

Homogenization approaches have been widely developed in order to account for micro-structural geometrical and material properties in the framework of multiscale analyses. Most of the approaches postulate the existence of a statistically Representative Volume Element (RVE). However, such representativity is not always ensured, in particular when studying the failure of composite materials, because of the existing micro-structural uncertainties. In this work we develop a stochastic multi-scale approach for unidirectional composite materials in order to predict the scatter existing at the structural behaviour.

Statistical characteristics of the micro-structure are first extracted from SEM images in order to build a Stochastic Volume Elements (SVE) [1] generator [2]. Probabilistic meso-scale stochastic behaviours are then extracted from direct numerical simulations of the generated SVEs.

Finally, in order to provide an efficient way of exploiting the meso-scale random fields, while keeping information such as stress/strain history at the micro-scale during the resolution of macro-scale stochastic finite element, a probabilistic Mean-Field-Homogenization (MFH) method is developed [3,4]. To this end, the phase parameters of the MFH are defined as random fields, which are identified from the stochastic homogenized behaviours obtained through the stochastic direct simulations of the SVEs. As a result, non-deterministic macro-scale behaviours can be studied while having access to the micro-scale different phase stress-strain evolution, allowing to predict composite failure in a probabilistic way.

[1] M. Ostoja-Starzewski, X. Wang, Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering 168 (14) (1999) 35 - 49,
[2] L. Wu, C. N. Chung, Z. Major, L. Adam, and L. Noels. "From SEM images to elastic responses: a stochastic multiscale analysis of UD fiber reinforced composites." Composite Structures 189C (2018): 206-227.
[3] L. Wu, L. Adam, and L. Noels. "A micro-mechanics-based inverse study for stochastic order reduction of elastic UD-fiber reinforced composites analyzes." International Journal for Numerical Methods in Engineering 115, no. 12 (2018): 1430-1456.
[4] L. Wu, V. D. Nguyen, L. Adam, and L. Noels. "An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites." Computer Methods in Applied Mechanics and Engineering 348 (2019): 97-138.