A stochastic Mean-Field-Homogenization-based micro-mechanical model of unidirectional composites failure

Homogenization approaches are commonly developed in order to account for micro-structural geometrical and material properties in the framework of multiscale analyses. Although most of the approaches postulate the existence of a statistically Representative Volume Element (RVE), 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) generator [1], allowing the extraction of probabilistic meso-scale stochastic behaviours from direct numerical simulations.

Finally, a probabilistic Mean-Field-Homogenization (MFH) method is developed [2,3] such that the phase parameters of the MFH are defined as random fields identified from the stochastic homogenized behaviours obtained through the direct simulations of the SVEs. As a result, non-deterministic macro-scale behaviours can be studied, allowing to predict composite failure in a probabilistic way.

[1] 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.
[2] 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.
[3] 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 (2019).