Abstract :
[en] Homogenization-based multiscale approaches have been widely developed in order to account for micro-structural geometrical and material properties in an accurate way. However, most of the approaches assume the existence of a statistically Representative Volume Element (RVE). Such a RVE does not always exist for composite materials due to the existing micro-structural uncertainties, motivating the development of a stochastic multi-scale approach for unidirectional composite materials.
First Stochastic Volume Elements (SVE) [1] are built from experimental measurements using statistical functions of the fibers features extracted from SEM images and used to generate statistical functions of the micro-structure. The dependent variables are then represented using the copula framework in order to generate micro-structures, which respect the statistical information, using a fiber additive process [1]. Probabilistic meso-scale stochastic behaviors are then extracted from direct numerical simulations of the generated SVEs, defining random fields of homogenized properties [2].
Finally, in order to generate in an efficient way meso-scale random fields, a probabilistic Mean-Field-Homogenization (MFH) method is developed. To this end, the phase parameters of the MFH are seen as random fields defined by inverse stochastic identification of the stochastic homogenized properties obtained through the stochastic direct simulations of the SVEs. As a result, non-deterministic macro-scale behaviors can be studied while having access to the micro-scale different phases 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, L. Noels. From SEM images to elastic responses: a stochastic multiscale analysis of UD fiber reinforced composites. Composite Structures 189C (2018), 206-227
[3] V. Lucas, J.-C. Golinval, S. Paquay, V.-D. Nguyen, L. Noels, L. Wu, A stochastic computational multiscale approach; Application to MEMS resonators, Computer Methods in Applied Mechanics and Engineering 294 (2015) 141 - 167
Name of the research project :
The research has been funded by the Walloon Region under the agreement no 1410246 - STOMMMAC (CT-INT2013-03-28) in the context of the M-ERA.NET Joint Call 2014.
