A stochastic Mean Field Homogenization model of Unidirectional composite materials

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), which does not always exist for composite materials due to the existing micro-structural uncertainties, in particular when studying the onset of failure. To address this lack of representativity, a stochastic multi-scale approach for unidirectional composite materials is developed with the aim of predicting scatter in the structural behavior.

The first step consists in building Stochastic Volume Elements (SVE) [1] from experimental measurements. Toward this end, statistical functions of the fibers features are extracted from SEM images to generate statistical functions of the micro-structure. The dependent variables are then represented using the copula framework, allowing generating micro-structures respecting the statistical information using a fiber additive process [2].

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 provide an efficient way of generating meso-scale random fields, while keeping information such as stress/strain fields at the micro-scale during the resolution of macro-scale stochastic finite element, a probabilistic Mean-Field-Homogenization (MFH) method is developed, first in the linear range [3] and then in the non-linear one. 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. The resulting micro-mechanics-based reduced order model allows studying 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. Submitted to Composite Structures.
[3] L. Wu, L. Adam, 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 (2018)