Subsampling and homogenization to investigate variability of composite material mechanical properties

Abstract

This paper presents an innovative homogenization sampling technique applied to multiscale modelling of composite materials. The goal is to build efficiently statistical variability of mechanical properties at mesoscopic scale from the heterogeneous media analysis at microscopic scale. It is applied to the transverse elastic properties of a unidirectional Long Fibres Reinforced Composite (LFRC). A large representative part of the ply – the cell – is modelled from a micrography and studied at microscopic scale with the Finite Element Analysis (FEA) under 2D plane strain hypothesis. The study consists in estimating the effective elastic properties of subcells, subparts of the previous cell, thanks to a specifically developed numerical procedure. A unique calculation is computed on the entire ply reduced to three basic loading cases is applied to the cell. Subsamples taken into the simulation cell are homogenized at post-processing level of strain and stress fields. A standard mechanics approach was considered. Various subsampling schemes are performed with various size and spatial distribution to generate variability functions of effective elastic properties at mesoscopic scale. A statistical inference is highlighted: the variability parameters vary with the way of sampling. Dispersion functions are finally obtained and discussed.