Stochastic identification of composite material properties from limited experimental databases, Part II: Uncertainty modelling

The objective of this work is to characterise stochastic macroscopic material properties of heterogeneous composite fabrics from limited-size macro-scale experimental measurements. The work is presented in a sequence of two papers. In the first paper (Part I), a database consisting of observations of heterogeneous Young's modulus fields is obtained by a set of deterministic inverse problems. In this paper (Part II), a data assimilation framework is considered to identify a stochastic random field model of the Young's modulus. Such a model is set up to account for both aleatory uncertainties, related to sample inter-variabilities, as well as epistemic uncertainties due to insufficiency of the available data. This uncertainty characterisation is achieved by discretising the random field using a spectral decomposition procedure known as the Karhunen–Loève expansion. Random variables of this representation are expanded in a Hermite Polynomial Chaos (PC) basis whose coefficients themselves are considered as random variables. While the Gaussian variables of the PC basis model the aleatory uncertainty, the PC coefficients represent the epistemic uncertainty. A Bayesian inference scheme with Markov Chain Monte Carlo sampler is implemented to characterise the PC coefficients according to the Maximum A posteriori Probability (MAP) estimator.

► Stochastic inverse method for macroscopic heterogeneous composite material identification. ► Spatial experimental realizations from several samples inferred from macro-scale measurements. ► Data assimilation of the random field entails spectral expansions with random coefficients. ► Bayesian posteriors for random coefficients identification to quantify epistemic uncertainty. ► Cross-validation method to examine stochastic representations given limited experimental data.