Title: A hierarchical bayesian calibration of data-driven models for composite laminate consolidation

Abstract

Composite modelling of consolidation processes is playing an important role in process and part design, by indicating the formation of possible unwanted defects (e.g. wrinkles(Dodwell, 2014) ) prior to expensive experimental iterative trial and development programmes. Composite material in their uncured state display complex constitutive behaviour, which has received much academic interest, and with this different models have been proposed ((Gutowski T. G., 1987),(Gutowski T. G., 1987),(Hubert, 1999),(Li, 2002),(Sakhaei, 2020) ). Errors from both the modelling assumptions and statistical variability which arise from the fitting of constitutive material models will propagate through any simulation in which the material model is used, leading to uncertainty in predictions. We propose a general hyperelastic polynomial representation, which can be readily implemented in various nonlinear finite element packages. In our case we choose, FEniCS(M.S Alnes, 2015). The coefficients are assumed uncertain, and therefore the distribution of parameters learnt using Bayesian inference, more explicitly Markov Chain Monte Carlo (MCMC) methods. In engineering the approach often followed is to select a single set of model parameters, which on average, best fits a set of experiments. There are good statistical reasons why this is not a rigorous approach to take. To overcome these challenges, we propose a hierarchical Bayesian framework (Gelman, 2013) in which population distribution of model parameters is inferred from an ensemble of experiments tests. The resulting sampled distribution of hyperparameters, are approximated using Maximum Entropy methods, so that the distribution of samples can be readily sampled when embedded within a stochastic finite element simulation at higher length scales. The methodology is validated and demonstrated on a set of consolidation experiments of AS4/8852 with various stacking sequences. The resulting distributions are then applied to a stochastic finite element simulations of the consolidation of curved part, leading to a distribution of possible model outputs. With this, the paper, as far as the authors are aware, represents the first stochastic finite element implementation in composite process modelling.