Probabilistic parameter estimation and uncertainty quantification of mode I fracture in wood

The characterisation of wood’s fracture behaviour is a challenging task due to its inherently complex microstructure and natural variability. Consequently, to accurately model wood for engineering applications, deterministic input parameters are rarely insufficient in, for example, finite element models; the stochastic nature of the material must be considered. In the present work, we aim to quantify the variability in the fracture behaviour of two wood species: Norway spruce, which is commonly used for structural purposes in Europe, and birch, which could be an advantageous complement to Norway spruce, mainly thanks to its stiffer and stronger mechanical properties. The fracture behaviour is characterised through the three parameters that govern a material’s brittleness: the stiffness, the strength and the specific fracture energy. By formulating a parameter estimation problem based in probability theory, we use Bayesian optimisation to estimate statistical distributions of the fracture parameters of interest. These distributions are multi-variate distributions and thus contain information about the mean values, variability and dependence among the parameters. It is shown that by using random samples from the acquired distributions as input parameters to finite element models, variability observed in experimental testing is recovered well. • Proposal of a non-deterministic Gaussian process-based Bayesian optimisation procedure for parameter estimation to assess variability in constitutive behaviour. • The fracture behaviour in terms of the stiffness, strength and specific fracture energy of Norway spruce ( Picea abies ) and birch ( Betula pendula ) has been estimated. • The procedure is promising with respect to computational efficiency, requiring less than 100 finite element simulations to characterise approximate statistical distributions of the parameters.