Experimental and Computational Analysis of Mode I Fracture in Wood : Likelihood-based inference and finite element model updating

This thesis covers the estimation of the fracture behaviour of the European woodspecies Norway spruce and birch. The fracture behavior of wood can be quantifiedthrough three material parameters: the stiffness, the strength, and the specific fractureenergy. In the present work, these parameters are characterized through two methods.The first method is purely experimental and only estimates one parameter, by useof the so-called work-of-fracture method. In this procedure, a single-edge-notchedbeam is loaded in three-point-bending under stable crack propagation until completefailure. The specific fracture energy, i.e. the energy dissipated during the creationof a unit crack surface, can then be evaluated as the work carried out to completefracture, divided by the fractured area. This method has previously been used ina large number of studies to establish the specific fracture energy of various woodspecies. In the present work, this experimental procedure is used to test 80 specimens,divided into four different series.The second method employed is based on the same experimental tests, but in combination with numerical models. The difference between the numerically and experimentally obtained force-displacement responses is quantified in a so-called cost function,which further is minimized through a finite element model updating (FEMU) procedure using a Bayesian optimization framework, to establish the optimal set of materialparameters. In addition, two commonly employed cost functions employed in FEMUare reformulated in the context of likelihood-based inference to estimate the uncertainty in the optimal set of parameters.It is shown that neither of the two commonly employed cost functions can recover thevariance in the experimental load-displacement curves. However, the mean behaviouris captured fairly well for both cost functions.