Improved prediction of out-of-plane stresses in shells with application to delamination initiation and propagation modelling by the XFEM
Conference contribution, 2015
The introduction of FRPs in the automotive industry is strongly dependent on accurate and efficient CAE tools to predict the correct energy absorption in crash simulations. From experimental observations during axial crushing, it is obvious that to obtain good predictability in the simulations, delamination growth needs to be accounted for. A proper representation of the separation of plies is crucial for capturing the correct deformation mode of the laminate and, consequently, the relevant energy absorbing failure mechanisms. However, due to industrial restrictions on the simulation time of crash simulations, detailed modelling of each ply as represented by separate elements through the thickness – to promote delamination modelling by cohesive interface elements – is not feasible.
In an attempt to remedy this, an enriched shell element formulation, based on first-order shear deformation theory (FSDT), has recently been proposed with the benefit that propagating delamination cracks can be kinematically represented independently of the finite element mesh. Hence, a structural model of a thinwalled laminate can thereby initially be built up by a single layer of shell elements through the thickness. During loading, the model is then enriched locally (and adaptively) in critical areas where delamination is predicted.
Although efficient, a known drawback of the FSDT shell formulation is the low accuracy of the predicted through-thickness distribution of the out-of-plane stress components, which are essential for prediction of delamination initiation. In this contribution the possibilities to improve the quality of out-of-plane stresses, without resorting to more costly higher-order shell formulations, is addressed. More specifically the potential of using post-processing stress recovery techniques is investigated. These techniques return to the momentum balance in order to integrate the gradient of the in-plane stresses to calculate the out-of-plane stresses. Even though the stress recovery techniques are based on the in-plane stresses, which maintain high quality in this type of shell formulation, the same cannot be guaranteed for the gradient of these stresses whereby a suitable, but not overly expensive or complicated, approach to estimate the stress gradients is needed. Various alternative methods have been investigated in the current work to find a best practise approach.
To show the potential of the proposed methodology in capturing propagating delaminations by combining the enriched shell element formulation with the post-processing of out-of-plane stresses, it has been validated against results obtained in mode I, mode II and mixed mode delamination experiments. We can conclude that the proposed methodology is suitable for the simulation of thinwalled structures undergoing substantial delaminations.