PREDICTION OF THROUGH-THICKNESS STRESS DISTRIBUTION IN LAMINATED SHELL STRUCTURES

Paper in proceeding, 2014

The ability to investigate the crashworthiness of fibre reinforced polymer (FRP) vehicle structures, by numerical simulations, is crucial for a widespread use of these materials in future cars. Consequently, for an accurate prediction of the crashworthiness performance, crucial mechanisms, e.g. initiation and propagation of delamination, needs to be accurately captured in the simulations. The modelling of the delamination failure mechanism has now reached a level of maturity such that the propagation of delamination cracks can be predicted well in many cases, although often at the cost of long simulation times. However, to enable full car crash Finite Element (FE) analyses in the automotive industry, computational efficiency is essential. In an attempt to meet this demand, a new shell element formulation, which by means of the eXtended Finite Element Method can represent multiple delaminations, has been developed within the group. A drawback of this shell approach 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. Aiming to improve the calculated stress distribution while still keeping a shell analysis approach, we have in the current contribution investigated the potential of using a fully coupled multiscale method (FE^2) based on numerical homogenisation. Following the standard FE^2 procedure, deformation measures originating from the macroscale shell analysis have been used to construct boundary conditions for a detailed 3D Representative Volume Element (RVE) analysis of the laminate. Several types of boundary conditions on the RVE have been investigated to find the most appropriate type with respect to accuracy in the though-thickness stress response. The outcome of this study will be presented and compared to the stress distribution obtained in a fully resolved 3D simulation (reference case) as well as a pure shell analysis. Initial results reveal that the stress distribution obtained in the pure shell analysis is recovered for the case of Taylor and Dirichlet boundary conditions, whereas periodic boundary conditions show additional potential. An alternative post-processing recovery approach to obtain the through-thickness stress distribution, based on the integration of the momentum balance equations, has also been investigated. So far, the conclusion is that for an isotropic case, the distributions correlate well with the reference case. Also results for a laminate with transversely isotropic properties will be presented.