Computationally efficient modelling of failure in laminated composites by utilising adaptive shell elements
Conference contribution, 2017
Modelling the failure of large, thin-walled structures made of structural composites is challenging both from the material and structural perspective. For a predictive response at a certain length scale, the models used for the laminate failure response (including various types of inter-, trans- and intraply failure modes) need to capture the failure mechanisms occurring. Consequently, a rather high level of detail is necessary in the damage modelling, which is often achieved by modelling laminates with separate finite elements for separate plies through the thickness. However, for large-scale applications (e.g. automotive crash applications), such detailed laminate modelling is unfeasible since it leads to too large simulation models. Thus, there is an apparent need for more efficient modelling of the structural response where not all details are included everywhere.
Aiming for a good compromise between model efficiency and detail, we are currently developing adaptive shell methods for modelling the growth of arbitrarily many delamination cracks in laminates. Hence, by using adaptivity, we can start the simulation in a state where the composite component is described only by a single layer of elements through the thickness. Wherever the risk of failure is detected with some probability, we can then automatically refine the model only in the areas of interest by adapting the through-thickness displacement approximation such that displacement discontinuities (e.g. delamination cracks) are introduced. The growth of these delamination cracks is then governed by a cohesive zone law.
In a recent paper, we have proposed such an adaptive shell approach based on the eXtended Finite Element Method (XFEM). In that paper, we could show that substantial shortening of the simulation time can be achieved by using an adaptive approach compared to when the laminate is fully resolved by separate elements for each ply. These findings were made by using an implementation of the adaptive shell approach in an open-source research Finite Element Solver (OOFEM – www.oofem.org). However, to make the approach also industrially available, we are currently developing an “industrialized” version to be made available as a user element for LS-DYNA. In the current contribution, we will describe the underlying assumptions and modelling strategy, and show results that verify and validate our approach.
As a further extension, we are also advancing the adaptive modelling by developing an approach based on the concept of Isogeometric Analysis (IgA), using splines as the underlying approximation functions. By using splines for the approximation, we are able to fully tailor the smoothness of the displacement fields to both obtain accurate predictions of delamination-initiating transverse stresses (requiring high in-plane smoothness) and to adaptively introduce delamination cracks (requiring through-thickness discontinuities). By using IgA, we can also refine the model in the areas of interest in a two stage process. In the first refinement stage, we introduce strain discontinuities between plies, which yields a better prediction of stresses and strains locally within the laminate. This will enable more accurate modelling of damage processes in separate plies as well as more accurate predictions of initiating delaminations. In the second stage, we can, similarly to the XFEM based approach, then introduce discontinuities in the displacement approximation through the thickness, which makes it possible to model delamination growth. Preliminary results indicate that this IgA-based approach is very promising in terms of both accuracy and efficiency, and that it in the future can, within reasonable efforts, be made commercially available.