Modelling multiple delaminations and through-thickness cracking in fibre composites using shells
Paper in proceedings, 2014
The ability to investigate the crashworthiness of fibre reinforced vehicle structures, by efficient numerical simulations, is crucial for FRP lightweight materials to see widespread use in future cars. Consequently, for an accurate prediction of the crashworthiness performance, careful considerations of the underlying failure mechanisms are necessary for the proper modelling of progressive laminate failure in this type of application. However, in addition to the relevance and accuracy of the adopted material model, also the computational efficiency of the structural analysis is essential in order to enable full car crash Finite Element (FE) analyses, meeting today’s development lead times in the automotive industry. One approach to meet the requirements of computational efficiency would be to restrict the finite element analysis to shells only, and to only allow one shell element through the thickness. This, however, poses at least two requirements on the shell formulation itself: that i) the stress variation through the laminate is accurately captured and that ii) the shell kinematics allows also for the modelling of failure mechanisms such as delaminations and cracks. In the current contribution we focus on the second challenge, thereby proposing an enhanced shell element formulation based on the eXtended Finite Element Method (XFEM) for mesh independent FE simulation of through-thickness and delamination crack propagation in orthotropic laminates. Consequently, kinematical enrichments are added to the basic shell representation in order to describe delamination cracks and through-thickness cracks. The proposed formulation herein is an extension of the recently proposed shell element for the analysis of multiple delaminations . This is also in line with previous developments using XFEM to model failure in composites, e.g. de Borst and Remmers  modelling arbitrary delaminations and Van der Meer et al.  modelling matrix cracks and delaminations by XFEM enhanced solid elements (matrix cracks) and interconnecting classical cohesive elements (delaminations). As a consequence of the adopted kinematics with local enrichments, propagation of both delamination and through-thickness cracks can be treated simultaneously and independently of the spatial discretisation, thereby reducing the computational effort required in large scale analyses. It is emphasised that the level of detail in the present approach is such that
individual delaminations can be analysed using a mixed mode cohesive zone approach; however, it is not fine enough to capture cracks growing through individual laminae. The latter are instead to be incorporated in a ’smeared’ sense by a material model including damage in the spirit of Maimi et al.  which incorporates the relevant failure mechanisms.
 Brouzoulis and Fagerström, In Proc. 19th Int. Conf. Composite Materials (2013)
 de Borst and Remmers, Compos. Sci. Technol., 66, 713–722 (2006)
 van der Meer, Sluys, Hallett and Wisnom, J. Compos. Mater., 46, 603–623 (2011)
 Maimí, Camanho, Mayugo and Dávila, Mech. Mater., 39, 897–908 (2007)