Adaptive modelling of delamination growth using isogeometric continuum shell elements

Paper i proceeding, 2017

A key to successful modelling of the complex progressive failure in layered composite materials is to have computationally efficient models and methods which can be adapted to the predominant failure mechanisms in each specific loading case. In particular, efficient approximation and solution methods for delamination modelling is crucial, since "high-fidelity" FE models with many elements through the component thickness interconnected with cohesive interface elements leads to unfeasible simulation times and memory requirements. For that purpose, several papers have been published that present alternative methods for modelling concepts which support laminate failure analyses requiring only one shell element through the thickness and where arbitrary delamination propagation is accounted for only in areas where it is needed, cf. Brouzoulis and Fagerström, Hosseini et al. and McElroy . The proposed new concepts however need to be further developed before they can be readily applied to solve engineering problems in which delamination cracks can initiate and propagate. For traditional finite element based shell models, such as the one presented by Brouzoulis and Fagerström (based on the eXtended Finite Element Method, XFEM), improved methods to predict the interlaminar stresses are needed for an accurate prediction of delamination initiation, since the transverse stresses predicted directly from the shell solution are of too low accuracy. This was recently done e.g. by Främby et al. who complemented an XFEM shell formulation with a stress recovery approach , performed over a patch of elements, thereby making the model fully adaptive. As for the alternative concept based on an isogeometric approach by Hosseini et al., there is a need to handle successive introduction of new discontinuities by means of knot-insertion in an automated fashion. A first step in this direction was taken by the authors in , outlining strategies for how to initiate and propagate delamination cracks using this framework. As a benefit over FE based C0 continuous shells, the necessary improvements of the interlaminar stresses for isogeometric shells can be performed element-wise since in-plane stresses are smooth over element boundaries. In this contribution we focus on the further development of the isogeometric solid-like shell element to allow for an automated insertion of discontinuities. The formulation adopts NURBS (or T-spline) basis functions for the discretisation of the shell mid-surface, whereas a higher-order B-spline functions are used for the interpolation in the thickness direction. A discontinuity can be incorporated in this latter function by so-called knot-insertion to account for ply interfaces (weak discontinuities) and delaminations (strong discontinuities) . In order to automatically enhance the element, various stress-based criteria using element local improved interlaminar stresses are investigated. In this way, the isogeometric continuum element can be used in an even more efficient fashion, allowing for the detailed analysis of large, thin-walled composite structures.