AN ADAPTIVE ISOGEOMETRIC CONTINUUM SHELL ELEMENT FOR EFFICIENT MODELLING OF DELAMINATION GROWTH

To accurately predict damage growth in large, thin-walled composite structures, it is required\ua0to have models that are both valid and computational efficient. In this respect, isogeometric\ua0continuum shell elements provide an interesting option. First of all, the higher order\ua0continuity achieved via isogeometric analysis yields an increased in-plane smoothness that enable\ua0the use of larger shell elements. In addition, the high in-plane continuity also leads to that\ua0in-plane derivatives of in-plane stresses are continuous across element edges, thereby allowing\ua0for element-local recovery procedures for the prediction of out-of-plane stresses [2, 3].\ua0Furthermore, as shown by Hosseini et al. [1], it is in an isogeometric continuum shell modelling framework rather straightforward to modify the through-thickness kinematics to incorporate\ua0weak and strong discontinuities. By introducing weak discontinuities at ply interfaces,\ua0the through-thickness strain discontinuities at these locations are explicitly accounted for. This\ua0enables a much better 3D strain and stress prediction, something which is key for a good estimation\ua0of the amount of intralaminar damage. By introducing strong discontinuities, the element\ua0is also capable to represent initiation and growth of one or several delamination cracks.In the current contribution, we extend the shell formulation from [1] into an adaptive continuum\ua0shell that allows for an update of the through-thickness kinematics at any required time\ua0instant during the simulation. The adaptivity is facilitated by that the through-thickness kinematical\ua0enrichment can be achieved by so-called ”knot insertion”, a step which can be fully\ua0automated due to the hierarchical nature of the isogeometric approximation functions.As a result, the current shell provides a good basis for an accurate but also computationally\ua0efficient prediction of the progressive failure in laminates, without a-priory knowledge of\ua0where damage will occur. Results show that the adaptive modelling framework works well,\ua0both to predict the full 3D stress states in multiaxial laminates, but also to capture growth of\ua0delaminations. Furthermore, in comparison to a fully resolved model, the adaptive approach\ua0gives significant time savings even for simple analyses where significant parts of the domain\ua0exhibit delamination growth. This implies that computational efforts (time and memory) can be\ua0considerably reduced when using this adaptive concept in large-scale analyses where damage develop only in a confined, but initially unknown area of the structure.[1] S. Hosseini, J.J.C. Remmers, C.V. Verhoosel, and R. de Borst (2015) Int. J. Numer. Meth.Eng., 102, 159–179.[2] M. Fagerstr\uf6m and J.J.C Remmers (2017) Adaptive modelling of delmination growth usingisogeometric continuum shell elements. Proc. ICCM21, Xian, China.[3] J.-E. Dufour, P. Antolin, G. Sangalli, F. Auricchio, A. Reali (2018) Composites Part B:Engineering, 138, 12-18