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

Other conference contribution, 2019

To accurately predict damage growth in large, thin-walled composite structures, it is required to have models that are both valid and computational efficient. In this respect, isogeometric continuum shell elements provide an interesting option. First of all, the higher order continuity achieved via isogeometric analysis yields an increased in-plane smoothness that enable the use of larger shell elements. In addition, the high in-plane continuity also leads to that in-plane derivatives of in-plane stresses are continuous across element edges, thereby allowing for element-local recovery procedures for the prediction of out-of-plane stresses [2, 3]. Furthermore, 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 weak and strong discontinuities. By introducing weak discontinuities at ply interfaces, the through-thickness strain discontinuities at these locations are explicitly accounted for. This enables a much better 3D strain and stress prediction, something which is key for a good estimation of the amount of intralaminar damage. By introducing strong discontinuities, the element is 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 shell that allows for an update of the through-thickness kinematics at any required time instant during the simulation. The adaptivity is facilitated by that the through-thickness kinematical enrichment can be achieved by so-called ”knot insertion”, a step which can be fully automated 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 efficient prediction of the progressive failure in laminates, without a-priory knowledge of where damage will occur. Results show that the adaptive modelling framework works well, both to predict the full 3D stress states in multiaxial laminates, but also to capture growth of delaminations. Furthermore, in comparison to a fully resolved model, the adaptive approach gives significant time savings even for simple analyses where significant parts of the domain exhibit delamination growth. This implies that computational efforts (time and memory) can be considerably 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. Fagerström and J.J.C Remmers (2017) Adaptive modelling of delmination growth using
isogeometric 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.